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ANSYS Mechanical APDL Feature Archive

Release 13.0ANSYS, Inc.November 2010Southpointe

275 Technology DriveCanonsburg, PA 15317 ANSYS, Inc. is

certified to ISO9001:2008.

[email protected]://www.ansys.com(T ) 724-746-3304(F) 724-514-9494

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Copyright and Trademark Information

© 2010 SAS IP, Inc. All rights reserved. Unauthorized use, distribution or duplication is prohibited.

ANSYS, ANSYS Workbench, Ansoft, AUTODYN, EKM, Engineering Knowledge Manager, CFX, FLUENT, HFSS and any andall ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks or trademarksof ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD is a trademark used by ANSYS, Inc.under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, service and feature namesor trademarks are the property of their respective owners.

Disclaimer Notice

THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFIDENTIALAND PROPRIETARY PRODUCTS OF ANSYS, INC., ITS SUBSIDIARIES, OR LICENSORS. The software products and document-ation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreement that contains pro-visions concerning non-disclosure, copying, length and nature of use, compliance with exporting laws, warranties,disclaimers, limitations of liability, and remedies, and other provisions. The software products and documentation maybe used, disclosed, transferred, or copied only in accordance with the terms and conditions of that software licenseagreement.

ANSYS, Inc. is certified to ISO 9001:2008.

U.S. Government Rights

For U.S. Government users, except as specifically granted by the ANSYS, Inc. software license agreement, the use, du-plication, or disclosure by the United States Government is subject to restrictions stated in the ANSYS, Inc. softwarelicense agreement and FAR 12.212 (for non-DOD licenses).

Third-Party Software

See the legal information in the product help files for the complete Legal Notice for ANSYS proprietary software andthird-party software. If you are unable to access the Legal Notice, please contact ANSYS, Inc.

Published in the U.S.A.

http://ai_ginfo.pdf/

http://ai_ginfo.pdf/

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Table of Contents

About This Archive ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viI. Legacy Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. Piping Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1. What the Piping Commands Can Do for You ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2. Modeling Piping Systems with Piping Commands ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1. Specify the Jobname and Title ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2. Set Up the Basic Piping Data ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.3. Define the Piping System's Geometry ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3.1. Review and Modify Your Piping Model ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3. Example Piping Model Input ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Subroutine usflex (Computes the flexibility factor for PIPE16 and PIPE18) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93. Restarting a Direct Coupled-Field Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1. Singleframe Restart ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.1. Singleframe Restart Requirements ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.2. Singleframe Restart Procedure ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.3. Restarting a Nonlinear Analysis From an Incompatible Database ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1.3.1. Re-establishing Boundary Conditions ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

II. Legacy Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17III. Legacy Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

BEAM4 ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63CONTAC12 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77PIPE16 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85PIPE18 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95PLANE42 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105SOLID45 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113CONTAC52 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121PIPE59 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129SHELL63 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147PLANE82 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157SOLID92 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165SOLID95 ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

IV. Legacy Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1791. Archived Theory Element Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

1.1. BEAM4 - 3-D Elastic Beam ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1811.1.1. Stiffness and Mass Matrices ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1811.1.2. Gyroscopic Damping Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1851.1.3. Pressure and Temperature Load Vector ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1851.1.4. Local to Global Conversion ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1851.1.5. Stress Calculations ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

1.2. CONTAC12 - 2-D Point-to-Point Contact ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

1.2.1. Element Matrices ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1891.2.2. Orientation of the Element ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1911.2.3. Rigid Coulomb Friction ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

1.3. PIPE16 - Elastic Straight Pipe ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1921.3.1. Assumptions and Restrictions ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1931.3.2. Stiffness Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1931.3.3. Mass Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1941.3.4. Gyroscopic Damping Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1941.3.5. Load Vector ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1951.3.6. Stress Calculation ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

iiRelease 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.

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1.4. PIPE18 - Elastic Curved Pipe ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031.4.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2041.4.2. Stiffness Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2041.4.3. Mass Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2071.4.4. Load Vector ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2071.4.5. Stress Calculations ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

1.5. PLANE42 - 2-D Structural Solid ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2081.5.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

1.6. SOLID45 - 3-D Structural Solid ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2091.6.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

1.7. CONTAC52 - 3-D Point-to-Point Contact ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2101.7.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111.7.2. Element Matrices ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111.7.3. Orientation of Element ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

1.8. PIPE59 - Immersed Pipe or Cable ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2121.8.1. Overview of the Element ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2131.8.2. Location of the Element ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2131.8.3. Stiffness Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2141.8.4. Mass Matrix ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

1.8.5. Load Vector ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2151.8.6. Hydrostatic Effects ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2161.8.7. Hydrodynamic Effects ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2181.8.8. Stress Output ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

1.9. SHELL63 - Elastic Shell ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2201.9.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2211.9.2. Foundation Stiffness ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2211.9.3. In-Plane Rotational Stiffness ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2221.9.4. Warping ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2221.9.5. Options for Non-Uniform Material ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2231.9.6. Extrapolation of Results to the Nodes ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

1.10. PLANE82 - 2-D 8-Node Structural Solid ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

1.10.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2251.10.2. Assumptions and Restrictions ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

1.11. SOLID92 - 3-D 10-Node Tetrahedral Structural Solid ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2261.11.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

1.12. SOLID95 - 3-D 20-Node Structural Solid ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2271.12.1. Other Applicable Sections ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

2. Hydrodynamic Loads on Line Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2292.1. Wave Theory ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

List of Figures

1.1. Order of Degrees of Freedom ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1821.2. Force-Deflection Relations for Standard Case ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1911.3. Force-Deflection Relations for Rigid Coulomb Option ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1921.4.Thermal and Pressure Effects ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1971.5. Elastic Pipe Direct Stress Output ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1991.6. Elastic Pipe Shear Stress Output ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1991.7. Stress Point Locations ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2021.8. Mohr Circles ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2021.9. Plane Element ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

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2.1. Velocity Profiles for Wave-Current Interactions ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

List of Tables

3.1. Restart Information for Nonlinear Analyses ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1. Stress Intensification Factors ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

2.1. Wave Theory Table ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

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About This Archive

The purpose of this archive is to provide a location for legacy feature, element, theory, and command doc-umentation.

The Mechanical APDL product continues to provide limited support for capabilities documented in thisarchive. In most cases, however, access via the graphical user interface (GUI) is no longer available.

As Mechanical APDL evolves and improves, be aware that ANSYS, Inc. may undocument and discontinuesupport for any legacy capability at a future release.

The following topics are available:

• Part I:Legacy Features (p. 1)

• Part II:Legacy Commands (p. 17)

• Part III:Legacy Elements (p. 61)

• Part IV:Legacy Theory (p. 179)

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Legacy Features

Following is the archived documentation for legacy Mechanical APDL features.

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Chapter 1: Piping Models

The ANSYS Multiphysics, ANSYS Mechanical, ANSYS Structural, and ANSYS Professional products offer agroup of commands that enable you to model piping systems and their loads in terms of conventionalpiping input data, instead of in terms of standard ANSYS direct-generation modeling operations. As you inppiping commands, the program internally converts your piping data to direct-generation model data, thenstores the converted information in the database. Once this information is stored, you can list it, display it,modify it, redefine it, etc., using any of the standard direct-generation commands.

The piping system modeling methods described here apply to straight-pipe PIPE16 and curved-pipe PIPE1elements. (Both elements are described in Part III: Legacy Elements.)

The following topics concerning piping models are available:1.1.What the Piping Commands Can Do for You

1.2. Modeling Piping Systems with Piping Commands1.3. Example Piping Model Input

1.1. What the Piping Commands Can Do for You

Some special features of the piping module are:

• Creates a line model of a piping network using straight-pipe PIPE16 and curved-pipe PIPE18 elements(Both elements are described in Part III: Legacy Elements (p. 61).) Node and element geometry are definin terms of incremental run lengths and bend radii, rather than in terms of absolute coordinates.

• Automatically calculates tangency points for bends.

• Relates standard piping designations (such as nominal diameter and schedule) to geometric values.

• Assigns pipe specifications to element real constants.

• Calculates and assigns flexibility and stress intensification factors based on the pressures and the temperatures specified in the pipe module before the creation of the piping elements as appropriate foreach element type. The flexibility factors are not be changed automatically if the pipe pressures ortemperatures are subsequently revised.

• Determines drag pressure loads from a pressure vs. height relationship.

1.2. Modeling Piping Systems with Piping Commands

Building a model with the piping commands consists of three primary tasks:1.2.1. Specify the Jobname and Title1.2.2. Set Up the Basic Piping Data1.2.3. Define the Piping System's Geometry

All piping commands referenced here are described in Part II:Legacy Commands (p. 17).

Other actions required for a piping system analysis include applying additional loads (D, F, etc.), obtainingthe solution, and reviewing the results. See the Basic Analysis Guide for more information.

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1.2.1. Specify the Jobname and Title

Perform these steps at the Begin level.

1. Specify the jobname you want to use for all files that are subsequently created by the analysis (/FIL-

NAME).

2. Write an analysis file (/TITLE).

3. Issue a "reminder" to yourself about the system of units you intend to use (/UNITS).

This step does not convert data from one system of units to another.

1.2.2. Set Up the Basic Piping Data

Set up the basic piping data as follows:

1. Enter PREP7 (/PREP7).

2. Define the material properties for all materials referenced by the model (MP, MPTEMP, etc.).

3. Select a system of units, if other than consistent (PUNIT).

The PUNIT command determines how the program interprets the data input for the PDRAG, BRANCH,RUN, BEND, MITER, REDUCE, VALVE, BELLOW, FLANGE, PSPRNG, PGAP, /PSPEC, PINSUL, and PCORROcommands. The difference between PUNIT and the /UNITS command is that PUNIT affects how theprogram behaves, whereas /UNITS does not.

4. Define the pipe specifications. These specifications are applied to the elements as they are generatedvia the RUN command.

a. Define pipe material and dimensions (PSPEC).

b. Define the contained fluid density for a piping run (PFLUID).

c. Define the external insulation constants in a piping run (PINSUL).

d. Specify the allowable exterior corrosion thickness for a piping run (PCORRO).

5. Select the piping analysis standard (POPT).:

The program calculates and assigns flexibility and stress intensification factors for curved pipe elementsbased on the pressures and the temperatures specified in the pipe module before the creation of thepiping elements as appropriate for each element type. The flexibility factors and stress intensificationfactors are not changed retroactively if the pipe pressures or temperatures are subsequently revised.

6. Select the pipe loadings.

a. Define the pipe wall temperatures in a piping run (PTEMP).

b. Define the internal pressure for a piping run (PPRES).

c. Define the external fluid drag loading for a piping run (PDRAG).

1.2.3. Define the Piping System's Geometry

Define the basic skeleton layout of your piping model as follows.

1. Specify the starting point of your piping system (BRANCH).

2. Follow up with a series of RUN commands to define incremental "straight" runs of pipe.

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Pipe elements are generated "straight" in the active coordinate system. Each RUN command useslength dimensions in the format specified by the PUNIT command to generate a node and a PIPE16element (along with its real constants, material properties, and loads).

3. Insert bends and other components (tees, valves, reducers, flanges, bellows, and spring restraints) intothe model at existing nodes that are shared by two or more existing pipe elements. The programautomatically updates your model's geometry to account for the inserted components. Inserted pipecomponents take their specifications and loadings from the adjacent straight pipes.

• To define a bend in a piping run, issue the BEND command.

• To define a mitered bend in a piping run, issue the MITER command.

• To define a tee in a piping run, issue the TEE command.

• To define a valve in a piping run, issue the VALVE command.

• To define a reducer in a piping run, issue the REDUCE command.

• To define a flange in a piping run, issue the FLANGE command.

• To define a bellows in a piping run, issue the BELLOW command.

• To define a spring constraint in a piping run, issue the PSPRNG command.

• To define a spring-gap constraint in a piping run, issue the PGAP command.

Another BRANCH command defines the junction point from which another run of pipe branches off of thepreviously defined run. Subsequent RUN commands define, in incremental fashion, another run of "straightpipe elements, starting from the last junction point.

1.2.3.1. Review and Modify Your Piping Model

When you have completed piping data input, you can review the information that has been stored in thedatabase via standard listing and display commands (NLIST, NPLOT, ELIST, EPLOT, SFELIST, BFELIST, etc.).

If necessary, you can modify the data using standard procedures for revising your model and your loads.

See "Loading" in the Basic Analysis Guide for details.

1.3. Example Piping Model Input

The following example input shows how to model this piping system:



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!

! Sample piping data input

!

/FILNAM,EXAMPLE

/TITLE, EXAMPLE PIPING INPUT

/UNITS,BIN ! A reminder that consistent units are U. S. Customary inches

!

/PREP7

! Define material properties for pipe elements

MP,EX,1,30e6

MP,PRXY,1,0.3

MP,ALPX,1,8e-6

MP,DENS,1,.283PUNIT,1 ! Units are read as ft+in+fraction and converted to

! decimal inches

PSPEC,1,8,STD ! 8" standard pipe

POPT,B31.1 ! Piping analysis standard: ANSI B31.1

PTEMP,200 ! Temperature = 200°

PPRES,1000 ! Internal pressure = 1000 psi

PDRAG,,,-.2 ! Drag = 0.2 psi in -Z direction at any height (Y)

BRANCH,1,0+12,0+12 ! Start first pipe run at (12",12",0")

RUN,,7+4 ! Run 7'-4" in +Y direction

RUN,9+5+1/2 ! Run 9'-5 1/2" in +X direction

RUN,,,-8+4 ! Run 8'-4" in -Z direction

RUN,,8+4 ! Run 8'-4" in +Y direction

/PNUM,NODE,1

/VIEW,1,1,2,3

EPLOT ! Identify node number at which 2nd run starts

BRANCH,4 ! Start second pipe run at node 4

RUN,6+2+1/2 ! Run 6'-2 1/2" in +X direction

TEE,4,WT ! Insert a tee at node 4

/PNUM,DEFA

/PNUM,ELEM,1

EPLOT ! Identify element numbers for bend and miter inserts

BEND,1,2,SR ! Insert a "short-radius" bend between elements 1 and 2

MITER,2,3,LR,2 ! Insert a two-piece miter between elements 2 and 3

/PNUM,DEFA

/PNUM,NODE,1

! Zoom in on miter bend to identify nodes for spring hangers

/ZOOM, 1, 242.93 , 206.62 , -39.059 , 26.866

PSPRNG,14,TRAN,1e4,,0+12 ! Insert Y-direction spring at node 14

PSPRNG,16,TRAN,1e4,,0+12 ! Insert Y-direction spring at node 16



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! List and display interpreted input data

/AUTO

/PNUM,DEFA

EPLOT

NLIST

ELIST

SFELIST

BFELIST

!

Although two hangers are provided, more restraints are needed before proceeding to the solution.



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Chapter 2: Subroutine usflex (Computes the flexibility factor for

PIPE16 and PIPE18)Legacy pipe elements PIPE16 and PIPE18 are described in Part III:Legacy Elements (p. 61).

*deck,usflex

subroutine usflex (etype,elem,rvrm,kff,prs,ex, flexi,flexo)

c *** primary function: to (re)compute the flexibility factor

c for pipe16, pipe17, pipe18, and pipe60

c this is accessed by inputting the flexibility factor

c as any negative number.

c *** secondary functions: none

c

c *** Notice - This file contains ANSYS Confidential information ***

c

c *** copyright(c) 2009 SAS IP, Inc. All rights reserved.

c *** ansys, inc.

c

c typ=int,dp,log,chr,dcp siz=sc,ar(n) intent=in,out,inout

c

c input arguments:

c variable (typ,siz,intent) description

c etype (int,sc,in) - pipe element type (16, 17, 18 or 60)

c elem (int,sc,in) - element number

c rvrm (dp,ar(*),in) - real constants

c kff (int,sc,in) - keyopt for flexibility factor

c (not used for pipe16 or pipe17)

c prs (dp,ar(5),in) - pressures

c ex (dp,sc,in) - young's Modulus

c flexi (dp,sc,inout) - effective in-plane flexibility factor

c flexo (dp,sc,inout) - effective out-of-plane flexibility factor


c

c output arguments:

c variable (typ,siz,intent) description

c flexi (dp,sc,inout) - effective in-plane flexibility factor

c flexo (dp,sc,inout) - effective out-of-plane flexibility factor


c


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Chapter 3: Restarting a Direct Coupled-Field Analysis

To restart a direct coupled-field analysis, ANSYS Inc. recommends using a singleframe restart. Direct couplefield analyses use a coupled-field element containing all necessary degrees of freedom. See the Coupled-

Field Analysis Guide for more information on this type of coupled-field analysis.

3.1. Singleframe Restart

A traditional restart requires that certain files from the initial run of the job are present, and requires thatyou make any changes to the input before the SOLVE command.

3.1.1. Singleframe Restart Requirements

When restarting from a static or full transient analysis, the following files must be available from the initialrun:

• Jobname.DB - The database file saved immediately after the initial SOLVE. If you save the databaseat any point later in the analysis, boundary conditions and other variables may be changed from theirinitial values, which would prevent the restart from running properly. (For non-converged solutions,the database file is saved automatically; see the note below.)

• Jobname.EMAT - Element matrices (if created).

• Jobname.ESAV or .OSAV - Element saved data (.ESAV) or old element saved data (.OSAV). Job-name.OSAV is required only if the .ESAV file is missing, incomplete, or otherwise corrupted becauseof a diverging solution; because the displacement limit was exceeded; or because of a negative pivot

(see Table 3.1: Restart Information for Nonlinear Analyses (p. 12)). It is written if KSTOP is set to 1 (defauor 2 on the NCNV command, or if automatic time stepping is active. If the .OSAV file is required, youmust rename it as Jobname.ESAV before restarting the analysis.

• Results file - Not required, but if available, results from the restart run will be appended to it with theproper, sequential load step and substep numbers. If the initial run terminated because the number ofresults sets on the results file were exceeded, you will need to rename the initial results file to a differename before restarting. To do so, issue the /ASSIGN command (Utility Menu> File> ANSYS File Optio

When restarting from a mode-superposition transient analysis, the following files must be available fromthe initial run:

• Jobname.DB -- The database file saved immediately after the initial solve operation (SOLVE). If you

save the database at any point later in the analysis, boundary conditions and other variables may bechanged from their initial values, which would prevent the restart from running properly.

• Jobname.RDSP -- The reduced displacement file with information from the last substep of the lastload step needed for restart.


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Note

In a nonlinear analysis, if the program terminates due to nonconvergence, time limits, the abortfile (Jobname.ABT), or other program-detected failure, the database is automatically saved, andthe solution output (Jobname.OUT) will list the files and other information required for restarting.See also Table 3.1: Restart Information for Nonlinear Analyses (p. 12) for a list of termination causesand the element saved data file needed to restart.

If the files .RDB, .LDHI, or .Rnnn /.Mnnn were accidentally created from a previous run, youmust delete them before performing a singleframe restart.

In interactive mode, an existing database file is first written to a backup file (Jobname.DBB). Inbatch mode, an existing database file is replaced by the current database information with nobackup.

Table 3.1 Restart Information for Nonlinear Analyses

Required Corrective ActionElement Saved

Data File

Cause of Termination

Add more load steps at the end of your job.Job-

name.ESAV

Normal (i.e., no errors)

Define a smaller time step, change the adaptivedescent option, or take other action to enhance

Job-

name.OSAV

Nonconvergence

convergence. Rename Jobname.OSAV as Job-name.ESAV before restarting.

If the solution was converging, allow more equilib-rium equations (NEQIT command).

Job-

name.ESAV

Nonconvergence due toinsufficient equilibriumiterations

Increase ITLIM on NCNV command.Job-

name.ESAV

Cumulative iteration

limit exceeded (NCNVcommand)

None (simply restart the analysis). (If you were run-ning the analysis interactively and you want to re-

Job-

name.ESAV

Time limit exceeded(NCNV)

start it from within the same ANSYS session, youmust reset the time limits before attempting therestart.)

(Same as for nonconvergence.)Job-

name.OSAV

Displacement limit ex-ceeded (NCNV)

(Same as for nonconvergence.)Job-

name.OSAV

Negative pivot

Make whatever changes are necessary to addressthe behavior that caused you to voluntarily termin-ate the analysis.

Job-

name.ESAV,Job-

name.OSAV

Jobname.ABT

• if solution was con-verging

• if solution was diver-ging



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Required Corrective ActionElement Saved

Data File

Cause of Termination

Could indicate a problem - check settings on CN-

VTOL, DELTIM, and NSUBST, or KEYOPT(7) forJob-

name.ESAV

"Full" results file (morethan 1000 substeps). Time steps output. contact elements. Or, specify larger number of res-

ults allowed on results file [/CONFIG,NRES] before

solution or reduce the number of results to be

output. Also rename results file (/ASSIGN).No restart is possible.Not applicable"Killed" job (system

break), system crash, orsystem time-limit ex-ceeded

Note

Singleframe restart does not support surface-to-surface, node-to-surface, line-to-line, or line-to-surface contact. Use multiframe restart if your model contains any of the following contact ele-ments: CONTA171, CONTA172, CONTA173, CONTA174, CONTA175, CONTA176, CONTA177.

3.1.2. Singleframe Restart Procedure

If you are performing a mode-superposition transient analysis, ANSYS sets up the parameters for a singlefrarestart by default.

The procedure for performing the restart analysis is as follows:

1. Enter the ANSYS program and specify the same jobname that was used in the initial run with /FILNA

(Utility Menu> File> Change Jobname).

2. Enter the SOLUTION processor using /SOLU (Main Menu> Solution), then resume the database file

using RESUME (Utility Menu> File> Resume Jobname.db).3. Indicate that this is a restart analysis by issuing ANTYPE,,REST (Main Menu> Solution> Restart).

4. Specify revised or additional loads as needed. Modified ramped loads start from their previous valueNewly applied ramped loads are ramped from zero; newly applied body loads start from initial valueDeleted loads which are reapplied are treated as new, not modified, loads. In static and full transientanalyses, surface and body loads to be deleted should be ramped to zero, or to the initial value, sothat the Jobname.ESAV and Jobname.OSAV files are consistent with the database.

For a mode-superposition transient analysis, steps 5, 6, 7, and 8 below do not apply.

Take whatever corrective action is necessary if you are restarting from a convergence failure.

5. If you are running a linear static or linear full transient analysis (with AUTOTS,OFF and the timestepfixed) using the sparse solver, you can realize additional savings by using the KeepFile field on theEQSLV command. Setting KeepFile = KEEP on your initial solve will force ANSYS to keep all necessfiles from the sparse solver in the working directory. In the subsequent singleframe restart, the sparsematrix files are available for reuse in conjunction with KUSE,1 (Main Menu> Preprocessor> Loads>

Other> Reuse LN22 Matrix).

By default, the ANSYS program calculates a new factorized matrix for the first load step of a restartrun. By issuing the KUSE,1 command, you can force the program to reuse the existing matrix at thefirst solve of the restart and at all subsequent solves, thereby saving a significant amount of compute


3.1.2. Singleframe Restart Procedure

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time. However, you can reuse factorized files such as Jobname.LNxx only under certain conditions,in particular if the specified DOF constraints have not changed and it is a linear analysis. See the Theory

Reference for the Mechanical APDL and Mechanical Applications for details.

By issuing KUSE,-1, you can cause ANSYS to redo the element matrices. This can be useful for debugginganalyses and for handling error cases.

Sometimes, you may have to analyze the same model for different constraint conditions, for instance

a quarter-symmetry model with symmetry-symmetry (SS), symmetry-antisymmetry (SA), antisymmetry-symmetry (AS), and antisymmetry-antisymmetry (AA) conditions. In such a situation, keep the followingpoints in mind:

• All four cases (SS, SA, AS, AA) require a new factorized matrix.

• You can use substructuring (with the constrained nodes as master DOF) to minimize computingtime. (See "Substructuring" in the Advanced Analysis Techniques Guide.)

6. Initiate the restart solution by issuing the SOLVE command. (See Obtaining the Solution for details.)

7. Repeat steps 4 and 6 for additional load steps, if any. For static and full transient analyses, you canalso use the load step file method to create and solve multiple load steps (not supported for modesuperposition transient analyses). Use the following commands:

Command(s): LSWRITE

GUI: Main Menu> Preprocessor> Loads> Write LS File

Main Menu> Solution> Write LS File

Command(s): LSSOLVE

GUI: Main Menu> Solution> From LS Files

8. Postprocess as desired, then exit the ANSYS program.

A sample restart input listing is shown below.

! Restart run:

/FILNAME,... ! JobnameRESUME

/SOLU

ANTYPE,,REST ! Specify restart of previous analysis

!

! Specify new loads, new load step options, etc.

! Take appropriate corrective action for nonlinear analyses.

!

SOLVE ! Initiate restart solution

SAVE ! Optional SAVE for possible subsequent singleframe restart

FINISH

!

! Postprocess as desired

!

/EXIT,NOSAV

3.1.3. Restarting a Nonlinear Analysis From an Incompatible Database

Sometimes, postprocessing is performed prior to a restart. If you issue SET and SAVE commands during thispostprocessing, the boundary conditions in your database might be altered and become inconsistent withthose needed for a restart. By default, the program saves your file automatically when you exit. At the endof solution, the boundary conditions for the last load step are stored in the database memory. (The databasecontains only one set of boundary conditions.)

A SET command in POST1 (other than SET,LAST) reads the boundary conditions for the specified results intothe database, and overwrites the database stored in memory. If you subsequently save your file or exit,



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ANSYS overwrites the boundary conditions in the database file with the D's and F's from the current resultfile. However, to perform a restart which ramps boundary conditions from the last solved substep, you neethe boundary conditions for the last successfully solved load substep.

3.1.3.1. Re-establishing Boundary Conditions

To re-establish the correct boundary conditions for the restart, first run a "dummy" load step. The proceduris as follows:

1. Rename Jobname.OSAV as Jobname.ESAV.

2. Enter the ANSYS program and specify the same jobname that was used in the initial run with /FILNA

(Utility Menu> File> Change Jobname).

3. Enter the SOLUTION processor using /SOLU (Main Menu> Solution), then resume the database fileusing RESUME (Utility Menu> File> Resume Jobname.db).

4. Indicate that this is a restart analysis by issuing ANTYPE,,REST (Main Menu> Solution> Restart).

5. Respecify boundary conditions from the last substep that was successfully solved. One substep is sufficient since the solution will converge immediately.

6. IssueSOLVE

(Main Menu> Solution> Current LS

orMain Menu> Solution> Run FLOTRAN

).7. Apply final loads and load step options as desired. You will need to adjust the number of substeps (o

time step size) if this load step is a "continuation" of the previous (before the dummy) load step. Timstep numbering may be altered from your initial intent. Use a small time increment in step 6 if youneed to preserve the time step numbering (such as for a transient analysis).

8. Continue the procedure as outlined in Restarting an Analysis.


3.1.3. Restarting a Nonlinear Analysis From an Incompatible Database

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Legacy Commands

Following is the archived documentation for legacy commands.

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BELLOW, NLOC , LENG, STIFF , FLEX , ELEM

Defines a bellows in a piping run.

PREP7:Piping

MP ME ST PR PRN <> <> <> <> <> <> PP <> EME MFS

NLOC

Node where bellows is to be placed. Defaults to current run starting point (RUN).LENG

Length of bellows (defaults to average pipe OD).

STIFF

Axial stiffness value (defaults to that of equivalent straight pipe).

FLEX

Bending flexibility factor (defaults to 1.0).

ELEM

Element number to be assigned to bellows (defaults to the previous maximum element number (MAXE+ 1).

Notes

Defines a bellows (straight-pipe element PIPE16 with adjusted specifications and loadings) at a given locatin a piping run.

Menu Paths

This command cannot be accessed from a menu.


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BEND, NEL1, NEL2, RAD, NDIV , ESTRT , EINC

Defines a bend in a piping run.

PREP7:Piping


NEL1, NEL2

Element numbers of the two intersecting straight pipes. Defaults to the last two straight pipe elementsnearest the intersection of the last two runs.

RAD

Bend radius. If LR, use long radius standard (1.5 x nominal diameter) (default). If SR, use short radiusstandard (1.0 x nominal diameter).

NDIV

Number of divisions (elements) along bend (defaults to 2). A node is generated at the end of each divi

ESTRT

Number to be assigned to first element of bend (defaults to MAXEL + 1).

EINC

Element number increment (defaults to 1).

Notes

Defines a bend of curved (elbow) pipe elements (PIPE18) in place of the intersection of two previouslydefined straight pipe elements (RUN). Two new nodes are generated at the ends of the bend (at the tangepoints). A node is also generated at the center of curvature point. The two straight pipes are automatically"shortened" to meet the ends of the bend. The bend specifications and loadings are taken from the corresponding two straight pipes. The flexibility factors are calculated from the internal pressure and EX (evaluatat TAVE) based on the current PPRES and PTEMP command specifications when the element is generated.

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BRANCH, NODE , X , Y , Z

Defines the starting point for a piping branch.

PREP7:Piping


NODE

Start branch at this node.X , Y , Z

Start branch at this location (in the active coordinate system). Used only if NODE is not input or inputbut the node itself is not previously defined. In either case a node is generated at this location and as-signed the number NODE (or 1 + previous maximum node number if NODE is not input).

Notes

See the RUN command in Part II:Legacy Commands (p. 17) for information relating to piping models.

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FLANGE, NLOC , LENG, MASS, SIF , FLEX , ARINS, ELEM

Defines a flange in a piping run.

PREP7:Piping


NLOC

Node where flange is to be placed (as described below). Defaults to current piping run starting point.LENG

Length of flange (defaults to larger pipe OD).

MASS

Dry mass (weight/gravity) of flange without insulation (defaults to equivalent straight pipe mass). Notethat acceleration [ACEL] must be nonzero for weight to be calculated.

SIF

Stress intensification factor (defaults to 1.0).

FLEX


ARINS

Insulation surface area (defaults to equivalent straight pipe insulation area). Units (length2) must beconsistent with the smallest unit of the system used (not mixed) regardless of the PUNIT option.

ELEM

Element number to be assigned to flange (defaults to the previous maximum element number (MAXEL+ 1).

Notes

Defines a flange (straight-pipe element PIPE16 with adjusted specifications and loadings) at a given locatioin a piping run. (See the RUN command, and other commands described here, in Part II:Legacy Com-

mands (p. 17).)

The FLANGE command is similar to the VALVE command except for a different flexibility factor default. Thelocation may be 1) between two adjacent colinear straight pipes, 2) between an adjacent straight pipe anda different piping component, or 3) at the end of a straight pipe.

For Case 1, two new nodes are generated at the ends of the flange. The two straight pipes are automatical"shortened" to meet the ends of the flange. The flange specifications and loadings are taken from the cor-responding two straight pipes.

For Case 2, one new node is generated at one end of the flange. The straight pipe is automatically "shortento meet this end of the flange. The other end of the flange meets the other piping component. The flange

specifications and loadings are taken from the straight pipe.

For Case 3, one new node is generated at the free end of the flange. The other end of the flange meets thestraight pipe. The flange specifications and loadings are taken from the straight pipe.

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MITER, NEL1, NEL2, RAD, NDIV , ESTRT , EINC

Defines a mitered bend in a piping run.

PREP7:Piping


NEL1, NEL2

Element numbers of the two intersecting straight pipes. Defaults to the last two straight pipe elementsnearest the intersection of the last two runs.

RAD

Bend radius. If LR, use long radius standard (1.5 x OD) (default). If SR, use short radius standard (1.0 xOD).

NDIV

Number of divisions (elements) along bend (defaults to 2). A node is generated at the end of each divi

ESTRT

Number to be assigned to first element of bend (defaults to MAXEL + 1).

EINC


Notes

Defines a mitered bend of piecewise straight-pipe PIPE16 elements in place of the intersection of two prevously defined straight pipe elements (RUN). This command is similar to the BEND command except thatstraight pipe elements are used to form the bend instead of curved (elbow) elements. (See the RUN andBEND command descriptions in Part II:Legacy Commands (p. 17).)

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PCORRO, CTK

Specifies the allowable exterior corrosion thickness for a piping run.

PREP7:Piping


CTK

Allowable corrosion thickness.

Notes

Specifies the allowable exterior corrosion thickness for a piping run. (See the RUN command description inPart II:Legacy Commands (p. 17).)

Menu Paths



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PDRAG, PX1, PY1, PZ1, H1, PX2, PY2, PZ2, H2, Kcord

Defines the external fluid drag loading for a piping run.

PREP7:Piping


PX1, PY1, PZ1

External fluid drag pressure (global Cartesian components) at heightH1

.H1

Height (along Kcord coordinate) for first drag pressure.

PX2, PY2, PZ2

External fluid drag pressure (global Cartesian components) at height H2.

H2

Height (along Kcord coordinate) for second drag pressure.

Kcord

Coordinate direction for height value (in the global Cartesian coordinate system):

X

X coordinate.

Y

Y coordinate (default).

Z

Z coordinate.

Notes

Defines the external fluid drag loading (pressure) as a function of height for a piping run. (See the RUNcommand description in Part II:Legacy Commands (p. 17).) The element drag pressure is determined fromthe centroid height and linear interpolation. Pressures are assigned to the elements as they are generated.

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PFLUID, DENS

Defines the contained fluid density for a piping run.

PREP7:Piping


DENS

Density of the contained fluid.

Notes

See the RUN command description in Part II:Legacy Commands (p. 17).

Distributed ANSYS Restriction This command is not supported in Distributed ANSYS.

Menu Paths



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PGAP, NLOC , K , DX , DY , DZ , GAP , ELEM

Defines a spring-gap constraint in a piping run.

PREP7:Piping


NLOC

Node where gap is to be placed. Defaults to current run starting point.K

Spring constant value (must be positive).

DX , DY , DZ

Increment (in terms of the active coordinate system components) to determine gap ground point. Elemlength must not be zero. Constraints are automatically generated at the ground point.

GAP

Gap size (defaults to the element length).

ELEM

Element number to be assigned to gap (defaults to MAXEL + 1).

Notes

Defines a spring-gap constraint (gap element CONTAC52) at a given location in a piping run. Gives springconstraint resistance after a specified gap is closed. (See the RUN command description in Part II:Legacy

Commands (p. 17).)

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PINSUL, DENS, ITK

Defines the external insulation constants in a piping run.

PREP7:Piping


DENS

Insulation density.ITK

Insulation thickness.

Command Default

No insulation.

Notes

Defines the external insulation constants in a piping run. (See the RUN command description in Part II:Lega

Commands (p. 17).)

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PIPE

Specifies "Pipe modeling" as the subsequent status topic.

PREP7:Status

MP ME ST PR PRN <> <> FL EM EH DY PP <> EME MFS

Notes

This is a status topic command. If status is requested for some items, it appears in the log file (Jobname.L This command should be followed immediately by a STAT command, which reports the status for the spectopic.

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PPRES, PRESS

Defines the internal pressure for a piping run.

PREP7:Piping


PRESS

Pipe internal pressure.

Notes

Defines the pipe internal pressure for a piping run (RUN). These pressures are assigned to the elements asthey are generated. (See the RUN command description in Part II:Legacy Commands (p. 17).)

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PSPEC, MAT , DNOM, SCHED, OD, TK

Defines pipe material and dimensions.

PREP7:Piping


MAT

Material number referring to a material property [MP

]. Material number must be between 1 and 40.DNOM , SCHED

Nominal diameter of pipe and schedule rating. Only valid ratings accepted. If these are specified, theOD and TK values are found from an internal table.

Valid values for DNOM are: 1, 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34,and 36.

Valid ratings for SCHED are: 5, 5S, 10, 10S, 20, 30, 40, 40S, 60, 80 80S, 100, 120, 140, 160, XS, XXS, andSTD.

OD

Outer diameter of pipe (ifDNOM

not specified). If bothDNOM

andOD

are not specified,OD

andTK

retaitheir previous values.

TK

Wall thickness of pipe (if OD specified).

Notes

Defines pipe material and dimensions. (See the RUN command description in Part II:Legacy Commands (p. 1

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PSPRNG, NLOC , TYPE , K , DX , DY , DZ , ELEM

Defines a spring constraint in a piping run.

PREP7:Piping


NLOC

Node where spring is to be placed. Defaults to current run starting point.TYPE

Type of spring:

TRAN Translational (default).

ROT

Rotational.

K

Spring constant value (must be positive).

DX , DY , DZ

Increment (in terms of the active coordinate system components) to determine spring ground point.Spring length must not be zero. Constraints are automatically generated at the ground point.

ELEM

Element number to be assigned to spring (defaults to the previous maximum element number (MAXEL+ 1)).

Notes

Defines a spring constraint (spring element COMBIN14) at a given location in a piping run. (See the RUNcommand description in Part II:Legacy Commands (p. 17).)

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PTEMP, TOUT , TIN

Defines the pipe wall temperatures in a piping run.

PREP7:Piping


TOUT

Outer pipe wall temperature. If NONE, reset temperature specification to none (BFUNIF

will be assigneTIN

Inner pipe wall temperature (defaults to TOUT ).

Command Default

Assign uniform temperature BFUNIF to elements.

Notes

Defines the pipe wall temperatures in a piping run. These temperatures are assigned to the elements asthey are generated. (See the RUN command description in Part II:Legacy Commands (p. 17).)

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PUNIT, KOPT

Selects the system of length units to be used in a piping run.

PREP7:Piping


KOPT

Units key:0

Input units are consistent (no conversions are done) (default).

FTIN or 1

English units (feet A, inch B, fraction of inch C/D). Use A+B+C/D format for PDRAG, BRANCH, RUN,BEND, MITER, REDUCE, VALVE, BELLOW, FLANGE, PSPRNG, and PGAP commands. Precede by "-'' signfor negative coordinates. (Example: 5+6+7/16 for 5 ft. 6-7/16 in., +3 for 3 in., -0+3 for -3 in., +0+9/16for 9/16 in.).

The two signs should not be consecutive. A, B, C, and D must be integers. Use B+C/D format forPSPEC, PINSUL, and PCORRO commands. (Example: 2 for 2 in., 3+1/2 for 3-1/2 in., +3/8 for 3/8 in.)

METRIC or 2Metric units (meter A, centimeter B, fraction of cm C/D). Use as explained for English units. (Example5+6+7/10 for 5 m 6-7/10 cm with PDRAG command.)

Command Default

Input units are consistent (no conversions are done).

Notes

Selects the system of length units to be used for the piping commands. Mixed length units require a + sigto delimit (or position) the units in the system and are converted to the smallest unit of the system (inchesor centimeters) upon input.

This conversion is local only to pure length units of the piping commands listed. Other units and units forother commands must be input to be consistent with the smallest length unit of the system used.

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RUN, DX , DY , DZ , NDIV , NEND, ESTRT , EINC

Defines a pipe run.

PREP7:Piping


DX , DY , DZ

Increment (in terms of the active coordinate system components) to determine run end point. Incremeis applied to branch starting point (BRANCH) or end point of previous run (whichever was later).

NDIV

Number of divisions (elements) along branch (defaults to 1). A node is generated at the end of each division.

NEND

Number to be assigned to end node of branch (defaults to MAXNP + NDIV ).

ESTRT

Number to be assigned to first element of branch (defaults to the previous maximum element number(MAXEL) + 1).

EINC Element number increment (defaults to 1).

Notes

Defines a pipe run from a previous point to an incremental point. Nodes (and elements) are generatedstraight (in the active coordinate system). Elements are of type PIPE16 straight pipes. Material properties,real constants, and loads are derived from the previously defined piping specifications. Piping loads andspecifications are defined via PCORRO, PDRAG, PFLUID, PINSUL, POPT, PPRES, PSPEC, PTEMP, and PUNITcommands.

Generated items may be listed (or displayed) with the standard commands (NLIST, ELIST, NPLOT, EPLOT,

ETLIST, RLIST, etc.).

Items may also be modified (NMODIF, EMODIF, RMODIF, etc.) or redefined as desired.

See Piping Models (p. 3) for more information.

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TEE, NCENT , TYPE , ELEM, EINC , L1, L2, L3

Defines a tee in a piping run.

PREP7:Piping


NCENT

Node where three straight pipes intersect forming a tee (or "Y"). Defaults to last starting branch node(BRANCH).

TYPE

Type of tee:

WT

Welding tee (default).

r = (D0 - tw) / 2

h = 4.4 tw / r

SIF = 0.9 / (h2/3

)

If (SIF < 1) SIF = 1

UFT

Unreinforced fabricated tee.

r = (D0 - tw) / 2

h = tw / r

SIF = 0.9 / (h2/3)

If (SIF < 1) SIF = 1

ELEM

Element number to be assigned to first tee leg (defaults to the previous maximum element number(MAXEL) + 1).

EINC


L1, L2, L3

Tee leg lengths (corresponding in order of increasing straight pipe element numbers). Must be less thathe straight pipe length. Defaults to 2 x OD of straight pipe (for each leg).

Notes

Defines a tee in place of the tee intersection of three previously defined straight pipe elements. (See theRUN command description in Part II:Legacy Commands (p. 17).)

The new tee is also composed of three PIPE16 straight pipe elements, but of the leg lengths specified andwith the appropriate tee factors calculated.

Three new nodes are generated at the ends of the tee.


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VALVE, NLOC , LENG, MASS, SIF , FLEX , ARINS, ELEM

Defines a valve in a piping run.

PREP7:Piping


NLOC

Node where valve is to be placed (as described below). Defaults to current run starting point.LENG

Length of valve (defaults to larger pipe OD).

MASS

Dry mass (weight/gravity) of valve without insulation (defaults to equivalent straight pipe mass). Note,acceleration (ACEL) must be nonzero for weight to be calculated.

SIF

Stress intensification factor (defaults to 1.0).

FLEX


ARINS

Insulation surface area (defaults to equivalent straight pipe insulation area). Units (length2) must beconsistent with the smallest unit of the system used (not mixed) regardless of the PUNIT option.

ELEM

Element number to be assigned to valve (defaults to the previous maximum element number (MAXEL)+ 1).

Notes

Defines a valve (straight-pipe element PIPE16 with adjusted specifications and loadings) at a given locationin a piping run. (See the RUN command description in Part II:Legacy Commands (p. 17).) The location may

be 1) between two adjacent colinear straight pipes, 2) between an adjacent straight pipe and a differentpiping component, or 3) at the end of a straight pipe.

For Case 1, two new nodes are generated at the ends of the valve. The two straight pipes are automatically"shortened" to meet the ends of the valve. The valve specifications and loadings are taken from the corresponding two straight pipes.

For Case 2, one new node is generated at one end of the valve. The straight pipe is automatically "shorteneto meet this end of the valve. The other end of the valve meets the other piping component. The valvespecifications and loadings are taken from the straight pipe.

For Case 3, one new node is generated at the free end of the valve. The other end of the valve meets the

straight pipe. The valve specifications and loadings are taken from the straight pipe.

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Legacy Elements

Following is the archived documentation for legacy elements.

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BEAM4

3-D Elastic Beam

MP ME ST PR PRN DS DSS <> <> <> <> PP <> EME MFSProduct Restrictions

BEAM4 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-technology element such as BEAM188 (KEYOPT(3) = 3).

BEAM4 is a uniaxial element with tension, compression, torsion, and bending capabilities. The element hassix degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about thenodal x, y, and z axes. Stress stiffening and large deflection capabilities are included. A consistent tangentstiffness matrix option is available for use in large deflection (finite rotation) analyses. A tapered unsymmetrical elastic beam is described in BEAM44 and a 3-D plastic beam in BEAM24.

Figure 1 BEAM4 Geometry

Θ

Θ

Θ Θ

Θ

Θ

Θ

Θ

Θ






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BEAM4 Input Data

The geometry, node locations, and coordinate systems for this element are shown in Figure 1 (p. 63). Theelement is defined by two or three nodes, the cross-sectional area, two area moments of inertia (IZZ andIYY), two thicknesses (TKY and TKZ), an angle of orientation (θ) about the element x-axis, the torsional momentof inertia (IXX), and the material properties. For stiffness purposes, the torsional moment of inertia, if IXX isequal to 0.0 or not specified, is assumed to be equal to the polar moment of inertia (IYY + IZZ). For inertial

purposes, the torsional (rotational) moment of inertia used is the polar moment of inertia, and is thereforenot affected by the value entered for IXX. The IXX value should be positive and is usually less than the polarmoment of inertia. An added mass per unit length may be input with the ADDMAS value.

The element x-axis is oriented from node I toward node J. For the two-node option, the default (θ = 0°) ori-entation of the element y-axis is automatically calculated to be parallel to the global X-Y plane. Several ori-entations are shown in Figure 1 (p. 63). For the case where the element is parallel to the global Z axis (orwithin a 0.01 percent slope of it), the element y axis is oriented parallel to the global Y axis (as shown). Foruser control of the element orientation about the element x-axis, use the θ angle (THETA) or the third nodeoption. If both are defined, the third node option takes precedence. The third node (K), if used, defines aplane (with I and J) containing the element x and z axes (as shown). If this element is used in a large deflectionanalysis, it should be noted that the location of the third node (K), or the angle (THETA), is used only to initially

orient the element. (For information about orientation nodes and beam meshing, see Meshing Your SolidModel in the Modeling and Meshing Guide.)

The initial strain in the element (ISTRN) is given by ∆ /L, where ∆ is the difference between the elementlength, L, (as defined by the I and J node locations) and the zero strain length. The shear deflection constants(SHEARZ and SHEARY) are used only if shear deflection is to be included. A zero value of SHEAR_ may beused to neglect shear deflection in a particular direction. See Shear Deflection for details.

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (i.e., a matrix composed of the maintangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses [NLGEOM,ON].You can often obtain more rapid convergence in a geometrically nonlinear analysis, such as a nonlinearbuckling or postbuckling analysis, by activating this option. However, you should not use this option if you

are using the element to simulate a rigid link or a group of coupled nodes. The resulting abrupt changes instiffness within the structure make the consistent tangent stiffness matrix unsuitable for such applications.

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamicanalyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in the positiveelement x direction). The element must be symmetric with this option (e.g., IYY = IZZ and SHEARY = SHEARZ).

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 63). Positive normal pressures act into theelement. Lateral pressures are input as a force per unit length. End "pressures" are input as a force. Temper-atures may be input as element body loads at the eight "corner" locations shown in Figure 1 (p. 63).Thefirst corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1.

If only T1 and T2 are input, T3 defaults to T2 and T4 defaults to T1. If only T1 and T4 are input, T2 defaultsto T1 and T3 defaults to T4. In both cases, T5 through T8 default to T1 through T4. For any other input pattern,unspecified temperatures default to TUNIF.

KEYOPT(9) is used to request output at intermediate locations. It is based on equilibrium (free body of aportion of the element) considerations and is not valid if:

• stress stiffening is turned on [SSTIF,ON]

• more than one component of angular velocity is applied [OMEGA]


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• any angular velocities or accelerations are applied with the CGOMGA, DOMEGA, or DCGOMG comma

A summary of the element input is given in "BEAM4 Input Summary" (p. 65). A general description of elemeinput is given in Element Input.

BEAM4 Input Summary

Nodes

I, J, K (K orientation node is optional)

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants

AREA, IZZ, IYY, TKZ, TKY, THETAISTRN, IXX, SHEARZ, SHEARY, SPIN, ADDMASSee Table 1: BEAM4 Real Constants (p. 66) for a description of the real constants.

Material Properties

EX, ALPX (or CTEX or THSX), DENS, GXY, DAMP

Surface Loads

Pressures --

face 1 (I-J) (-Z normal direction)face 2 (I-J) (-Y normal direction)face 3 (I-J) (+X tangential direction)face 4 (I) (+X axial direction)face 5 (J) (-X axial direction)(use negative value for opposite loading)

Body Loads

Temperatures --

T1, T2, T3, T4, T5, T6, T7, T8

Special Features

Stress stiffeningLarge deflectionBirth and death

KEYOPT(2)

Stress stiffening option:

0 --

Use only the main tangent stiffness matrix when NLGEOM is ON. (Stress stiffening effects used in

linear buckling or other linear prestressed analyses must be activated separately with PSTRES,ON.)1 --

Use the consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffnessmatrix plus the consistent stress stiffness matrix) when NLGEOM is ON. (SSTIF,ON will be ignoredfor this element when KEYOPT(2) = 1 is activated.) Note that if SOLCONTROL is ON and NLGEOM

is ON, KEYOPT(2) is automatically set to 1; i.e., the consistent tangent will be used.


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2 --

Turn off consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffnessmatrix plus the consistent stress stiffness matrix) when SOLCONTROL is ON. Sometimes it is necessaryto turn off the consistent tangent stiffness matrix if the element is used to simulate rigid bodies byusing a very large real constant number . KEYOPT(2) = 2 is the same as KEYOPT(2) = 0, however,KEYOPT(2) = 0 is controlled by SOLCONTROL, ON or OFF, while KEYOPT(2) = 2 is independent of SOLCONTROL.

KEYOPT(6)Member force and moment output:

0 --

No printout of member forces or moments

1 --

Print out member forces and moments in the element coordinate system

KEYOPT(7)

Gyroscopic damping matrix:

0 --

No gyroscopic damping matrix

1 --

Compute gyroscopic damping matrix. Real constant SPIN must be greater than zero. IYY must equalIZZ.

KEYOPT(9)Output at intermediate points between ends I and J:

N --

Output at N intermediate locations (N = 0, 1, 3, 5, 7, 9)

Table 1 BEAM4 Real Constants

DescriptionNameNo.

Cross-sectional areaAREA1

Area moment of inertiaIZZ2

Area moment of inertiaIYY3

Thickness along Z axis TKZ4

Thickness along Y axis TKY5

Orientation about X axis THETA6

Initial strainISTRN7

Torsional moment of inertiaIXX8

Shear deflection constant Z [1]SHEARZ9Shear deflection constant Y [2]SHEARY10

Rotational frequency (required if KEYOPT(7) = 1)SPIN11

Added mass/unit lengthADDMAS12

1. SHEARZ goes with IZZ; if SHEARZ = 0, there is no shear deflection in the element Y direction.

2. SHEARY goes with IYY; if SHEARY = 0, there is no shear deflection in the element Z direction.


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BEAM4 Output Data

The solution output associated with the element is in two forms:

• Nodal displacements included in the overall nodal solution

• Additional element output as shown in Table 2: BEAM4 Element Output Definitions (p. 67).

Several items are illustrated inFigure 2

(p. 67). The maximum stress is computed as the direct stress plus the absolute values of both bending stresses. Thminimum stress is the direct stress minus the absolute value of both bending stresses. A general descriptioof solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

Figure 2 BEAM4 Stress Output

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method(ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R colum

indicates the availability of the items in the results file.

In either the O or R columns,“Y” indicates that the item is always available, a number refers to a tablefootnote that describes when the item is conditionally available, and “-” indicates that the item is not availa

Table 2 BEAM4 Element Output Definitions

RODefinitionName

YYElement numberEL

YYElement node number (I and J)NODES

YYMaterial number for the elementMAT

Y-Element volumeVOLU:

3YLocation where results are reportedXC, YC, ZC

YY Temperatures at integration points T1, T2, T3, T4, T5, T6, T7, T8

TEMP

YYPressure P1 at nodes I, J; OFFST1 at I, J; P2 at I, J; OFFST2at I, J; P3 at I, J; OFFST3 at I, J; P4 at I; P5 at J

PRES

11Axial direct stressSDIR


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RODefinitionName

11Bending stress on the element +Y side of the beamSBYT

11Bending stress on the element -Y side of the beamSBYB

11Bending stress on the element +Z side of the beamSBZT

11Bending stress on the element -Z side of the beamSBZB

11Maximum stress (direct stress + bending stress)SMAX

11Minimum stress (direct stress - bending stress)SMIN

11Axial elastic strain at the endEPELDIR

11Bending elastic strain on the element +Y side of the beamEPELBYT

11Bending elastic strain on the element -Y side of the beamEPELBYB

11Bending elastic strain on the element +Z side of the beamEPELBZT

11Bending elastic strain on the element -Z side of the beamEPELBZB

11Axial thermal strain at the endEPTHDIR

11Bending thermal strain on the element +Y side of the beamEPTHBYT

11Bending thermal strain on the element -Y side of the beamEPTHBYB

11Bending thermal strain on the element +Z side of the beamEPTHBZT

11Bending thermal strain on the element -Z side of the beamEPTHBZB

11Initial axial strain in the elementEPINAXL

Y2Member forces in the element coordinate system X, Y, Zdirections

MFOR(X, Y,Z)

Y2Member moments in the element coordinate system X, Y,Z directions

MMOM(X, Y,Z)

1. The item repeats for end I, intermediate locations (see KEYOPT(9)), and end J.

2. If KEYOPT(6) = 1.

3. Available only at centroid as a *GET item.

The following tables list output available through the ETABLE command using the Sequence Numbermethod. See The General Postprocessor (POST1) of the Basic Analysis Guide and The Item and SequenceNumber Table of this manual for more information. The following notation is used in Table 3: BEAM4 Item

and Sequence Numbers (KEYOPT(9) = 0) (p. 69) through Table 8: BEAM4 Item and Sequence Numbers (KEYOPT(9)

= 9) (p. 75):

Nameoutput quantity as defined in the Table 2: BEAM4 Element Output Definitions (p. 67)

Itempredetermined Item label for ETABLE command

E

sequence number for single-valued or constant element data

I,J

sequence number for data at nodes I and J


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ILN

sequence number for data at Intermediate Location N

Table 3 BEAM4 Item and Sequence Numbers (KEYOPT(9) = 0)

ETABLE and ESOL Command InputOutput

Quant-

ity

Name

JIEItem

61-LSSDIR

72-LSSBYT

83-LSSBYB

94-LSSBZT

105-LSSBZB

61-LEPELEPELDIR

72-LEPELEPELBYT

83-LEPELEPELBYB

94-LEPELEPELBZT

105-LEPELEPELBZB

31-NMISCSMAX

42-NMISCSMIN

61-LEPTHEPTHDIR

72-LEPTHEPTHBYT

83-LEPTHEPTHBYB

94-LEPTHEPTH-BZT

105-LEPTHEPTH-BZB

--11LEPTHEPINAXL

71-SMISCMFORX

82-SMISCMFORY

93-SMISCMFORZ

104-SMISCMMOMX

115-SMISCMMOMY

126-SMISCMMOMZ

1413-SMISCP1

1615-SMISCOFFST1

1817-SMISCP2

2019-SMISCOFFST2

2221-SMISCP3

2423-SMISCOFFST3


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Quant-

ity

Name

JIEItem

-25-SMISCP4

26--SMISCP5

Pseudo Node

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ity

Name

JIL1IEItem

1161-LSSDIR1272-LSSBYT

1383-LSSBYB

1494-LSSBZT

15105-LSSBZB

1161-LEPELEPELDIR

1272-LEPELEPELBYT

1383-LEPELEPELBYB

1494-LEPELEPELBZT

15105-LEPELEPELBZB

531-NMISCSMAX

642-NMISCSMIN

1161-LEPTHEPTHDIR

1272-LEPTHEPTHBYT

1383-LEPTHEPTHBYB

1494-LEPTHEPTH-BZT

15105-LEPTHEPTH-

BZB---16LEPTHEPINAXL

1371-SMISCMFORX

1482-SMISCMFORY

1593-SMISCMFORZ

16104-SMISCMMOMX

17115-SMISCMMOMY


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Name

JIL1IEItem

18126-SMISCMMOMZ

20-19-SMISCP1

22-21-SMISCOFFST124-23-SMISCP2

26-25-SMISCOFFST2

28-27-SMISCP3

30-29-SMISCOFFST3

--31-SMISCP4

32---SMISCP5

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Name

JIL3IL2IL1IEItem

21161161-LSSDIR

22171272-LSSBYT

23181383-LSSBYB

24191494-LSSBZT

252015105-LSSBZB

21161161-LEPELEPELDIR

22171272-LEPELEPELBYT

23181383-LEPELEPELBYB

24191494-LEPELEPELBZT

252015105-LEPELEPELBZB

97531-NMISCSMAX

108642-NMISCSMIN

21161161-LEPTHEPTHDIR

22171272-LEPTHEPTHBYT

23181383-LEPTHEPTHBYB

24191494-LEPTHEPTH-BZT


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Name

JIL5IL4IL3IL2IL1IEItem

131197531-NMISCSMAX

1412108642-NMISCSMIN

312621161161-LEPTHEPTHDIR322722171272-LEPTHEPTHBYT

332823181383-LEPTHEPTHBYB

342924191494-LEPTHEPTH-BZT

3530252015105-LEPTHEPTH-BZB

-------36LEPTHEPINAXL

373125191371-SMISCMFORX

383226201482-SMISCMFORY

393327211593-SMISCMFORZ

4034282216104-SMISCMMOMX

4135292317115-SMISCMMOMY

4236302418126-SMISCMMOMZ

44-----43-SMISCP1

46-----45-SMISCOFFST1

48-----47-SMISCP2

50-----49-SMISCOFFST2

52-----51-SMISCP354-----53-SMISCOFFST3

------55-SMISCP4

56-------SMISCP5

Pseudo Node

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ity

Name

JIL7IL6IL5IL4IL3IL2IL1IEItem

4136312621161161-LSSDIR

4237322722171272-LSSBYT

4338332823181383-LSSBYB


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JIL7IL6IL5IL4IL3IL2IL1IEItem

4439342924191494-LSSBZT

45403530252015105-LSSBZB

4136312621161161-LEPELEPELDIR4237322722171272-LEPELEPELBYT

4338332823181383-LEPELEPELBYB

4439342924191494-LEPELEPELBZT

45403530252015105-LEPELEPELBZB

1715131197531-NMISCSMAX

18161412108642-NMISCSMIN

4136312621161161-LEPTHEPTHDIR

4237322722171272-LEPTHEPTHBYT

4338332823181383-LEPTHEPTHBYB4439342924191494-LEPTHEPTH-

BZT

45403530252015105-LEPTHEPTH-BZB

---------46LEPTHEPINAXL

4943373125191371-SMISCMFORX

5044383226201482-SMISCMFORY

5145393327211593-SMISCMFORZ

52464034282216104-SMISCMMOMX53474135292317115-SMISCMMOMY

54484236302418126-SMISCMMOMZ

56-------55-SMISCP1

58-------57-SMISCOFFST1

60-------59-SMISCP2


64-------63-SMISCP3


--------67-SMISCP468---------SMISCP5


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Pseudo Node

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Quant-ity

Name

JIL9IL8IL7IL6IL5IL4IL3IL2IL1IEItem

51464136312621161161-LSSDIR

52474237322722171272-LSSBYT

53484338332823181383-LSSBYB

54494439342924191494-LSSBZT

555045403530252015105-LSSBZB

51464136312621161161-LEPELEPELDIR

52474237322722171272-LEPELEPELBYT53484338332823181383-LEPELEPELBYB

54494439342924191494-LEPELEPELBZT

555045403530252015105-LEPELEPELBZB

21191715131197531-NMISCSMAX

222018161412108642-NMISCSMIN

51464136312621161161-LEPTHEPTHDIR

52474237322722171272-LEPTHEPTHBYT

53484338332823181383-LEPTHEPTHBYB

54494439342924191494-LEPTHEPTH-BZT

555045403530252015105-LEPTHEPTH-BZB

-----------56LEPTHEPINAXL

61554943373125191371-SMISCMFORX

62565044383226201482-SMISCMFORY

63575145393327211593-SMISCMFORZ

645852464034282216104-SMISCMMOMX

655953474135292317115-SMISCMMOMY666054484236302418126-SMISCMMOMZ

68---------67-SMISCP1

70---------69-SMISCOFFST1

72---------71-SMISCP2


76---------75-SMISCP3


BEAM4

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Quant-

ity

Name

JIL9IL8IL7IL6IL5IL4IL3IL2IL1IEItem


----------79-SMISCP4

80-----------SMISCP5

Pseudo Node

87654321

87654321LBFE TEMP

BEAM4 Assumptions and Restrictions

• The beam must not have a zero length or area. The moments of inertia, however, may be zero if largedeflections are not used.

• The beam can have any cross-sectional shape for which the moments of inertia can be computed. Thestresses, however, will be determined as if the distance between the neutral axis and the extreme fiberis one-half of the corresponding thickness.

• The element thicknesses are used only in the bending and thermal stress calculations.

• The applied thermal gradients are assumed to be linear across the thickness in both directions andalong the length of the element.

• If you use the consistent tangent stiffness matrix (KEYOPT(2) = 1), take care to use realistic (that is, "toscale") element real constants. This precaution is necessary because the consistent stress-stiffeningmatrix is based on the calculated stresses in the element. If you use artificially large or small cross-sec-tional properties, the calculated stresses will become inaccurate, and the stress-stiffening matrix willsuffer corresponding inaccuracies. (Certain components of the stress-stiffening matrix could even

overshoot to infinity.) Similar difficulties could arise if unrealistic real constants are used in a linearprestressed or linear buckling analysis [PSTRES,ON].

• Eigenvalues calculated in a gyroscopic modal analysis can be very sensitive to changes in the initialshift value, leading to potential error in either the real or imaginary (or both) parts of the eigenvalues.

BEAM4 Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element inaddition to the general assumptions and restrictions given in the previous section.

ANSYS Professional

• The SPIN real constant (R11) is not available. Input R11 as a blank.

• The DAMP material property is not allowed.

• KEYOPT(2) can only be set to 0 (default).


• The only special features allowed are stress stiffening and large deflections.


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CONTAC12

2-D Point-to-Point Contact

MP ME ST PR PRN <> <> <> <> <> <> PP <> EME MFSProduct Restrictions

CONTAC12 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as CONTA178.To use CONTA178 as you would CONTAC12, constrain the UZ degree of freedom to simulate 2-D behavior. CONTA178 does not support the circular gap option of CONTAC12.

CONTAC12 represents two surfaces which may maintain or break physical contact and may slide relative toeach other. The element is capable of supporting only compression in the direction normal to the surfacesand shear (Coulomb friction) in the tangential direction. The element has two degrees of freedom at eachnode: translations in the nodal x and y directions.

The element may be initially preloaded in the normal direction or it may be given a gap specification. Aspecified stiffness acts in the normal and tangential directions when the gap is closed and not sliding.

Figure 1 CONTAC12 Geometry

θ

θ

δ

δ

CONTAC12 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 77). Theelement is defined by two nodes, an angle to define the interface, two stiffnesses (KN and KS), an initialdisplacement interference or gap (INTF), and an initial element status (START). An element coordinate syste(s-n) is defined on the interface. The angle θ (THETA) is input (or calculated) in degrees and is measuredfrom the global X axis to the element s-axis. The orientation of the interface may be defined (KEYOPT(2)) by

THETA or by the node locations.

The normal stiffness, KN, should be based upon the stiffness of the surfaces in contact. See Performing aNode-to-Node Contact Analysis in the Contact Technology Guide for guidelines on choosing a value for KN.In some cases (such as initial interference analyses, nonconvergence, or over penetration), it may be usefulto change the KN value between load steps or in a restart in order to obtain an accurate, converged soluti The sticking stiffness, KS, represents the stiffness in the tangential direction when elastic Coulomb frictionis selected ( > 0.0 and KEYOPT(1) = 0). The coefficient of friction is input as material property MU and isevaluated at the average of the two node temperatures. Stiffnesses may also be computed from the maxim






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expected force divided by the maximum allowable surface displacement. KS defaults to KN. Stiffnesses shouldbe on a full 360° basis for an axisymmetric analysis.

The initial displacement interference, ∆, defines the displacement interference (if positive) or the gap size(if negative). The value may be input as a real constant (INTF) or automatically calculated from the inputnode locations if KEYOPT(4) = 1. Stiffness is associated with a zero or positive interference. The initial elementstatus (START) is used to define the "previous" condition of the interface to be used at the start of the firstsubstep. This input is used to override the condition implied by the interference specification and is useful

in anticipating the final interface configuration and in reducing the number of iterations required for con-vergence.

The force deflection relationships for the interface element can be separated into the normal and tangential(sliding) directions as shown in Figure 2 (p. 81). The element condition at the beginning of the first substepis determined from the START parameter. If the interface is open, no stiffness is associated with this elementfor this substep. If the interface is closed and sticking, KN is used in the gap resistance and KS is used in thesliding resistance. If the interface is closed but sliding, KN is used in the gap resistance and the limit frictionforce FN is used for the sliding resistance.

In the normal direction, when the normal force (FN) is negative, the interface remains in contact and respondsas a linear spring. As the normal force becomes positive, contact is broken and no force is transmitted.

KEYOPT(3) can be used to specify a "weak spring" across an open interface, which is useful for preventingrigid body motion that could occur in a static analysis. The weak spring stiffness is computed by multiplyingthe normal stiffness KN by a reduction factor. The default reduction factor of 1E-6 can be overridden withreal constant REDFACT.

In the tangential direction, for FN < 0 and the absolute value of the tangential force (FS) less than (|FN|),the interface sticks and responds as a linear spring in the tangential direction. For FN < 0 and FS = |FN|,sliding occurs.

If KEYOPT(1) = 1, rigid Coulomb friction is selected, KS is not used, and the elastic sticking capability is re-moved. This option is useful for displacement controlled problems or for certain dynamic problems where

sliding dominates. With this option, no tangential resistance is assumed for the first substep.

The only material property used is the interface coefficient of friction MU. A zero value should be used forfrictionless surfaces. Temperatures may be input at the element nodes (for material property evaluationonly). The node I temperature T(I) defaults to TUNIF. The node J temperature defaults to T(I). The circulargap option (KEYOPT(2)) is useful where the final contact point (and thus the orientation angle) is not known,such as with concentric cylinders. With this option the angular orientation THETA is initially set to 0.0 andthen internally calculated from the relative displacements of the nodes at the end of the substep for use inthe next substep. The user specified THETA (if any) is ignored. A negative interference (gap) and a zerocoefficient of friction is used with this option.

For analyses involving friction, using NROPT,UNSYM is useful (and, in fact, sometimes required) for problemswhere the normal and tangential (sliding) motions are strongly coupled, such as in a wedge insertionproblem.

A summary of the element input is given in "CONTAC12 Input Summary" (p. 79). A general description of element input is given in Element Input.


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CONTAC12 Input Summary

Nodes

I, J

Degrees of Freedom

UX, UY

Real Constants

See Table 1: CONTAC12 Real Constants (p. 80) for details on these real constants

Material Properties

MU

Surface Loads

None

Body Loads

Temperatures --

T(I), T(J)

Special Features

NonlinearAdaptive descent

KEYOPT(1)

Type of friction (only with MU > 0.0):

0 --

Elastic coulomb friction (KS used for sticking stiffness)

1 --

Rigid coulomb friction (resisting force only)

KEYOPT(2)

Orientation angle:0 --

Orientation angle based on Theta real constant

1 --

Circular gap option (THETA orientation determined from direction of motion) (ignore THETA realconstant)

KEYOPT(3)

Weak spring across open gap:

0 --No weak spring across an open gap

1 --Use a weak spring across an open gap

KEYOPT(4)

Interference or gap:

0 --

Interference (or gap) based on INTF real constant

1 --

Interference (or gap) based on initial node locations (ignore INTF real constant)


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KEYOPT(7)

Element level time incrementation control. Note that this option should be activated first at the procedurelevel if SOLCONTROL is ON. SOLCONTROL,ON,ON is the most frequent usage with this element. If SOLCONTROL,ON,OFF, this keyoption is not activated.

0 --

Predictions are made to achieve the minimum time (or load) increment whenever a change in contactstatus occurs

1 --Predictions are made to maintain a reasonable time (or load) increment (recommended)

Table 1 CONTAC12 Real Constants

DescriptionNameNo.

Interference angle THETA1

Normal stiffnessKN2

Initial displacement interference or gap. A negative INTF (inter-ference) assumes an initially open gap.

INTF3

Initial element statusSTART4

If = 0.0 or blank, initial condition of gap status is determinedfrom real constant INTFIf = 1.0, gap is initially closed and not sliding (if MU ≠ 0.0), orsliding node J is positive (if MU = 0.0)If = 2.0, gap is initially closed and node J is sliding to the rightof node IIf = -2.0, gap is initially closed and node J is sliding to the leftof node IIf = 3.0, gap is initially open

Sticking stiffnessKS5

KN reduction factorREDFACT6

CONTAC12 Output Data


• nodal displacements included in the overall nodal solution

• additional element output as shown in Table 2: CONTAC12 Element Output Definitions (p. 81).

Several items are illustrated in Figure 2 (p. 81).

The value of USEP is determined from the normal displacement (un) (in the element x-direction) betweenthe interface nodes at the end of this substep. That is: USEP = (un) J - (un) I - ∆. This value is used in determ-

ining the normal force, FN. For an axisymmetric analysis, the element forces are expressed on a full 360°basis. The value represented by UT is the total translational displacement. The maximum value printed forthe sliding force, FS, is |FN|. STAT describes the status of the element at the end of this substep. If STAT =1, the gap is closed and no sliding occurs. If STAT = 3, the gap is open. A value of STAT = +2 indicates thenode J slides positive relative to node I as shown in Figure 4.12-1. STAT = -2 indicates a negative slide. Fora frictionless surface ( = 0.0), the element status is either STAT = ±2 or 3. The value of THETA is either the


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input orientation angle (if KEYOPT(2) = 0), or the calculated angle (if KEYOPT(2) = 1). A general descriptionof solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

Figure 2 CONTAC12 Force-Deflection Relationship

δ

µ

µ


A colon (:) in the Name column indicates that the item can be accessed by the Component Name method(ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R columindicates the availability of the items in the results file.


Table 2 CONTAC12 Element Output Definitions

RODefinitionName

YYElement NumberELYYNodes - I, JNODES

3YLocation where results are reportedXC, YC

YY Temperatures T(I), T(J) TEMP

YYGap size or interferenceUSEP

YYNormal forceFN

11Element statusSTAT

11Stat value of the previous time stepOLDST

YYOrientation angle THETA

22Coefficient of frictionMU

22Relative displacement in tangential direction(positive for node J moving to right of node I)

UT

22 Tangential forceFS

1. Element status values:

1 - Contact, no sliding


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2 - Sliding contact with node J moving to right of node I

-2 - Sliding contact with node J moving to left of node I

3 - Gap open

2. Only if MU > 0.0 and KEYOPT(2) = 0.


Table 3: CONTAC12 Item and Sequence Numbers (p. 82) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) of the Basic Analysis Guide and The Item and Sequence Number Table of this manual for more information. The following notation is usedin Table 3: CONTAC12 Item and Sequence Numbers (p. 82):

Name

output quantity as defined in the Table 2: CONTAC12 Element Output Definitions (p. 81)

Item

predetermined Item label for ETABLE command

E


Table 3 CONTAC12 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

1SMISCFN

2SMISCFS

1NMISCSTAT

2NMISCOLDST

3NMISCUSEP

4NMISCUT

5NMISCMU

6NMISC THETA

CONTAC12 Assumptions and Restrictions

• The 2-D interface element must be defined in an X-Y plane and the Y-axis must be the axis of symmetryfor axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.

• The element operates bilinearly only in a static or a nonlinear transient dynamic analysis.

• If used in other analysis types, the element maintains its initial status throughout the analysis.

• The element is nonlinear and requires an iterative solution.

• Convergence is also based on forces when friction or the circular gap option is present.

• Nodes I and J may be coincident since the orientation of the interface is defined only by the angle THETA.


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• The orientation of the interface does not change (with KEYOPT(2) = 0) during a large deflection analyUse CONTA175 if this effect is desired.

• No moment effects due to noncoincident nodes are included. That is, if the nodes are offset from a linperpendicular to the interface, moment equilibrium may not be satisfied.

• The element is defined such that a positive normal displacement (in the element coordinate system)of node J relative to node I tends to open the gap, as shown in Figure 1 (p. 77). If, for a given set of conditions, node I and J are interchanged, or if the interface is rotated by 180°, the gap element acts

as a hook element, i.e., the gap closes as the nodes separate. The element may have rotated nodal co-ordinates since a displacement transformation into the element coordinate system is included.

• The element stiffness KN cannot be exactly zero.

• Unreasonably high stiffness values also should be avoided.

• The rate of convergence decreases as the stiffness increases. Note that, although it is permissible tochange KN, it is not permissible to change any other real constants between load steps. Therefore, if you plan to change KN, you cannot allow the value of KS to be defined by default, because the prograwould then attempt to redefine KS as KN changed.

• You must explicitly define KS whenever KN changes, to maintain a consistent value throughout all loasteps.

• The element may not be deactivated with the EKILL command.

• If is nonzero, the element is nonconservative as well as nonlinear. Nonconservative elements requirethat the load be applied very gradually, along the actual load history path, and in the proper sequence(if multiple loadings exist).

CONTAC12 Product Restrictions


ANSYS Professional

• This element is frictionless. Specifically, MU is not allowed as a material property and KS is not allowedas a real constant.

• Temperature body loads are not applicable.

• KEYOPT(1) is not applicable.


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PIPE16

Elastic Straight Pipe


PIPE16 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as PIPE288.

PIPE16 is a uniaxial element with tension-compression, torsion, and bending capabilities. The element hassix degrees of freedom at two nodes: translations in the nodal x, y, and z directions and rotations about thenodal x, y, and z axes. See PIPE16 - Elastic Straight Pipe (p. 192) for more details about this element.

Figure 1 PIPE16 Geometry

PIPE16 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 85). Theelement input data include two or three nodes, the pipe outer diameter and wall thickness, stress intensification and flexibility factors, internal fluid density, exterior insulation density and thickness, corrosion thicknallowance, insulation surface area, pipe wall mass, axial pipe stiffness, rotordynamic spin, and the isotropicmaterial properties.

The element X-axis is oriented from node I toward node J. For the two-node option, the element Y-axis isautomatically calculated to be parallel to the global X-Y plane. Several orientations are shown in Figure




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1 (p. 85). For the case where the element is parallel to the global Z-axis (or within a 0.01 percent slope of it), the element Y-axis is oriented parallel to the global Y-axis (as shown). For user control of the elementorientation about the element X-axis, use the third node option. The third node (K), if used, defines a plane(with I and J) containing the element X and Z axes (as shown). Input and output locations around the pipecircumference identified as being at 0° are located along the element Y-axis, and similarly 90° is along theelement Z-axis.

The stress intensification factor (SIF) modifies the bending stress. Stress intensification factors may be input

at end I (SIFI) and end J (SIFJ), if KEYOPT(2) = 0, or determined by the program using a tee-joint calculationif KEYOPT(2) = 1, 2, or 3. SIF values less than 1.0 are set equal to 1.0. The flexibility factor (FLEX) is dividedinto the cross-sectional moment of inertia to produce a modified moment of inertia for the bending stiffnesscalculation. FLEX defaults to 1.0 but may be input as any positive value.

The element mass is calculated from the pipe wall material, the external insulation, and the internal fluid. The insulation and the fluid contribute only to the element mass matrix. The corrosion thickness allowancecontributes only to the stress calculations. A positive wall mass real constant overrides the pipe wall masscalculation. A nonzero insulation area real constant overrides the insulation surface area calculation (fromthe pipe outer diameter and length). A nonzero stiffness real constant overrides the calculated axial pipestiffness.

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 85). Internal pressure (PINT) and externalpressure (POUT) are input as positive values. The internal and external pressure loads are designed for closed-loop static pressure environments and therefore include pressure loads on fictitious "end caps" so that thepressure loads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needs to berepresented, such as a pipe venting to a lower pressure area or the internal flow is past a constriction in thepipe, these end cap loads may need to be modified by applying a nodal force normal to the cross-sectionof the pipe with the magnitude representing the change in pressure. Alternatively, the precomputed endcap loads can be removed using KEYOPT(8) = 1 and the appropriate end cap loads added by the user. Thetransverse pressures (PX, PY, and PZ) may represent wind or drag loads (per unit length of the pipe) andare defined in the global Cartesian directions. Positive transverse pressures act in the positive coordinate

directions. The normal component or the projected full pressure may be used (KEYOPT(5)). Tapered pressuresare not recognized. Only constant pressures are supported for this element. See PIPE16 - Elastic Straight

Pipe (p. 192) for more information.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradients ordiametral gradients (KEYOPT(1)). The average wall temperature at θ = 0° is computed as 2 * TAVG - T(180)and the average wall temperature at θ = -90° is computed as 2 * TAVG - T(90). The element temperaturesare assumed to be linear along the length. The first temperature at node I (TOUT(I) or TAVG(I)) defaults to TUNIF. If all temperatures after the first are unspecified, they default to the first. If all temperatures at nodeI are input, and all temperatures at node J are unspecified, the node J temperatures default to the corres-ponding node I temperatures. For any other pattern of input temperatures, unspecified temperatures defaultto TUNIF.

For piping analyses, the PIPE module of PREP7 may be used to generate the input for this element. KEYOPT(4)is used to identify the element type for output labeling and for postprocessing operations.

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamicanalyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in the positiveelement x direction).


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A summary of the element input is given in "PIPE16 Input Summary" (p. 87). A general description of elemeinput is given in Element Input.

PIPE16 Input Summary

Nodes

I, J, K (K, the orientation node, is optional)

Degrees of FreedomUX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants

OD, TKWALL, SIFI, SIFJ, FLEX, DENSFL,DENSIN, TKIN, TKCORR, AREAIN, MWALL, STIFF,SPINSee Table 1: PIPE16 Real Constants (p. 89) for a description of the real constants

Material Properties

EX, ALPX (or CTEX or THSX),

PRXY (or NUXY), DENS, GXY, DAMPSurface Loads

Pressures --

1-PINT, 2-PX, 3-PY, 4-PZ, 5-POUT

Body Loads

Temperatures --

TOUT(I), TIN(I), TOUT(J), TIN(J) if KEYOPT (1) = 0, or TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J) if KEYOPT (1) = 1

Special Features

Stress stiffeningLarge deflectionBirth and death

KEYOPT(1)

Temperatures represent:

0 --

The through-wall gradient

1 --

The diametral gradient

KEYOPT(2)Stress intensification factors:

0 --

Stress intensity factors from SIFI and SIFJ

1 --

Stress intensity factors at node I from tee joint calculation

2 --

Stress intensity factors at node J from tee joint calculation


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3 --

Stress intensity factors at both nodes from tee joint calculation

KEYOPT(4)

Element identification (for output and postprocessing):

0 --

Straight pipe

1 -- Valve

2 --

Reducer

3 --

Flange

4 --

Expansion joint

5 --

Mitered bend

6 -- Tee branch

KEYOPT(5)

PX, PY, and PZ transverse pressures:

0 --

Use only the normal component of pressure

1 --

Use the full pressure (normal and shear components)

KEYOPT(6)

Member force and moment output:

0 --

Do not print member forces or moments

2 --

Print member forces and moments in the element coordinate system

KEYOPT(7)Gyroscopic damping matrix:

0 --

No gyroscopic damping matrix

1 --

Compute gyroscopic damping matrix. Real constant SPIN must be greater than zero. DENSFL andDENSIN must be zero.

Note

The real constant MWALL is not used to compute the gyroscopic damping matrix.

KEYOPT(8)

End cap loads:


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0 --

Internal and external pressures cause loads on end caps

1 --

Internal and external pressures do not cause loads on end caps

Table 1 PIPE16 Real Constants

DescriptionNameNo.Pipe outer diameterOD1

Wall thickness TKWALL2

Stress intensification factor (node I)SIFI3

Stress intensification factor (node J)SIFJ4

Flexibility factorFLEX5

Internal fluid densityDENSFL6

Exterior insulation densityDENSIN7

Insulation thickness TKIN8

Corrosion thickness allowance TKCORR9Insulation surface area (replaces program-calculated value)AREAIN10

Pipe wall mass (replaces program-calculated value)MWALL11

Axial pipe stiffness (replaces program-calculated value)STIFF12

Rotordynamic spin (required if KEYOPT(7) = 1)SPIN13

PIPE16 Output Data



• Additional element output as shown in Table 2: PIPE16 Element Output Definitions (p. 90)


The direct stress (SAXL) includes the internal pressure (closed end) effect. The direct stress does not includthe axial component of the transverse thermal stress (STH). The principal stresses and the stress intensityinclude the shear force stress component, and are based on the stresses at the two extreme points on op-posite sides of the neutral axis. These quantities are computed at the outer surface and might not occur atthe same location around the pipe circumference. Angles listed in the output are measured as shown (θ) inFigure 2 (p. 90). A general description of solution output is given in Solution Output. See the Basic Analysis

Guide for ways to view results.


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Figure 2 PIPE16 Stress Output


A colon (:) in the Name column indicates that the item can be accessed by the Component Name method(ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R columnindicates the availability of the items in the results file.

In either the O or R columns,“Y” indicates that the item is always available, a number refers to a tablefootnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 2 PIPE16 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, JNODES

YYMaterial numberMAT

Y-VolumeVOLU:

6YLocation where results are reportedXC, YC, ZC11Corrosion thickness allowanceCORAL

22 TOUT(I), TIN(I), TOUT(J), TIN(J) TEMP

33 TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J) TEMP

YYPINT, PX, PY, PZ, POUTPRES

YYStress intensification factors at nodes I and JSFACTI, SFACTJ

YYStress due to maximum thermal gradient throughthe wall thickness

STH

Y-Hoop pressure stress for code calculationsSPR2

Y-Moment stress at nodes I and J for code calculationsSMI, SMJY-Direct (axial) stressSDIR

Y-Maximum bending stress at outer surfaceSBEND

Y-Shear stress at outer surface due to torsionST

Y-Shear stress due to shear forceSSF

YYMaximum principal stress, minimum principal stress,maximum stress intensity, maximum equivalent

S:(1MX, 3MN, INT-MX, EQVMX)


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RODefinitionName

stress (over eight points on the outside surface atboth ends of the element)

44Axial, radial, hoop, and shear stressesS:(AXL, RAD, H, XH)

44Maximum principal stress, minimum principal stress,stress intensity, equivalent stress

S:(1, 3, INT, EQV)

44Axial, radial, hoop, and shear strainsEPEL:(AXL, RAD, H,XH)

44Axial, radial, and hoop thermal strainEPTH:(AXL, RAD, H)

Y5Member forces for nodes I and J (in the elementcoordinate system)

MFOR:(X, Y, Z)

Y5Member moments for nodes I and J (in the elementcoordinate system)

MMOM:(X, Y, Z)

1. If the value is greater than 0.

2. If KEYOPT(1) = 0

3. If KEYOPT(1) = 1

4. The item repeats at 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315° at node I, then at node J, all at the outersurface.

5. If KEYOPT(6) = 2


The following tables list output available through the ETABLE command using the Sequence Numbermethod. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and SequenceNumber Table of this manual for more information. The following notation is used in Table 3: PIPE16 Item

and Sequence Numbers (Node I) (p. 91) through Table 5: PIPE16 Item and Sequence Numbers (p. 93):

Nameoutput quantity as defined in the Table 2: PIPE16 Element Output Definitions (p. 90)

Item


E


I, J


Table 3 PIPE16 Item and Sequence Numbers (Node I)


Quant-

ity

Name

Circumferential LocationEItem

315°270°225°180°135°90°45°0°

2925211713951-LSSAXL

30262218141062-LSSRAD

31272319151173-LSSH


PIPE16

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Quant-

ity

Name


315°270°225°180°135°90°45°0°

6258545046423834-LEPELEPELRAD

6359555147433935-LEPELEPELH

6460565248444036-LEPELEPELXH6157534945413733-LEPTHEPTHAXL

6258545046423834-LEPTHEP- THRAD

6359555147433935-LEPTHEPTHH

--------7SMISCMFORX

--------8SMISCMFORY

--------9SMISCMFORZ

--------10SMISCMMOMX

--------11SMISCMMOMY--------12SMISCMMOMZ

--------15SMISCSDIR

--------16SMISCST

7671666156514641-NMISCS1

7873686358534843-NMISCS3

7974696459544944-NMISCSINT

8075706560555045-NMISCSEQV

--------92NMISCSBEND

--------93NMISCSSF-11-10-9-12-LBFE TOUT

-15-14-13-16-LBFE TIN

Table 5 PIPE16 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

17SMISCSTH18SMISCPINT

19SMISCPX

20SMISCPY

21SMISCPZ

22SMISCPOUT

81NMISCSFACTI


PIPE16

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ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

82NMISCSFACTJ

83NMISCSPR2

84NMISCSMI85NMISCSMJ

86NMISCS1MX

87NMISCS3MN

88NMISCSINTMX

89NMISCSEQVMX

PIPE16 Assumptions and Restrictions

• The pipe must not have a zero length or wall thickness. In addition, the OD must not be less than or

equal to zero, the ID must not be less than zero, and the corrosion thickness allowance must be lessthan the wall thickness.

• The element temperatures are assumed to vary linearly along the length.

• The element may be used for both thin and thick-walled situations; however, some of the stress calcu-lations are based on thin-wall theory.

• The pipe element is assumed to have "closed ends" so that the axial pressure effect is included.

• Shear deflection capability is also included in the element formulation.

• Eigenvalues calculated in a gyroscopic modal analysis can be very sensitive to changes in the initialshift value, leading to potential error in either the real or imaginary (or both) parts of the eigenvalues.

PIPE16 Product Restrictions


ANSYS Professional

• The SPIN real constant (R13) is not available.


• The only special features allowed are stress stiffening and large deflections.

• KEYOPT(7) (gyroscopic damping) is not allowed.


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PIPE18

Elastic Curved Pipe


PIPE18 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as ELBOW290.

PIPE18, also known as an elbow element, is a circularly uniaxial element with tension, compression, torsion,and bending capabilities. The element has six degrees of freedom at each node: translations in the nodal xy, and z directions and rotations about the nodal x, y, and z axes.

Options are available to include various flexibility and stress intensification factors in the formulation. Theelement can account for insulation, contained fluid, and a corrosion allowance. See PIPE18 - Elastic Curved

Pipe (p. 203) for more details about this element.

Figure 1 PIPE18 Geometry

PIPE18 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 95). The

element input data include three nodes, the pipe outer diameter, wall thickness, radius of curvature, optionstress intensification and flexibility factors, internal fluid density, exterior insulation density and thickness,corrosion thickness allowance, and the isotropic material properties. The internal fluid and external insulaticonstants are used only to determine the added mass effects for these components.

Although the curved pipe element has only two endpoints (nodes I and J), the third node (K) is required todefine the plane in which the element lies. This node must lie in the plane of the curved pipe and on thecenter-of-curvature side of line I-J. A node point belonging to another element (such as the other node of




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a connecting straight pipe element) may be used. Input and output locations around the pipe circumferenceidentified as being at 0° are located along the element y-axis, and similarly 90° is along the element z-axis.

Only the lumped mass matrix is available.

The flexibility and stress intensification factors included in the element are calculated as follows:

ANSYS Flexibility Factor = 1.65/(h(1 + PrXk /tE)) or 1.0 (whichever is greater) (used if KEYOPT(3)

= 0 or 1 and FLXI not input)

Karman Flexibility Factor = (10 + 12h2)/(1 + 12h2) (used if KEYOPT(3) = 2 and FLXI not input)

User Defined Flexibility Factors = FLXI (in-plane) and FLXO (out-of-plane) (may be input asany positive value)

FLXO defaults to FLXI for all cases.

Stress Intensification Factor = 0.9/h2/3 or 1.0 (whichever is greater) (used for SIFI or SIFJ if factor not input or if input less than 1.0 (must be positive))

where:

h = tR/r2

t = thicknessR = radius of curvaturer = average radiusE = modulus of elasticity

Xk = 6 (r/t)4/3 (R/r)1/3 if KEYOPT(3) = 1 and R/r ≥ 1.7, otherwise Xk = 0

P = Pi - Po if Pi - Po > 0, otherwise P = 0, P i = internal pressure, Po = external pressure

Do not use KEYOPT(3) = 1 if the included angle of the complete elbow is less than 360/(π(R/r)) degrees.

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 95). Internal pressure (PINT) and externalpressure (POUT) are input as positive values. The internal and external pressure loads are designed for closed-loop static pressure environments and therefore include pressure loads on fictitious "end caps" so that thepressure loads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needs to berepresented, such as a pipe venting to a lower pressure area or the internal flow is past a constriction in thepipe, these end cap loads may need to be modified by applying a nodal force normal to the cross-sectionof the pipe with the magnitude representing the change in pressure. Alternatively, the precomputed endcap loads can be removed using KEYOPT(8) = 1 and the appropriate end cap loads added by the user. Notethat when using KEYOPT(8) = 1, the pressure load will be acting on only the wall of the elbow element sothat the total pressure load will not be self-equilibrating. The transverse pressures (PX, PY, and PZ) mayrepresent wind or drag loads (per unit length of the pipe) and are defined in the global Cartesian directions.Positive transverse pressures act in the positive coordinate directions. Tapered pressures are not recognized.Only constant pressures are supported for this element.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradients ordiametral gradients (KEYOPT(1)). The average wall temperature at θ = 0° is computed as 2 * TAVG - T(180)and the average wall temperature at θ = -90° is computed as 2 * TAVG - T(90). The element temperaturesare assumed to be linear along the length. The first temperature at node I (TOUT(I) or TAVG(I)) defaults to TUNIF. If all temperatures after the first are unspecified, they default to the first. If all temperatures at node


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I are input, and all temperatures at node J are unspecified, the node J temperatures default to the corres-ponding node I temperatures. For any other pattern of input temperatures, unspecified temperatures defauto TUNIF.

For piping analyses, the PIPE module of PREP7 may be used to generate the input for this element.

A summary of the element input is given below. A general description of element input is given in ElemenInput.

PIPE18 Input Summary

Nodes

I, J, K - where node K is in the plane of the elbow, on the center of curvature side of line I-J

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants

OD, TKWALL, RADCUR, SIFI, SIFJ, FLXI,DENSFL, DENSIN, TKIN, TKCORR, (Blank), FLXO

See Table 1: PIPE18 Real Constants (p. 98) for a description of the real constantsMaterial Properties

EX, ALPX (or CTEX or THSX), PRXY (or NUXY), DENS, GXY, DAMP

Surface Loads

Pressures --1-PINT, 2-PX, 3-PY, 4-PZ, 5-POUT

Body Loads

Temperatures --

TOUT(I), TIN(I), TOUT(J), TIN(J) if KEYOPT (1) = 0, or

TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J) if KEYOPT (1) = 1

Special Features

Large deflectionBirth and death

KEYOPT(1)

Temperatures represent:

0 --

The through-wall gradient

1 --

The diametral gradient

KEYOPT(3)Flex factor (if FLEX is not specified):

0 --

Use ANSYS flexibility factor (without pressure term)

1 --

Use ANSYS flexibility factor (with pressure term)


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2 --

Use KARMAN flexibility factor

KEYOPT(6)

Member force and moment output:

0 --

Do not print member forces or moments

2 -- Print member forces and moments in the element coordinate system

KEYOPT(8)

End cap loads:

0 --

Internal and external pressures cause loads on end caps

1 --

Internal and external pressures do not cause loads on end caps

Table 1 PIPE18 Real Constants

DescriptionNameNo.

Pipe outer diameterOD1

Wall thickness TKWALL2

Radius of curvatureRADCUR3

Stress intensification factor (node I)SIFI4

Stress intensification factor (node J)SIFJ5

Flexibility factor (in-plane)FLXI6

Internal fluid densityDENSFL7

Exterior insulation densityDENSIN8

Insulation thickness TKIN9

Corrosion thickness allowance TKCORR10

--(Blank)11

Flexibility factor (out-of-plane). FLXO defaults to FLXI in all cases.FLXO12

PIPE18 Output Data



• Additional element output as shown in Table 2: PIPE18 Element Output Definitions (p. 99)


The stresses are computed with the outer diameter of the pipe reduced by twice the corrosion thicknessallowance. The direct stress includes the internal pressure (closed end) effect. Also printed for each end arethe maximum and minimum principal stresses and the stress intensity. These quantities are computed atthe outer surface and may not occur at the same location around the pipe circumference. Some of thesestresses are shown in Figure 2 (p. 99). The direct stress does not include the axial component of the transverse


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RODefinitionName

Y-Hoop pressure stress for code calculationsSPR2

Y-Moment stress at nodes I and J for code calculationsSMI, SMJ

Y-Direct (axial) stressSDIR

Y-Maximum bending stress at outer surfaceSBEND

Y-Shear stress at outer surface due to torsionST

Y-Shear stress due to shear forceSSF

YYMaximum principal stress, minimum principal stress,maximum stress intensity, maximum equivalent

S(1MX, 3MN,INTMX,EQVMX)


55Maximum principal stress, minimum principal stress,stress intensity, equivalent stress

S(1, 3, INT, EQV)

55Axial, radial, hoop, and shear stressesS(AXL, RAD, H, XH)

55Axial, radial, hoop, and shear strainsEPEL(AXL, RAD, H,XH)

55Axial, radial, and hoop thermal strainEPTH(AXL, RAD, H)

1. If the value is greater than 0.

2. If KEYOPT(1) = 0

3. If KEYOPT(1) = 1

4. If KEYOPT(6) = 2

5. The item repeats at 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315° at node I, then at node J (all at the outersurface)


The following tables list output available through the ETABLE command using the Sequence Numbermethod. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and SequenceNumber Table of this manual for more information. The following notation is used in Table 3: PIPE18 Item

and Sequence Numbers (Node I) (p. 101) through Table 5: PIPE18 Item and Sequence Numbers (p. 103):

Name

output quantity as defined in the Table 2: PIPE18 Element Output Definitions (p. 99)

Item


E



PIPE18

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I,J


Table 3 PIPE18 Item and Sequence Numbers (Node I)


Quant-

ity

Name


315°270°225°180°135°90°45°0°

2925211713951-LSSAXL

30262218141062-LSSRAD

31272319151173-LSSH

32282420161284-LSSXH

2925211713951-LEPELEPELAXL


31272319151173-LEPELEPELH

32282420161284-LEPELEPELXH

2925211713951-LEPTHEPTHAXL

30262218141062-LEPTHEP- THRAD

31272319151173-LEPTHEPTHH

36312621161161-NMISCS1

38332823181383-NMISCS3

39342924191494-NMISCSINT

403530252015105-NMISCSEQV


--------92NMISCSSF

--------1SMISCMFORX

--------2SMISCMFORY

--------3SMISCMFORZ

--------4SMISCMMOMX

--------5SMISCMMOMY

--------6SMISCMMOMZ

--------13SMISCSDIR

--------14SMISCST

-3-2-1-4-LBFE TOUT


PIPE18

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Quant-

ity

Name


315°270°225°180°135°90°45°0°

-7-6-5-8-LBFE TIN

Table 4 PIPE18 Item and Sequence Numbers (Node J)


Quant-

ity

Name


315°270°225°180°135°90°45°0°

6157534945413733-LSSAXL

6258545046423834-LSSRAD

6359555147433935-LSSH

6460565248444036-LSSXH

6157534945413733-LEPELEPELAXL


6359555147433935-LEPELEPELH

6460565248444036-LEPELEPELXH

6157534945413733-LEPTHEPTHAXL

6258545046423834-LEPTHEP- THRAD

6359555147433935-LEPTHEPTHH

7671666156514641-NMISCS1

7873686358534843-NMISCS3

7974696459544944-NMISCSINT

8075706560555045-NMISCSEQV


--------94NMISCSSF

--------7SMISCMFORX

--------8SMISCMFORY

--------9SMISCMFORZ


--------11SMISCMMOMY

--------12SMISCMMOMZ

--------15SMISCSDIR

--------16SMISCST

-11-10-9-12-LBFE TOUT


PIPE18

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315°270°225°180°135°90°45°0°

-15-14-13-16-LBFE TIN

Table 5 PIPE18 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

81NMISCSFACTI

82NMISCSFACTJ

83NMISCSPR2

84NMISCSMI

85NMISCSMJ

86NMISCS1MX

87NMISCS3MN

88NMISCSINTMX

89NMISCSEQVMX

90NMISCFFACT

17SMISCSTH

18SMISCPINT

19SMISCPX

20SMISCPY21SMISCPZ

22SMISCPOUT


• The curved pipe must not have a zero length or wall thickness. In addition, the OD must not be lessthan or equal to zero and the ID must not be less than zero.

• The corrosion allowance must be less than the wall thickness.

• The element is limited to having an axis with a single curvature and a subtended angle of 0° < θ ≤ 90

• Shear deflection capability is also included in the element formulation.

• The elbow is assumed to have "closed ends" so that the axial pressure effect is included.

• When used in a large deflection analysis, the location of the third node (K) is used only to initially oriethe element.

• The element temperatures are assumed to be linear along the length. The average wall temperatureat θ = 0° is computed as 2 * TAVG - T(180) and the average wall temperature at θ = -90° is computedas 2 * TAVG - T(90).


PIPE18

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• Stress intensification factors input with values less than 1.0 are set to 1.0.

• The element formulation is based upon thin-walled theory. The elbow should have a large radius-to-thickness ratio since the integration points are assumed to be located at the midthickness of the wall.

• Only the lumped mass matrix is available.



ANSYS Professional


• The only special feature allowed is large deflection.


PIPE18

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Items in parentheses refer to data tables associated with the TB command.

KEYOPT(1)

Element coordinate system defined:

0 --

Element coordinate system is parallel to the global coordinate system

1 --

Element coordinate system is based on the element I-J sideKEYOPT(2)

Extra displacement shapes:

0 --

Include extra displacement shapes

1 --Suppress extra displacement shapes

KEYOPT(3)

Element behavior:

0 --

Plane stress

1 --

Axisymmetric

2 --

Plane strain (Z strain = 0.0)

3 --

Plane stress with thickness input

KEYOPT(5)

Extra stress output:

0 -- Basic element solution

1 --

Repeat basic solution for all integration points

2 --

Nodal stress solution

KEYOPT(6)

Extra surface output:

0 --

Basic element solution

1 --Surface solution for face I-J also.

2 --Surface solution for both faces I-J and K-L also. (Surface solution available for linear materials only)

3 --

Nonlinear solution at each integration point also.


PLANE42

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4 --

Surface solution for faces with nonzero pressure

PLANE42 Output Data



• Additional element output as shown in Table 1: PLANE42 Element Output Definitions (p. 108)


The element stress directions are parallel to the element coordinate system. Surface stresses are availableon any face. Surface stresses on face IJ, for example, are defined parallel and perpendicular to the IJ lineand along the Z axis for a plane analysis or in the hoop direction for an axisymmetric analysis. A generaldescription of solution output is given in Solution Output. See the Basic Analysis Guide for ways to viewresults.

Figure 2 PLANE42 Stress Output

Stress directions shown are for KEYOPT(1) = 0




Table 1 PLANE42 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, J, K, LNODES


YYAverage thickness THICK

YYVolumeVOLU:


PLANE42


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Quant-

ity

Name

LK JIEItem

191494-NMISCS:INT

2015105-NMISCS:EQV

24232221-NMISCFLUEN----25NMISC THICK

See Surface Solution of this manual for the item and sequence numbers for surface output for the ETABLE

command.

PLANE42 Assumptions and Restrictions

• The area of the element must be nonzero.

• The element must lie in a global X-Y plane as shown in Figure 1 (p. 105) and the Y-axis must be the axof symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quad

• A triangular element may be formed by defining duplicate K and L node numbers (see Triangle, Prismand Tetrahedral Elements).

• The extra shapes are automatically deleted for triangular elements so that a constant strain elementresults.

• Surface stress printout is valid only if the conditions described in Element Solution are met.

PLANE42 Product Restrictions


ANSYS Professional


• Fluence body loads are not applicable.

• The only special feature allowed is stress stiffening.

• KEYOPT(6) = 3 is not applicable.


PLANE42

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• Additional element output as shown in Table 1: SOLID45 Element Output Definitions (p. 117)

Several items are illustrated in Figure 2 (p. 117). The element stress directions are parallel to the element coordinate system. The surface stress outputs are in the surface coordinate systems and are available for anyface (KEYOPT(6)). The coordinate systems for faces IJNM and KLPO are shown in Figure 1 (p. 113). The othersurface coordinate systems follow similar orientations as indicated by the pressure face node description.Surface stress printout is valid only if the conditions described in Element Solution are met. A general de-scription of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view result

Figure 2 SOLID45 Stress Output

Stress directions shown are for KEYOPT(4) = 0

When KEYOPT(2) = 1 (the element is using uniform reduced integration), all the outputs for the element

integration points are output in the same style as the full integration outputs. The number of points for fuintegration is used for consistency of output within the same element type.




Table 1 SOLID45 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, J, K, L, M, N, O, PNODES


YYVolumeVOLU:



SOLID45



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RODefinitionName

YYPressures P1 at nodes J, I, L, K; P2 at I, J, N, M; P3 atJ, K, O, N; P4 at K, L, P, O; P5 at L, I, M, P; P6 at M, N,O, P

PRES

YY Temperatures T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P) TEMP

YYFluences FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O),

FL(P)

FLUEN

YYStressesS:X, Y, Z, XY, YZ, XZ

YYPrincipal stressesS:1, 2, 3

YYStress intensityS:INT

YYEquivalent stressS:EQV

YYElastic strainsEPEL:X, Y, Z, XY, YZ,XZ

-YPrincipal elastic strainsEPEL:1, 2, 3

YYEquivalent elastic strain [4]EPEL:EQV

5-Average thermal strainsEPTH:X, Y, Z, XY, YZ,XZ

5-Equivalent thermal strain [4]EPTH:EQV

11Average plastic strainsEPPL:X, Y, Z, XY, YZ,XZ

11Equivalent plastic strain [4]EPPL:EQV

11Average creep strainsEPCR:X, Y, Z, XY, YZ,XZ

11Equivalent creep strain [4]EPCR:EQV

11Average swelling strainEPSW:

11Average equivalent plastic strainNL:EPEQ

11Ratio of trial stress to stress on yield surfaceNL:SRAT

11Average equivalent stress from stress-strain curveNL:SEPL

1Hydrostatic pressureNL:HPRES

22Face labelFACE

22Face areaAREA

22Surface average temperature TEMP

22Surface elastic strains (X ,Y, XY)EPEL

22Surface pressurePRESS

22Surface stresses (X-axis parallel to line defined byfirst two nodes which define the face)

S(X, Y, XY)

22Surface principal stressesS(1, 2, 3)

22Surface stress intensitySINT

22Surface equivalent stressSEQV

Y-Integration point locationsLOCI:X, Y, Z


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1. Nonlinear solution, output only if the element has a nonlinear material

2. Surface output (if KEYOPT(6) is 1, 2, or 4)

3. Available only at centroid as a *GET item

4. The equivalent strains use an effective Poisson's ratio: for elastic and thermal this value is set by theuser (MP,PRXY); for plastic and creep this value is set at 0.5.

5. Output only if element has a thermal load.

Table 2 SOLID45 Miscellaneous Element Output

RONames of Items OutputDescription

-1EPPL, EPEQ, SRAT, SEPL,HPRES, EPCR, EPSW

Nonlinear Integration Pt.Solution

-2 TEMP, S(X, Y, Z, XY, YZ, XZ),SINT, SEQV, EPEL

Integration Point StressSolution

-3 TEMP, S(X, Y, Z, XY, YZ, XZ),SINT, SEQV, EPEL

Nodal Stress Solution

1. Output at each of eight integration points, if the element has a nonlinear material and KEYOPT(6) = 3

2. Output at each integration point, if KEYOPT(5) = 1

3. Output at each node, if KEYOPT(5) = 2

Table 3: SOLID45 Item and Sequence Numbers (p. 119) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide an The Item and Sequence Number Table of this manual for more information. The following notation is usedin Table 3: SOLID45 Item and Sequence Numbers (p. 119):

Name

output quantity as defined in the Table 1: SOLID45 Element Output Definitions (p. 117)

Item


I,J,...,Psequence number for data at nodes I,J,...,P

Table 3 SOLID45 Item and Sequence Numbers


Quant-

ity

Name

PONMLK JIItem

----3412SMISCP1

--78--65SMISCP2

-1112--109-SMISCP3

1516--1413--SMISCP4

20--1917--18SMISCP5

24232221----SMISCP6


SOLID45

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Quant-

ity

Name

PONMLK JIItem

36312621161161NMISCS:1

37322722171272NMISCS:2

38332823181383NMISCS:339342924191494NMISCS:INT

403530252015105NMISCS:EQV

4847464544434241NMISCFLUEN

See Surface Solution in this manual for the item and sequence numbers for surface output for the ETABLE

command.

SOLID45 Assumptions and Restrictions

• Zero volume elements are not allowed.

• Elements may be numbered either as shown in Figure 1 (p. 113) or may have the planes IJKL and MNOPinterchanged.

• The element may not be twisted such that the element has two separate volumes. This occurs mostfrequently when the elements are not numbered properly.

• All elements must have eight nodes.

– A prism-shaped element may be formed by defining duplicate K and L and duplicate O and P nodenumbers (see Triangle, Prism, and Tetrahedral Elements).

– A tetrahedron shape is also available. The extra shapes are automatically deleted for tetrahedronelements.

SOLID45 Product Restrictions


ANSYS Professional


• Fluence body loads are not applicable.




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The normal stiffness, KN, should be based upon the stiffness of the surfaces in contact. See NonlinearStructural Analysis in the Structural Analysis Guide for guidelines on choosing a value for KN. In some cases(such as initial interference analyses, nonconvergence, or over penetration), it may be useful to change theKN value between load steps or in a restart in order to obtain an accurate, converged solution. The stickingstiffness, KS, represents the stiffness in the tangential direction when elastic Coulomb friction is selected (µ> 0.0 and KEYOPT(1) = 0). The coefficient of friction µ is input as material property MU and is evaluated atthe average of the two node temperatures. Stiffnesses may also be computed from the maximum expectedforce divided by the maximum allowable surface displacement. KS defaults to KN.

The initial gap defines the gap size (if positive) or the displacement interference (if negative). This input isthe opposite of that used for CONTAC12 (described in the Feature Archive). If you do not specify the gapdirection (by means of real constants NX, NY, and NZ), an interference causes the nodes to separate. Thegap size may be input as a real constant (GAP) or automatically calculated from the input node locations(as the distance between node I and node J) if KEYOPT(4) = 1. Interference must be input as a real constant.Stiffness is associated with a zero or negative gap. The initial element status (START) is used to define the"previous" condition of the interface to be used at the start of the first substep. This input is used to overridethe condition implied by the interference specification and is useful in anticipating the final interface config-uration and in reducing the number of iterations required for convergence.

You can specify the gap direction by means of real constants NX, NY, and NZ (the global Cartesian X, Y, andZ components of the gap direction vector). If you do not specify the gap direction, the program will calculatethe direction based on the initial positions of the I and J nodes, such that a positive normal displacement(in the element coordinate system) of node J relative to node I tends to open the gap. You should alwaysspecify the gap direction if nodes I and J have the same initial coordinates, if the model has an initial inter-ference condition in which the underlying elements' geometry overlaps, or if the initial open gap distanceis very small. If the gap is initially geometrically open, the correct normal (NX, NY, NZ) usually points fromnode I toward node J.

The only material property used is the interface coefficient of friction µ. A zero value should be used forfrictionless surfaces. Temperatures may be specified at the element nodes (for material property evaluationonly). The node I temperature T(I) defaults to TUNIF. The node J temperature defaults to T(I).

The force deflection relationships for the interface element can be separated into the normal and tangential(sliding) directions as shown in Figure 2 (p. 125). The element condition at the beginning of the first substepis determined from the START parameter. If the interface is closed and sticking, KN is used in the gap resistanceand KS is used for sticking resistance. If the interface is closed but sliding, KN is used in the gap resistanceand the constant friction force µFN is used for the sliding resistance.

In the normal direction, when the normal force (FN) is negative, the interface remains in contact and respondsas a linear spring. As the normal force becomes positive, contact is broken and no force is transmitted.

KEYOPT(3) can be used to specify a "weak spring" across an open interface, which is useful for preventingrigid body motion that could occur in a static analysis. The weak spring stiffness is computed by multiplying

the normal stiffness KN by a reduction factor. The default reduction factor of 1E-6 can be overridden withreal constant REDFACT.

This "weak spring" capability is not analogous to overlaying an actual spring element (such as COMBIN14)with a low stiffness value. The REDFACT capability will not limit gap separation when a tensile force is applied.

In the tangential direction, for FN < 0 and the absolute value of the tangential force (FS) less than µ|FN|, theinterface sticks and responds as a linear spring. For FN < 0 and FS = µ|FN|, sliding occurs. If contact is broken,FS = 0.


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KEYOPT(4)

Basis for gap size:

0 --

Gap size based on gap real constant

1 --

Gap size determined from initial node locations (ignore gap real constant)

KEYOPT(7)Element-level time incrementation control. Note that this option should be activated first at the procedurelevel if SOLCONTROL is ON. SOLCONTROL,ON,ON is the most frequent usage with this element. If SOLCONTROL,ON,OFF, this keyoption is not activated.

0 --

Change in contact predictions made to achieve the minimum time/load increment whenever achange in contact status occurs

1 --Change in contact predictions made to maintain a reasonable time/load increment (recommended)

Table 1 CONTAC52 Real Constants

DescriptionNameNo.

Normal stiffnessKN1

Initial gap size; a negative value assumes an initial interferencecondition.

GAP2

Initial condition:

START3

If = 0.0 or blank, initial status of element is determined fromgap inputIf = 1.0, gap is initially closed and not sliding (if MU ≠ 0.0), orsliding (if MU = 0.0)

If = 2.0, gap is initially closed and slidingIf = 3.0, gap initially open

Sticking stiffnessKS4

Default reduction factor 1E-6REDFACT5

Defined gap normal - X componentNX6

Defined gap normal - Y componentNY7

Defined gap normal - Z componentNZ8

CONTAC52 Output Data



• Additional element output as shown in Table 2: CONTAC52 Element Output Definitions (p. 125).

Force-deflection curves are illustrated in Figure 2 (p. 125).

The value of USEP is determined from the normal displacement (un) (in the element x-direction) between

the interface nodes at the end of a substep, that is: USEP = (u n)J - (un)I + GAP. This value is used in determ-


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RODefinitionName


YY T(I), T(J) TEMP

YYGap sizeUSEP

YYNormal force (along I-J line)FN

11Element statusSTAT

YYElement orientation anglesALPHA, BETA

22Coefficient of frictionMU

22Displacement (node J - node I) in element y and z dir-ections

UT(Y, Z)

22 Tangential (friction) force (vector sum)FS

22Principal angle of friction force in element y-z planeANGLE

1. If the value of STAT is:

1 - Contact, no sliding

2 - Sliding contact

3 - Gap open

2. If MU > 0.0


Table 3: CONTAC52 Item and Sequence Numbers (p. 126) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table of this manual for more information. The following notation is usedin Table 3: CONTAC52 Item and Sequence Numbers (p. 126):

Name

output quantity as defined in the Table 2: CONTAC52 Element Output Definitions (p. 125)

Item


E


Table 3 CONTAC52 Item and Sequence Numbers

ETABLE and

ESOL Command

Input

Output

Quant-ity

Name EItem

1SMISCFN

2SMISCFS

1NMISCSTAT

2NMISCOLDST


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θd(j) = Direction of drift current at location j (Degrees) (see Figure 2 (p. 130))

Re(k) = Twelve Reynolds number values (if used, all 12 must be input in ascending order)CD(k) = Twelve corresponding normal drag coefficients (if used, all 12 must be input)CT(k) = Twelve corresponding tangential drag coefficients (if used, all 12 must be input) T(j) = Temperature at Z(j) water depth (Degrees)

A(i) = Wave peak-to-trough height (0.0 ≤ A(i) < DEPTH) (Length) (if KWAVE = 2, A(1) is entire waveheight and A(2) through A(5) are not used)

τ(i) = Wave period (τ(i) > 0.0) (Time/Cycle)φ(i) = Adjustment for phase shift (Degrees)

WL(i) = Wave length (0.0 ≤ WL(i) < 1000.0*DEPTH) (Length)

(defaultWL i

ACELZ i DEPTH

WL i( )

( ( ))tanh

( )=

τπ

π2

2

2

)Use 0.0 with Stokes theory (KWAVE = 2).

Table 2 PIPE59 Water Motion Table

MeaningConstant

θwDENSWDEPTHKCRCKWAVE1-5

θd(2)W(2)Z(2)θd(1)W(1)Z(1)7-12

θd(4)W(4)Z(4)θd(3)W(3)Z(3)13-18

θd(6)W(6)Z(6)θd(5)W(5)Z(5)19-24

θd(8)W(8)Z(8)θd(7)W(7)Z(7)25-30

Re(6)Re(5)Re(4)Re(3)Re(2)Re(1)31-36

Re(12)Re(11)Re(10)Re(9)Re(8)Re(7)37-42

CD(6)CD(5)CD(4)CD(3)CD(2)CD(1)43-48

CD(12)CD(11)CD(10)CD(9)CD(8)CD(7)49-54

CT(6)CT(5)CT(4)CT(3)CT(2)CT(1)55-60CT(12)CT(11)CT(10)CT(9)CT(8)CT(7)61-66

T(6) T(5) T(4) T(3) T(2) T(1)67-72

T(8) T(7)73-74

For KWAVE = 0, 1, or 2WL(1)φ(1)τ(1)A(1)79-82

WL(2)φ(2)τ(2)A(2)85-88For KWAVE = 2, useonly A(1), τ(1), φ(1)etc.etc.

WL(20)φ(20)τ(20)A(20)193-196

For KWAVE = 3 (See for defini-tions other than φ(1))

φ(1)Not UsedX(1)/(H*T*G)79-81

DPT/LOX(2)/(H*T*G)85-86

L/LOX(3)/(H*T*G)91-92

H/DPTX(4)/(H*T*G)97-98

Ψ /(G*H*T)X(5)/(H*T*G)103-104

X(6)/(H*T*G)109

etc.etc.


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MeaningConstant

X(20)/(H*T*G)193

The distributed load applied to the pipe by the hydrodynamic effects is computed from a generalized Morison's equation. This equation includes the coefficient of normal drag (CD) (perpendicular to the element

axis) and the coefficient of tangential drag (C T), both of which are a functions of Reynolds numbers (Re).

These values are input as shown in Table 1: PIPE59 Real Constants (p. 132) and Table 2: PIPE59 Water Motion

Table (p. 134).

The Reynolds numbers are determined from the normal and tangential relative particle velocities, the pipegeometry, the water density, and the viscosity (input as VISC). The relative particle velocities include theeffects of water motion due to waves and current, as well as motion of the pipe itself. If both Re(1) andCD(1) are positive, the value of CD from the real constant table (Table 1: PIPE59 Real Constants (p. 132)) is ign

and a log-log table based on Constants 31 through 54 of the water motion table (Table 2: PIPE59 Water Mo

Table (p. 134)) is used to determine CD. If this capability is to be used, the viscosity, Re, and CD constants

must be input and none may be less than or equal to zero.

Similarly, if both Re(1) and CT(1) are positive, the value of C T from the real constant table (Table 1: PIPE59

Real Constants (p. 132)) is ignored, and a log-log table based on Constants 31 through 42 and 55 through 6of the water motion table (Table 2: PIPE59 Water Motion Table (p. 134)) is used to determine C T. If this capab

ility is to be used, the viscosity, Re, and C T constants must be input and none may be less than or equal to

zero.

Various wave theories may be selected with the KWAVE constant of the water motion table ( Table 2: PIPE59

Water Motion Table (p. 134)). These are:

• Small Amplitude Wave Theory with empirical modification of depth decay function (KWAVE = 0)

• Small Amplitude Airy Wave Theory without modifications (KWAVE = 1)

• Stokes Fifth Order Wave Theory (KWAVE = 2)

• Stream Function Wave Theory (KWAVE = 3).

The wave loadings can be altered (KEYOPT(5)) so that horizontal position has no effect on the wave-induceforces.

Wave loading depends on the acceleration due to gravity (ACELZ), and it may not change between substepor load steps. Therefore, when performing an analysis using load steps with multiple substeps, the gravitymay only be "stepped on" [KBC,1] and not ramped.

With the stream function wave theory (KWAVE = 3), the wave is described by alternate Constants 79 throug193 as shown in Table 2: PIPE59 Water Motion Table (p. 134). The definitions of the constants correspond exato those given in the tables in for the forty cases of ratio of wave height and water depth to the deep wa

wave length. The other wave-related constants that the user inputs directly are the water density (DENSW)water depth (DEPTH), wave direction (Φ), and acceleration due to gravity (ACELZ). The wave height, length,and period are inferred from the tables. The user should verify the input by comparing the interpreted resu(the columns headed DIMENSIONLESS under the STREAM FUNCTION INPUT VALUES printout) with the datapresented in the tables. Note that this wave theory uses the current value defined for time [TIME] (whichdefaults to 1.0 for the first load step).


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Several adjustments to the current profile are available with the KCRC constant of the water motion tableas shown in Figure 3 (p. 136). The adjustments are usually used only when the wave amplitude is large relativeto the water depth, such that there is significant wave/current interaction. Options include

1. use the current profile (as input) for wave locations below the mean water level and the top currentprofile value for wave locations above the mean water level (KCRC = 0)

2. "stretch" (or compress) the current profile to the top of the wave (KCRC = 1)

3. same as (2) but also adjust the current profile horizontally such that total flow continuity is maintainedwith the input profile (KCRC = 2) (all current directions (θ(j)) must be the same for this option).

Figure 3 PIPE59 Velocity Profiles for Wave-current Interactions

Horizontal arrows represent

input velocities

Mean Water Surface

Mud Line

Constant (KCRC = 0)

Stretch (KCRC = 1)

Continuity (KCRC = 2)

Water Surface

Z

Nonlinear Stretch (KCRC = 3)

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 129). Internal pressure (PINT) and externalpressure (POUT) are input as positive values. These pressures are in addition to the linearly varying pressureof the fluids on the inside and outside of the pipe. In handling the pressures, each element is assumed tobe capped (that is, have closed ends). The internal and external pressure loads are designed for closed-loopstatic pressure environments and therefore include pressure loads on fictitious "end caps" so that the pressureloads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needs to be represented,such as a pipe venting to a lower pressure area or the internal flow is past a constriction in the pipe, theseend cap loads may need to be modified by applying a nodal force normal to the cross-section of the pipe

with the magnitude representing the change in pressure. Alternatively, the precomputed end cap loads canbe removed using KEYOPT(8) = 1 and the appropriate end cap loads added by the user. The transversepressures (PX, PY, and PZ) may represent wind or drag loads (per unit length of the pipe) and are definedin the global Cartesian directions. Positive transverse pressures act in the positive coordinate directions. Thenormal component or the projected full pressure may be used (KEYOPT(9)). See the Theory Reference for the

Mechanical APDL and Mechanical Applications for more details.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradients ordiametral gradients (KEYOPT(3)). Diametral gradients are not valid for the cable option. The average wall


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Figure 4 PIPE59 Stress Output

J

SDIR

SBEND

SAXL

TorsionalMoment

ShearForce

SH

STJ

x x




Table 3 PIPE59 Element Output Definitions

RODefinitionName

YYElement numberEL

YYNodes - I, JNODES


Y-VolumeVOLU:

9-Location where results are reportedXC, YC, ZC-YLengthLEN

YYPressures PINTE (average effective internal pressure),PX, PY, PZ, POUTE (average effective external pres-sure)

PRES

YYStress due to maximum thermal gradient throughthe wall thickness

STH

1-Hoop pressure stress for code calculationsSPR2

1-Moment stress at nodes I and J for code calculationsSMI, SMJ

1-Direct (axial) stressSDIR

1-Maximum bending stress at outer surfaceSBEND

1-Shear stress at outer surface due to torsionST

1-Shear stress due to shear forceSSF

11Maximum principal stress, minimum principal stress,maximum stress intensity, maximum equivalent

S(1MX, 3MN, INT-MX, EQVMX)



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Quant-

ity

Name


315°270°225°180°135°90°45°0°

6359555147433935-LEPTHEPTHH

--------7SMISCMFORX

--------8SMISCMFORY--------9SMISCMFORZ


--------11SMISCMMOMY

--------12SMISCMMOMZ

--------15SMISCSDIR

--------16SMISCST

7671666156514641-NMISCS1

7873686358534843-NMISCS3

7974696459544944-NMISCSINT8075706560555045-NMISCSEQV


--------91NMISCSSF

-11-10-9-12-LBFE TOUT

-15-14-13-16-LBFE TIN

Table 6 PIPE59 Item and Sequence Numbers (Pipe Options)

ETABLE and

ESOL CommandInput

Output

Quant-ity

Name EItem

17SMISCSTH

18SMISCPINTE

19SMISCPX

20SMISCPY

21SMISCPZ

22SMISCPOUTE

81NMISCSPR282NMISCSMI

83NMISCSMJ

84NMISCS1MX

85NMISCS3MN

86NMISCSINTMX


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ETABLE and

ESOL Command

Input

Output

Quant-

ity

Name EItem

87NMISCSEQVMX

Table 7 PIPE59 Item and Sequence Numbers (Cable Option)

ETABLE and ESOL Command In-

putOutput

Quant-

ity

NameNode

J

Node

I

EItem

41LSSAXL

52LSSRAD

63LSSH

41LEPELEPELAXL

52LEPELEPELRAD63LEPELEPELH

41LEPTHEPTHAXL

91LBFE TOUT

135LBFE TIN

94NMISCSINT

105NMISCSEQV

61SMISCFAXL

13SMISCSTH

14SMISCPINTE15SMISCPX

16SMISCPY

17SMISCPZ

18SMISCPOUTE

Table 8: PIPE59 Item and Sequence Numbers (Additional Output) (p. 143) lists additional print and post data fioutput available through the ETABLE command if KEYOPT(7) = 1.

Table 8 PIPE59 Item and Sequence Numbers (Additional Output)

ETABLE and ESOL Command InputOutput Quant-

ity Name E- Second Integ-

ration Point

E- First Integra-

tion Point

Item

N + 31, N + 32,N + 33

N + 1, N + 2, N+ 3

NMISCGLOBAL CO-ORD

N + 34N + 4NMISCVR

N + 35N + 5NMISCVZ


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ETABLE and ESOL Command InputOutput Quant-

ity Name E- Second Integ-

ration Point

E- First Integra-

tion Point

Item

N + 36N + 6NMISCAR

N + 37N + 7NMISCAZ

N + 38N + 8NMISCPHDY

N + 39N + 9NMISCETA

N + 40N + 10NMISC TFLUID

N + 41N + 11NMISCVISC

N + 42N + 12NMISCREN

N + 43N + 13NMISCRET

N + 44N + 14NMISCCT

N + 45N + 15NMISCCTW

N + 46N + 16NMISCURT

N + 47N + 17NMISCFX

N + 48N + 18NMISCCD

N + 49N + 19NMISCCDW

N + 50, N + 51N + 20, N + 21NMISCURN

N + 52N + 22NMISCABURN

N + 53N + 23NMISCFY

N + 54N + 24NMISCCM

N + 55N + 25NMISCCMW

N + 56, N + 57N + 26, N + 27NMISCAN

N + 58N + 28NMISCFZN + 59N + 29NMISCARGU

Note

For the pipe option (KEYOPT(1) = 0 or 2): N = 99. For the cable option (KEYOPT(1) = 1): N = 10.

Material Properties -- WATER Specifications

TB,WATER (water motion table data for PIPE59)

NTEMP :Not used.

NPTS :

Not used.

TBOPT :

Not used.


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• The pipe must not have a zero length. In addition, the O.D. must not be less than or equal to zero andthe I.D. must not be less than zero.

• Elements input at or near the water surface should be small in length relative to the wave length.

• Neither end of the element may be input below the mud line (ocean floor). Integration points that mobelow the mud line are presumed to have no hydrodynamic forces acting on them.

• If the element is used out of water, the water motion table (Table 2: PIPE59 Water Motion Table (p. 134))need not be included.

• The element should also be used with caution in the reduced transient dynamic analysis since thisanalysis type ignores the element load vector. Fluid damping, if any, should be handled via the hydro-dynamic load vector rather than α (mass matrix) damping.

• When performing a transient analysis, the solution may be unstable with small time steps due to thenature of Morrison's equation.

• The applied thermal gradient is assumed to vary linearly along the length of the element.

• The same water motion table (Table 2: PIPE59 Water Motion Table (p. 134)) should not be used for differ

wave theories in the same problem.• The lumped mass matrix formulation [LUMPM,ON] is not allowed for PIPE59 when using "added mass

on the outside of the pipe (CI ≥ 0.0).


There are no product-specific restrictions for this element.


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SHELL63

Elastic Shell

MP ME ST PR PRN DS <> <> <> <> <> PP <> EME MFSProduct Restrictions

SHELL63 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SHELL181 (KEYOPT(3) = 2).

SHELL63 has both bending and membrane capabilities. Both in-plane and normal loads are permitted. Theelement has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotatioabout the nodal x, y, and z-axes. Stress stiffening and large deflection capabilities are included. A consistentangent stiffness matrix option is available for use in large deflection (finite rotation) analyses. See SHELL63for more details about this element. Similar elements are SHELL181 (plastic capability) and SHELL281 (midsnode capability). The ETCHG command converts SHELL157 elements to SHELL63.

Figure 1 SHELL63 Geometry

zIJ

z

y

LK

JI

JI

5

3

6

2

1

4

xIJ

yIJ

x

K,L

Triangular Option

Z

X

Y1

2

34

5

6

78

xIJ = Element x-axis if ESYS is not supplied.

x = Element x-axis if ESYS is supplied.

SHELL63 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 147). Thelement is defined by four nodes, four thicknesses, an elastic foundation stiffness, and the orthotropic ma-terial properties. Orthotropic material directions correspond to the element coordinate directions. The elemcoordinate system orientation is as described in Coordinate Systems. The element x-axis may be rotated byan angle THETA (in degrees).






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The thickness is assumed to vary smoothly over the area of the element, with the thickness input at the fournodes. If the element has a constant thickness, only TK(I) need be input. If the thickness is not constant, allfour thicknesses must be input.

The elastic foundation stiffness (EFS) is defined as the pressure required to produce a unit normal deflectionof the foundation. The elastic foundation capability is bypassed if EFS is less than, or equal to, zero.

For certain nonhomogeneous or sandwich shell applications, the following real constants are provided: RMI

is the ratio of the bending moment of inertia to be used to that calculated from the input thicknesses. RMIdefaults to 1.0. CTOP and CBOT are the distances from the middle surface to the extreme fibers to be usedfor stress evaluations. Both CTOP and CBOT are positive, assuming that the middle surface is between thefibers used for stress evaluation. If not input, stresses are based on the input thicknesses. ADMSUA is theadded mass per unit area.

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 147). Positive pressures act into the element.Because shell edge pressures are input on a per-unit-length basis, per-unit-area quantities must be multipliedby the shell thickness. The lateral pressure loading may be an equivalent (lumped) element load applied atthe nodes (KEYOPT(6) = 0) or distributed over the face of the element (KEYOPT(6) = 2). The equivalent elementload produces more accurate stress results with flat elements representing a curved surface or elementssupported on an elastic foundation since certain fictitious bending stresses are eliminated.

Temperatures may be input as element body loads at the "corner" locations (1-8) shown in Figure 1 (p. 147). The first corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1. If only T1 and T2 are input, T1 is used for T1, T2, T3, and T4, while T2 (as input) is used for T5, T6, T7,and T8. For any other input pattern, unspecified temperatures default to TUNIF.

KEYOPT(1) is available for neglecting the membrane stiffness or the bending stiffness, if desired. A reducedout-of-plane mass matrix is also used when the bending stiffness is neglected.

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (that is, a matrix composed of the maintangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses [NLGEOM,ON].

You can often obtain more rapid convergence in a geometrically nonlinear analysis, such as a nonlinearbuckling or postbuckling analysis, by activating this option. However, you should not use this option if youare using the element to simulate a rigid link or a group of coupled nodes. The resulting abrupt changes instiffness within the structure make the consistent tangent stiffness matrix unsuitable for such applications.

KEYOPT(3) allows you to include (KEYOPT(3) = 0 or 2) or suppress (KEYOPT(3) = 1) extra displacement shapes.It also allows you to choose the type of in-plane rotational stiffness used:

• KEYOPT(3) = 0 or 1 activates a spring-type in-plane rotational stiffness about the element z-axis

• KEYOPT(3) = 2 activates a more realistic in-plane rotational stiffness (Allman rotational stiffness - theprogram uses default penalty parameter values of d1 = 1.0E-6 and d2 = 1.0E-3).

Using the Allman stiffness will often enhance convergence behavior in large deflection (finite rotation)analyses of planar shell structures (that is, flat shells or flat regions of shells).

KEYOPT(7) allows a reduced mass matrix formulation (rotational degrees of freedom terms deleted). Thisoption is useful for improved bending stresses in thin members under mass loading.

KEYOPT(8) allows a reduced stress stiffness matrix (rotational degrees of freedom deleted). This option canbe useful for calculating improved mode shapes and a more accurate load factor in linear buckling analysesof certain curved shell structures.


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Table 2 SHELL63 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYNodes - I, J, K, LNODES


YYAREAAREA


YYPressures P1 at nodes I, J, K, L; P2 at I, J, K, L; P3

at J, I; P4 at K, J; P5 at L, K; P6 at I, L

PRES

YY Temperatures T1, T2, T3, T4, T5, T6, T7, T8 TEMP

YYIn-plane element X, Y, and XY forces T(X, Y, XY)

YYElement X, Y, and XY momentsM(X, Y, XY)

-YFoundation pressure (if nonzero)FOUND.PRESS

YY Top, middle, or bottomLOC

YYCombined membrane and bending stressesS:X, Y, Z, XY

YYPrincipal stressS:1, 2, 3



YYAverage elastic strainEPEL:X, Y, Z, XY

Y-Equivalent elastic strain [2]EPEL:EQV

YYAverage thermal strainEPTH:X, Y, Z, XY

Y-Equivalent thermal strain [2]EPTH:EQV


2. The equivalent strains use an effective Poisson's ratio: for elastic and thermal this value is set by theuser (MP,PRXY).

Table 3 SHELL63 Miscellaneous Element Output


-1 TEMP, S(X, Y, Z, XY ), SINT,SEQV

Nodal Stress Solu-tion

1. Output at each node, if KEYOPT(5) = 2, repeats each location


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Table 4: SHELL63 Item and Sequence Numbers (p. 154) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this manual for more information. The following notation is usedin Table 4: SHELL63 Item and Sequence Numbers (p. 154):

Name

output quantity as defined in the Table 2: SHELL63 Element Output Definitions (p. 153)

Item


E


I,J,K,Lsequence number for data at nodes I,J,K,L

Table 4 SHELL63 Item and Sequence Numbers


Quant-

ity

Name

LK JIEItem

----1SMISC TX

----2SMISC TY

----3SMISC TXY

----4SMISCMX

----5SMISCMY

----6SMISCMXY

1211109-SMISCP1

16151413-SMISCP2

--1718-SMISCP3

-1920--SMISCP4

2122---SMISCP5

24--23-SMISCP6

Top

161161-NMISCS:1

171272-NMISCS:2

181383-NMISCS:3

191494-NMISCS:INT2015105-NMISCS:EQV

Bot

36312621-NMISCS:1

37322722-NMISCS:2

38332823-NMISCS:3

39342924-NMISCS:INT


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40353025-NMISCS:EQV

SHELL63 Assumptions and Restrictions

• Zero area elements are not allowed. This occurs most often whenever the elements are not numberedproperly.

• Zero thickness elements or elements tapering down to a zero thickness at any corner are not allowed

• The applied transverse thermal gradient is assumed to vary linearly through the thickness and vary bilinearly over the shell surface.

• An assemblage of flat shell elements can produce a good approximation of a curved shell surfaceprovided that each flat element does not extend over more than a 15° arc. If an elastic foundationstiffness is input, one-fourth of the total is applied at each node. Shear deflection is not included in ththin-shell element.

• A triangular element may be formed by defining duplicate K and L node numbers as described in TriaPrism, and Tetrahedral Elements. The extra shapes are automatically deleted for triangular elements sothat the membrane stiffness reduces to a constant strain formulation. For large deflection analyses, if KEYOPT(1) = 1 (membrane stiffness only), the element must be triangular.

• For KEYOPT(1) = 0 or 2, the four nodes defining the element should lie as close as possible to a flatplane (for maximum accuracy), but a moderate amount of warping is permitted. For KEYOPT(1) = 1, thewarping limit is very restrictive. In either case, an excessively warped element may produce a warningor error message. In the case of warping errors, triangular elements should be used (see Triangle, Prismand Tetrahedral Elements). Shell element warping tests are described in detail in tables of Applicabilityof Warping Tests and Warping Factor Limits in the Theory Reference for the Mechanical APDL and Mech-

anical Applications.

• If the lumped mass matrix formulation is specified [LUMPM,ON], the effect of the implied offsets onthe mass matrix is ignored for warped SHELL63 elements.

SHELL63 Product Restrictions


ANSYS Professional


• The only special features allowed are stress stiffening and large deflection.• KEYOPT(2) can only be set to 0 (default).



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PLANE82

2-D 8-Node Structural Solid

MP ME ST PR PRN DS <> <> <> <> <> PP <> EME MFSProduct Restrictions

PLANE82 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as PLANE183.

PLANE82 provides accurate results for mixed (quadrilateral-triangular) automatic meshes and can tolerateirregular shapes without as much loss of accuracy. The eight-node elements have compatible displacemenshapes and are well suited to model curved boundaries.

The 8-node element is defined by eight nodes having two degrees of freedom at each node: translations ithe nodal x and y directions. The element may be used as a plane element or as an axisymmetric element. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.Various printout options are also available. See SOLID273 for a description of an axisymmetric element whi

accepts nonaxisymmetric loading.

Figure 1 PLANE82 Geometry

O

K

N

J

M

P

L

I

IJ

K, L, O

P N

MTri OptionX (or radial)

Y(or axial)

3

1

2

4

PLANE82 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 157).

A triangular-shaped element may be formed by defining the same node number for nodes K, L and O. Besithe nodes, the element input data includes a thickness (TK) (for the plane stress option only) and the orthtropic material properties. Orthotropic material directions correspond to the element coordinate directions

The element coordinate system orientation is as described in Coordinate Systems.

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 157). Positive pressures act into the element Temperatures and fluences may be input as element body loads at the nodes. The node I temperature T(I)defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner node temperatuare specified, each midside node temperature defaults to the average temperature of its adjacent cornernodes. For any other input temperature pattern, unspecified temperatures default to TUNIF. Similar defaultsoccurs for fluence except that zero is used instead of TUNIF.










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Birth and deathAdaptive descent


KEYOPT(3)

Element behavior:

0 --

Plane stress

1 --

Axisymmetric

2 --

Plane strain (Z strain = 0.0)

3 --

Plane stress with thickness (TK) real constant input

KEYOPT(5)

Extra element output:

0 -- Basic element solution

1 --

Repeat basic solution for all integration points

2 --

Nodal Stress Solution

KEYOPT(6)


0 --Basic element solution

1 --Surface solution for face I-J also

2 --

Surface solution for both faces I-J and K-L also (surface solution valid for linear materials only)

3 --

Nonlinear solution at each integration point also

4 --

Surface solution for faces with nonzero pressure

PLANE82 Output Data



• Additional element output as shown in Table 1: PLANE82 Element Output Definitions (p. 160)



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RODefinitionName


Y-Equivalent elastic strain [4]EPEL:EQV

YYAverage thermal strainsEPTH:X, Y, Z, XY

Y-Equivalent thermal strain [4]EPTH:EQV

22Average plastic strainsEPPL:X, Y, XY, Z

2-Equivalent plastic strain [4]EPPL:EQV

22Average creep strainsEPCR:X, Y, XY, Z

2-Equivalent creep strain [4]EPCR:EQV

22Swelling strainEPSW:

22Equivalent plastic strainNL:EPEQ


22Equivalent stress on stress-strain curveNL:SEPL

2-Hydrostatic pressureNL:HPRES

11Face labelFACE

11Surface elastic strains (parallel, perpendicular, Z orhoop)

EPEL(PAR, PER, Z)

11Surface average temperature TEMP

11Surface stresses (parallel, perpendicular, Z or hoop)S(PAR, PER, Z)




1. Surface output (if KEYOPT(6) is 1, 2 or 4)

2. Nonlinear solution (if the element has a nonlinear material)



Table 2 PLANE82 Miscellaneous Element Output


-1EPPL, EPEQ, SRAT, SEPL, HPRES, EP-CR, EPSW

Nonlinear Integration Pt. Solution

-2 TEMP, SINT, SEQV, EPEL, SIntegration Point Stress Solution-3 TEMP, S, SINT, SEQVNodal Stress Solution

1. Output at each integration point, if the element has a nonlinear material and KEYOPT(6) = 3


3. Output at each vertex node, if KEYOPT(5) = 2


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Note

For axisymmetric solutions, the X, Y, XY, and Z stress and strain outputs correspond to the radial,axial, in-plane shear, and hoop stresses and strains.

Table 3: PLANE82 Item and Sequence Numbers (p. 162) lists output available through the ETABLE commandusing the Sequence Number method. See Creating an Element Table in the Basic Analysis Guide and The

Item and Sequence Number Table in this manual for more information. The following notation is used inTable 3: PLANE82 Item and Sequence Numbers (p. 162):

Name

output quantity as defined in the Table 1: PLANE82 Element Output Definitions (p. 160)

Item


E


I,J,...,P

sequence number for data at nodes I,J,...,P

Table 3 PLANE82 Item and Sequence Numbers


Quant-

ity

Name

PONMLK JIEItem

------12-SMISCP1

-----34--SMISCP2

----56---SMISCP3

----8--7-SMISCP4----161161-NMISCS:1

----171272-NMISCS:2

----181383-NMISCS:3

----191494-NMISCS:INT

----2015105-NMISCS:EQV

2827262524232221-NMISCFLUEN

--------29NMISC THICK

See Surface Solution in this manual for the item and sequence numbers for surface output for the ETABLEcommand.

PLANE82 Assumptions and Restrictions

• The area of the element must be positive.

• The element must lie in a global X-Y plane as shown in Figure 1 (p. 157) and the Y-axis must be the axisof symmetry for axisymmetric analyses. An axisymmetric structure should be modeled in the +X quadrants.


PLANE82

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SOLID92

3-D 10-Node Tetrahedral Structural Solid


SOLID92 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SOLID187.

SOLID92 has a quadratic displacement behavior and is well suited to model irregular meshes (such as prodfrom various CAD/CAM systems).

The element is defined by ten nodes having three degrees of freedom at each node: translations in thenodal x, y, and z directions. The element also has plasticity, creep, swelling, stress stiffening, large deflectionand large strain capabilities.

Figure 1 SOLID92 Geometry

Y

Z

X

1

2 3

4

L

PR

Q

K

N

J

MI

O

SOLID92 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 165).

Beside the nodes, the element input data includes the orthotropic material properties. Orthotropic materiadirections correspond to the element coordinate directions. The element coordinate system orientation isas described in Coordinate Systems.

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on theelement faces as shown by the circled numbers on Figure 1 (p. 165). Positive pressures act into the element Temperatures and fluences may be input as element body loads at the nodes. The node I temperature T(I)defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner node temperatuare specified, each midside node temperature defaults to the average temperature of its adjacent cornernodes. For any other input temperature pattern, unspecified temperatures default to TUNIF. Similar defaultsoccurs for fluence except that zero is used instead of TUNIF.








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You cannot set initial state conditions (INISTATE) using this element. You can set initial state conditionsusing current-technology elements only (such as LINK180,SHELL181). To continue using initial state conditionsin future versions of ANSYS, consider using a current element technology. For more information, see Legacyvs. Current Element Technologies in the Element Reference. For more information about setting initial statevalues, see the INISTATE command documentation and Initial State Loading in the Basic Analysis Guide.

You can include the effects of pressure load stiffness in a geometric nonlinear analysis using SOLCONTROL,,,IN-CP. Pressure load stiffness effects are included in linear eigenvalue buckling automatically. If an unsymmetric

matrix is needed for pressure load stiffness effects, use NROPT,UNSYM.

A summary of the element input is given in "SOLID92 Input Summary" (p. 166). A general description of elementinput is given in Element Input.

SOLID92 Input Summary

Nodes

I, J, K, L, M, N, O, P, Q, R

Degrees of Freedom

UX, UY, UZ

Real ConstantsNone

Material Properties

EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), PRXY, PRYZ, PRXZ (or NUXY,NUYZ, NUXZ), DENS, GXY, GYZ, GXZ, DAMP

Surface Loads

Pressures --

face 1 (J-I-K), face 2 (I-J-L), face 3 (J-K-L), face 4 (K-I-L)

Body Loads

Temperatures -- T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P), T(Q), T(R)

Fluences --

FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O), FL(P), FL(Q), FL(R)

Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)

Stress stiffeningLarge deflectionLarge strainBirth and deathAdaptive descent


KEYOPT(5)



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Table 1 SOLID92 Element Output Definitions

RODefinitionName

YYElement NumberEL

YYCorner nodes - I, J, K, LNODESYYMaterial numberMAT

YYVolumeVOLU:


YYPressures P1 at nodes J, I, K; P2 at I, J, L; P3 at J, K,L; P4 at K, I, L

PRES

YY Temperatures T(I), T(J), T(K), T(L) TEMP

YYFluences FL(I), FL(J), FL(K), FL(L), FL(M), FL(N), FL(O),FL(P), FL(Q), FL(R)

FLUEN






YYPrincipal elastic strainsEPEL:1, 2, 3

-YEquivalent elastic strains [4]EPEL:EQV

11 Thermal strainsEPTH:X, Y, Z, XY, YZ,XZ

11Equivalent thermal strains [4]EPTH:EQV

11Plastic strainsEPPL:X, Y, Z, XY, YZ,XZ

11Equivalent plastic strains [4]EPPL:EQV

11Creep strainsEPCR:X, Y, Z, XY, YZ,XZ

11Equivalent creep strains [4]EPCR:EQV




11Equivalent stress from stress-strain curveNL:SEPL


22Face labelFACE

-2Nodes on this face TRI

22Face areaAREA

22Face average temperature TEMP


SOLID92

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RODefinitionName

22Surface elastic strainsEPEL(X, Y, XY)

22Surface pressurePRES

22Surface stressesS(X, Y, XY)





1. Nonlinear solution (output if the element has a nonlinear material)

2. Surface output (if KEYOPT(6) = 4 and a nonzero pressure face)





-1 TEMP, SINT, SEQV, EPEL, S, EPPL,EPCR, EPSW, EPEQ, SRAT, SEPL,HPRES

Integration Point Stress Solution

-2LOCATION, TEMP, SINT, SEQV, SNodal Stress Solution


2. Output at each vertex node, if KEYOPT(5) = 2

Table 3: SOLID92 Item and Sequence Numbers (p. 169) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide an The Item and Sequence Number Table in this manual for more information. The following notation is usedin Table 3: SOLID92 Item and Sequence Numbers (p. 169):

Name

output quantity as defined in the Table 1: SOLID92 Element Output Definitions (p. 168)

Item


I,J,...,R

sequence number for data at nodes I,J,...,R



Quantity

NameM,...,RLK JIItem

--312SMISCP1

-6-54SMISCP2


SOLID92

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SOLID95

3-D 20-Node Structural Solid


SOLID95 Element Description

Although this legacy element is available for use in your analysis, ANSYS recommends using a current-tech-nology element such as SOLID186 (KEYOPT(2) = 1, or KEYOPT(2) = 0 for nonlinear analyses).

SOLID95 is a higher-order version of the 3-D 8-node solid element SOLID45. It can tolerate irregular shapeswithout as much loss of accuracy. SOLID95 elements have compatible displacement shapes and are wellsuited to model curved boundaries.

The element is defined by 20 nodes having three degrees of freedom per node: translations in the nodal xy, and z directions. The element may have any spatial orientation. SOLID95 has plasticity, creep, stress stiff-ening, large deflection, and large strain capabilities. Various printout options are also available.

Figure 1 SOLID95 Geometry

5

6

2 3

P

X

M

4

1

Y

I

QJ

T

L

W

O

A

K

R

SZ

BU

N

Z

X

Y

Tetrahedral Option

M,N,O,P,U,V,W,X

Y A,B

K,L,SR

JQ

I T

Z

Pyramid Option

M,N,O,P,U,V,W,X

Y

I

JQR

K

AZ

S

B

LT

Prism Option

O,P,W

A,B

K,L,S

RJ

Q

I

Y

MX

U

T

ZN

V

V

SOLID95 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 1 (p. 171). Aprism-shaped element may be formed by defining the same node numbers for nodes K, L, and S; nodes A




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and B; and nodes O, P, and W. A tetrahedral-shaped element and a pyramid-shaped element may also beformed as shown in Figure 1 (p. 171). A similar, but 10-node tetrahedron, element is SOLID187.

Besides the nodes, the element input data includes the orthotropic material properties. Orthotropic materialdirections correspond to the element coordinate directions. The element coordinate system orientation isas described in Coordinate Systems.

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on the

element faces as shown by the circled numbers on Figure 1 (p. 171). Positive pressures act into the element. Temperatures may be input as element body loads at the nodes. The node I temperature T(I) defaults to TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner node temperatures arespecified, each midside node temperature defaults to the average temperature of its adjacent corner nodes.For any other input temperature pattern, unspecified temperatures default to TUNIF.

A lumped mass matrix formulation, which may be useful for certain analyses, may be obtained with LUMPM.While the consistent matrix gives good results for most applications, the lumped matrix may give betterresults with reduced analyses using Guyan reduction. The KEYOPT(5) and (6) parameters provide variouselement printout options (see Element Solution).

You cannot set initial state conditions (INISTATE) using this element. You can set initial state conditions

using current-technology elements only (such as LINK180,SHELL181). To continue using initial state conditionsin future releases, consider using a current element technology. For more information, see Legacy vs. CurrentElement Technologies in the Element Reference. For more information about setting initial state values, seethe INISTATE command documentation and Initial State Loading in the Basic Analysis Guide.

You can include the effects of pressure load stiffness using SOLCONTROL,,,INCP. If an unsymmetric matrixis needed for pressure load stiffness effects, use NROPT,UNSYM.

A summary of the element input is given in "SOLID95 Input Summary" (p. 172). A general description of elementinput is given in Element Input.

SOLID95 Input Summary

Nodes

I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A, B

Degrees of Freedom

UX, UY, UZ

Real Constants

None

Material Properties

EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), PRXY, PRYZ, PRXZ (or NUXY,NUYZ, NUXZ), DENS, GXY, GYZ, GXZ, DAMP

Surface Loads

Pressures --

face 1 (J-I-L-K), face 2 (I-J-N-M), face 3 (J-K-O-N),face 4 (K-L-P-O), face 5 (L-I-M-P), face 6 (M-N-O-P)

Body Loads

Temperatures --

T(I), T(J), ..., T(Z), T(A), T(B)


SOLID95




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Special Features

Plasticity (BISO, MISO, BKIN, MKIN, KINH, DP, ANISO)Creep (CREEP, RATE)Swelling (SWELL)Elasticity (MELAS)Other material (USER)Stress stiffening

Large deflectionLarge strainBirth and deathAdaptive descent


KEYOPT(5)


0 --

Basic element printout

1 -- Repeat basic solution for all integration points

2 --Nodal stress printout

KEYOPT(6)


0 --

Basic element printout

1 --

Surface printout for face I-J-N-M

2 --Surface printout for face I-J-N-M and face K-L-P-O (Surface printout valid for linear materials only)

3 --

Nonlinear printout at each integration point

4 --

Surface printout for faces with nonzero pressure

KEYOPT(11)

Integration rule:

0 --

No reduced integration (default)

1 --

2 x 2 x 2 reduced integration option for brick shape

See Failure Criteria in the Theory Reference for the Mechanical APDL and Mechanical Applications for an explaation of the three predefined failure criteria. For a complete discussion of failure criteria, please refer toFailure Criteria.


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RODefinitionName


YYVolumeVOLU:


YYPressures P1 at nodes J, I, L, K; P2 at I, J, N, M; P3at J, K, O, N; P4 at K, L, P, O; P5 at L, I, M, P; P6 at

M, N, O, P

PRES

YY Temperatures T(I), T(J), ..., T(Z), T(A), T(B) TEMP







YYEquivalent elastic strain [4]EPEL:EQV11Average thermal strainsEPTH:X, Y, Z, XY, YZ,

XZ

11Equivalent thermal strain [4]EPTH:EQV

11Average plastic strainsEPPL:X, Y, Z, XY, YZ,XZ

11Equivalent plastic strain [4]EPPL:EQV

11Average creep strainsEPCR:X, Y, Z, XY, YZ,XZ

11Equivalent creep strain [4]EPCR:EQV




11Average equivalent stress from stress-strain curveNL:SEPL


22Face labelFACE

22Face areaAREA

22Face average temperature TEMP

22Surface elastic strainsEPEL(X, Y, XY)22Surface pressurePRES

22Surface stresses (X-axis parallel to line defined byfirst two nodes which define the face)

S(X, Y, XY)





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RODefinitionName


1. Nonlinear solution (output only if the element has a nonlinear material)

2. Surface output (if KEYOPT(6) is 1, 2, or 4)

3. Available only at centroid as a *GET item




-1EPPL, EPEQ, SRAT, SEPL, HPRES, EP-CR

Nonlinear Integration Pt. Solution

-2 TEMP, S, SINT, SEQV, EPELIntegration Point Stress Solution

-3 TEMP, S, SINT, SEQV, EPELNodal Stress Solution

1. Output at each integration point, if the element has a nonlinear material and KEYOPT(6) = 3


3. Output at each node, if KEYOPT(5) = 2

Table 3: SOLID95 Item and Sequence Numbers (p. 176) lists output available through the ETABLE commandusing the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this manual for more information. The following notation is usedin Table 3: SOLID95 Item and Sequence Numbers (p. 176):

Name

output quantity as defined in Table 1: SOLID95 Element Output Definitions (p. 174)

Item


I,J,...,P

sequence number for data at nodes I,J,...,P



Quant-

ity

Name

PONMLK JIItem

----3412SMISCP1

--78--65SMISCP2

-1112--109-SMISCP3

1516--1413--SMISCP4

20--1917--18SMISCP5

24232221----SMISCP6


SOLID95

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Quant-

ity

Name

PONMLK JIItem

36312621161161NMISCS:1

37322722171272NMISCS:2

38332823181383NMISCS:339342924191494NMISCS:INT

403530252015105NMISCS:EQV

Note

N refers to the failure criterion number: N = 1 for the first failure criterion, N = 2 for the secondfailure criterion, and so on.

See Surface Solution in this manual for the item and sequence numbers for surface output for the ETABLE

command.

SOLID95 Assumptions and Restrictions

• The element must not have a zero volume.

• The element may not be twisted such that the element has two separate volumes. This occurs mostfrequently when the element is not numbered properly.

• Elements may be numbered either as shown in Figure 1 (p. 171) or may have the planes IJKL and MNOinterchanged.

• An edge with a removed midside node implies that the displacement varies linearly, rather than para-bolically, along that edge. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide

for more information on the use of midside nodes.• Degeneration to the form of pyramid should be used with caution. The element sizes, when degenera

should be small in order to minimize the stress gradients. Pyramid elements are best used as filler ele-ments or in meshing transition zones.

SOLID95 Product Restrictions


ANSYS Professional





SOLID95

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Legacy Theory

Following is archived theory information for legacy capabilities.

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Chapter 1: Archived Theory Element Library

Following is archived theory information for legacy elements.

1.1. BEAM4 - 3-D Elastic Beam

J

I

z , w

x , u

y , v

Y

X

Z

x

θ

Integration PointsShape FunctionsMatrix or Vector

NoneEquation 12–15, Equation 12–16, Equa-tion 12–17, and Equation 12–18

Stiffness and Mass Matrices

NoneEquation 12–7 and Equation 12–8Stress Stiffness and DampingMatrices

NoneEquation 12–15, Equation 12–16, and Equa-tion 12–17

Pressure Load Vector and Temperatures

DistributionLoad Type

Bilinear across cross-section, linear along lengthElement Temperature

Constant across cross-section, linear along lengthNodal Temperature

Linear along lengthPressure

1.1.1. Stiffness and Mass Matrices The order of degrees of freedom (DOFs) is shown in Figure 1.1 (p. 182).


























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Figure 1.1 Order of Degrees of Freedom

I

J

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

The stiffness matrix in element coordinates is (Przemieniecki):

(1–1)[ ]K

AE L

a

a

GJ L

c e

c eAE L

a

z

y

y y

z zℓ =

−

−−

0

0 0

0 0 0

0 0 0

0 0 0 00 0 0 0 0

0

Symmetric

zz z

y y

y y

z z

z

y

c

a c

GJ L

c f

c f

AE L

a

a

GJ

0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0

0

0 0

0 0 0

−−

−−

LL

c e

c e

y y

z z

0 0 0

0 0 0 0−

where:

A = cross-section area (input as AREA on R command)E = Young's modulus (input as EX on MP command)L = element lengthG = shear modulus (input as GXY on MP command)

JJ I

I I

x x

x x

= = =

≠

torsional moment of inertiaif

if

0

0

Ix = input torsional moment of inertia (input as IXX on RMORE command)

Jx = polar moment of inertia = Iy + Iz




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az = a(Iz,φy)

ay = a(Iy,φz)

bz = b(Iz,φy)

⋮

f z = f(Iz,φy)

f y = f(Iy,φz)

a I EIL

( , )( )

φφ

=+

1213

c IEI

L( , )

( )φ

φ=

+

6

12

e IEI

L( , )

( )

( )φ

φφ

= +

+4

1

f IEI

L( , )

( )

( )φ

φφ

= −

+2

1

φy z

zsEI

GA L= 12 2

φzy

ys

EI

GA L=

12

2

Ii = moment of inertia normal to direction i (input as Iii on R command)

A A Fis

is= =shear area normal to direction i /

F is = shear coefficient (input as SHEARi on command)RMORE

The consistent mass matrix (LUMPM,OFF) in element coordinates LUMPM,OFF is (Yokoyama):

(1–2)[ ]M M

A

A

J A

C E

C E

B

t

z

y

x

y y

z z

z

ℓ =

−

1 3

0

0 0

0 0 0 3

0 0 0

0 0 0 0

1 6 0 0 0 0 0

0

Symmetric

00 0 00 0 0 0

0 0 0 6 0 0

0 0 0 0

0 0 0 0

1 3

00 0

0 0 0 3

0

DB D

J A

D F

D F

AA

J A

z

y y

x

y y

z z

z

y

x

−

−

00 0

0 0 0 0

C E

C E

y y

z z−

where:


1.1.1. Stiffness and Mass Matrices

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(1–3)[ ]M

Mt

ℓ = 2

1

0 1

0 0 1

0 0 0 0

0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0

Symmetric

00 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

1

0 1

0 0 1

0 0 0 0

0 0 0 0 0

0 0 0 0 0 0

1.1.2. Gyroscopic Damping Matrix

The element gyroscopic damping matrix is the same as for PIPE16.

1.1.3. Pressure and Temperature Load Vector

The pressure and temperature load vector are computed in a manner similar to that of BEAM3.

1.1.4. Local to Global Conversion

The element coordinates are related to the global coordinates by:

(1–4) [ ] u T uRℓ =

where:

uℓ = vector of displacements in element Cartesian coordinattes

u = vector of displacements in global Cartesian coordinates

[ ]T

T

T

T

T

R =

0 0 0

0 0 0

0 0 0

0 0 0

[T] is defined by:

(1–5)[ ] ( ) ( )

(

T

C C S C S

C S S S C S S S C C S C

C S C S S

= − − − +− −

1 2 1 2 2

1 2 3 1 3 1 2 3 1 3 3 2

1 2 3 1 33 1 2 3 1 3 3 2) ( )− −

S S C C S C C

where:


1.1.4. Local to Global Conversion

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S

Y Y

LL d

L d

xyxy

xy

1

2 1

=

−>

0.0 <

if

if

SZ Z

L2

2 1= −

S3 = sin (θ)

C

X X

LL d

L d

xyxy

xy

1

2 1

1 0

=

−>

<

if

if

.

CL

L

xy2 =

C3 = cos (θ)

X1, etc. = x coordinate of node 1, etc.

Lxy = projection of length onto X-Y plane

d = .0001 Lθ = user-selected adjustment angle (input as THETA on R command)

If a third node is given, θ is not used. Rather C3 and S3 are defined using:

V1 = vector from origin to node 1



V4 = unit vector parallel to global Z axis, unless element is almost parallel to Z axis, in which case it is

parallel to the X axis.

Then,

(1–6) V V V5 3 1= − = vector between nodes I and K

(1–7) V V V6 2 1= − = vector along element X axis

(1–8) V V V7 6 4= ×

(1–9) V V V8 6 5= ×

and



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(1–17)σz ibnd y i z

y

M t

I,,=

2

(1–18)σy ibnd z i y

z

M t

I,,=

2

where:

σz ibnd,

= bending stress in element x direction on the elemennt

+ z side of the beam at end i (output as SBZ)

σy ibnd, = bending stess on the element in element x directionn

- y side of the beam at end i (output as SBY)

My,i = moment about the element y axis at end i

Mz,i = moment about the element z axis at end i

tz = thickness of beam in element z direction (input as TKZ on R command)ty = thickness of beam in element y direction (input as TKY on R command)

The maximum and minimum stresses are:

(1–19)σ σ σ σi idir

z ibnd

y ibndmax

, ,= + +

(1–20)σ σ σ σi idir

z ibnd

y ibndmin

, ,= − −

The presumption has been made that the cross-section is a rectangle, so that the maximum and minimumstresses of the cross-section occur at the corners. If the cross-section is of some other form, such as an ellipse,the user must replace Equation 1–19 (p. 188) and Equation 1–20 (p. 188) with other more appropriate expressions.

For long members, subjected to distributed loading (such as acceleration or pressure), it is possible that thepeak stresses occur not at one end or the other, but somewhere in between. If this is of concern, the usershould either use more elements or compute the interior stresses outside of the program.



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1.2. CONTAC12 - 2-D Point-to-Point Contact

N o d e s m a y b e c o i n c i d e n t

I

J

θ

s

n

X o r r a d i a l

Y o r a x i a l


NoneNone (nodes may be coincident)Stiffness Matrix


None - average used for material property evaluationElement Temperature

None - average used for material property evaluationNodal Temperature

1.2.1. Element Matrices

CONTAC12 may have one of three conditions if the elastic Coulomb friction option (KEYOPT(1) = 0) is usedclosed and stuck, closed and sliding, or open. The following matrices are derived assuming that θ is inputas 0.0.

1. Closed and stuck. This occurs if:

(1–21)µ F Fn s>

where:

µ = coefficient of friction (input as MU on TB command with Lab = FRIC or MP command)Fn = normal force across gap

Fs = sliding force parallel to gap

The normal force is:

(1–22)F k u un n n J n I= − −( ), , ∆

where:

k n = normal stiffness (input as KN on R command

un,I = displacement of node I in normal direction


1.2.1. Element Matrices


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un,J = displacement of node J in normal direction

∆ = interferenceinput as INTF on command if KEYOPT(4) = 0

=

R

- d if KEYOPT(4) = 1

d = distance between nodes

The sliding force is:

(1–23)F k u u us s s J s I o= − −( ), ,

where:

k s = sticking stiffness (input as KS on R command)

us,I = displacement of node I in sliding direction

us,J = displacement of node J in sliding direction

uo = distance that nodes I and J have slid with respect to each other

The resulting element stiffness matrix (in element coordinates) is:

(1–24)[ ]K

k k

k k

k k

k k

s s

n n

s s

n n

ℓ =

−−

−−

0 0

0 0

0 0

0 0

and the Newton-Raphson load vector (in element coordinates) is:

(1–25) F

F

F

F

F

nr

s

n

s

n

ℓ =−−

2. Closed and sliding. This occurs if:

(1–26)µ F Fn s=

In this case, the element stiffness matrix (in element coordinates) is:



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(1–27)[ ]Kk k

k k

n n

n n

ℓ = −

−

0 0 0 0

0 0

0 0 0 0

0 0

and the Newton-Raphson load vector is the same as in Equation 1–25 (p. 190). If the unsymmetric optis chosen (NROPT,UNSYM), then the stiffness matrix includes the coupling between the normal andsliding directions; which for STAT = 2 is:

(1–28)[ ]K

k k

k k

k k

k k

n n

n n

n n

n n

ℓ =

−−

−−

0 0

0 0

0 0

0 0

µ µ

µ µ

3. Open - When there is no contact between nodes I and J. There is no stiffness matrix or load vector.Figure 1.2 (p. 191) shows the force-deflection relationships for this element. It may be seen in these figuresthat the element is nonlinear and therefore needs to be solved iteratively. Further, since energy lost in theslider cannot be recovered, the load needs to be applied gradually.

Figure 1.2 Force-Deflection Relations for Standard Case

F

n

1

k

n

( µ ) − ( µ ) − δ

n

n

J

I

F

s

F

n

m | |

F

n

m | |

-

1

k

s

F

n

F o r < 0 , a n d n o

r e v e r s e d l o a d i n g

( µ ) − ( µ )

s

s

J

I

1.2.2. Orientation of the Element

The element is normally oriented based on θ (input as THETA on R command). If KEYOPT(2) = 1, however,θ is not used. Rather, the first iteration has θ equal to zero, and all subsequent iterations have the orientatioof the element based on the displacements of the previous iteration. In no case does the element use itsnodal coordinates.

1.2.3. Rigid Coulomb Friction

If the user knows that a gap element will be in sliding status for the life of the problem, and that the relatidisplacement of the two nodes will be monotonically increasing, the rigid Coulomb friction option (KEYOP= 1) can be used to avoid convergence problems. This option removes the stiffness in the sliding direction


1.2.3. Rigid Coulomb Friction

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as shown in Figure 1.3 (p. 192). It should be noted that if the relative displacement does not increase mono-tonically, the convergence characteristics of KEYOPT(1) = 1 will be worse than for KEYOPT(1) = 0.

Figure 1.3 Force-Deflection Relations for Rigid Coulomb Option

F

n

1

k

n

( µ ) − ( µ ) − δ

n

n

J

I

F

s

F

n

m | |

F

n

m | |

-

F

n

F o r < 0 , a n d n o

r e v e r s e d l o a d i n g

( µ ) − ( µ )

s

s

J

I

1.3. PIPE16 - Elastic Straight Pipe

I

z , w

y , v

x , u

θ

J

Y

X

Z

x


NoneEquation 12–15,Equation 12–16,Equation 12–17,and Equation 12–18

Stiffness and MassMatrices

NoneEquation 12–16 and Equation 12–17Stress Stiffness andDamping Matrices

NoneEquation 12–15, Equation 12–16, and Equa-tion 12–17Pressure and ThermalLoad Vectors


Linear thru thickness or across diameter, and along lengthElement Temperature

Constant across cross-section, linear along lengthNodal Temperature

Internal and External: constant along length and around circumfer-ence. Lateral: constant along length

Pressure

























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1.3.1. Assumptions and Restrictions

The element is assumed to be a thin-walled pipe except as noted. The corrosion allowance is used only inthe stress evaluation, not in the matrix formulation.

1.3.2. Stiffness Matrix

The element stiffness matrix of PIPE16 is similar to that of a 3-D elastic beam, except that

(1–29)A A D Dwo i= = − =

π4

2 2( ) pipe wall cross-sectional area

(1–30)I I I D DC

y z o If

= = = − =π

64

14 4( ) bending moment of inertia

(1–31)J D D

o i= − =

π

32

4 4( ) torsional moment of inertia

and,

(1–32)AA

si = =2 0.

shear area

where:

π = 3.141592653

Do = outside diameter (input as OD on R command)

Di = inside diameter = Do - 2tw

tw = wall thickness (input as TKWALL on R command)

Cf

f =

1 0. if f = 0.0

if f > 0.0

f = flexibility factor (input as FLEX on R command)

Further, the axial stiffness of the element is defined as

(1–33)KA E

L

w

ℓ( , )11 =

if k = 0.0

if k > 0.0k

where:

Kℓ( , )11 = axial stiffness of element

E = Young's modulus (input as EX on MP command)L = element length



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k = alternate axial pipe stiffness (input as STIFF on RMORE command)

1.3.3. Mass Matrix

The element mass matrix of PIPE16 is the same as for a 3-D elastic beam, except total mass of the elementis assumed to be:

(1–34)m m A A Le e

w

fl

fl

in

in

= + +( )ρ ρ

where:

me = total mass of element

mA L

m ifew

w

w

= =>

=ρ if m

m

w

w

pipe wall mass0 0

0 0

.

.

mw = alternate pipe wall mass (input as MWALL on RMORE command)

ρ = pipe wall density (input as DENS on MP command)

ρfl = internal fluid density (input as DENSFL on R command)

A Dfli=

π4

2

ρin = insulation density (input as DENSIN on RMORE command)

A

D D A

A t

LA

ino o s

in

in in

sin

=− =

>

=+

π4

0 0

0 0

2 2( ) if

if

ins

.

.

uulation cross-sectional area

Do+ = Do + 2tin

tin

= insulation thickness (input as TKIN on RMORE command)As

in = alternate representation of the surface area of the outside of the pipe element (input as AREAIN

on RMORE command)

Also, the bending moments of inertia (Equation 1–30 (p. 193)) are used without the Cf term.

1.3.4. Gyroscopic Damping Matrix

The element gyroscopic damping matrix is:



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(1–35)[ ]C AL

g

h

h i

g

e =

−

−− −

−

2

0

0 0

0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 0

0 0Ωρ

Antisymmetric

00 0

0 0 0 0

0 0 0 0 0 0

0 0 0 0

0 0 0 0

0

0 0

0 0

0 0 0 0

0 0 0 0

0 0 0 0

−−

−− −

−

−

h

g h

h j

h j

g

h

h i

where:

Ω = rotation frequency about the positive x axis (input as SPIN on RMORE command)

gr

L=

+

6 5

1

2

2 2

/

( )φ

hr

L=

− −

+

( )

( )

110 1 2

1

2

2

φ

φ

ir

= + +

+

( )

( )

2 15 1 6 1 3

1

2 2

2

φ φ

φ

j

r

=

− + −

+

( )

( )

1 30 1 6 1 6

1

2 2

2

φ φ

φ

r I A= /

φ =12

2

EI

GA Ls

G = shear modulus (input as GXY on MP command)

As = shear area ( = Aw /2.0)

1.3.5. Load Vector

The element pressure load vector is

(1–36) F

F

F

F

ℓ⋮

=

1

2

12

where:


1.3.5. Load Vecto

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F1 = FA + FP

F7 = -FA + FP

F A EAw

xpr= ε

εxpr = axial strain due to pressure load, defined below

F P LCp A=

0 0

21

. if KEYOPT(5) = 0

if KEYOPT(5) = 1

F FP LCA

2 82

2= =

F FP LCA

3 93

2= =

F4 = F10 = 0.0

F FP L CA

5 113

2

12

= − =

F FP L CA

6 122

2

12= − =

P1 = parallel pressure component in element coordinate system (force/unit length)

P2, P3 = transverse pressure components in element coordinate system (force/unit length)

CA =

1.0

positive sine of the angle between

the axis of the eleement and the

direction of the pressures, as

defined by P ,1 P and P

if KEYOPT(5) = 0

if KEYOPT(5) = 1

2 3

The transverse pressures are assumed to act on the centerline, and not on the inner or outer surfaces. Thetransverse pressures in the element coordinate system are computed by

(1–37)

P

P

P

T

P

P

P

X

Y

Z

1

2

3

=

[ ]

where:

[T] = conversion matrixPX = transverse pressure acting in global Cartesian X direction) (input using face 2 on SFE command)

PY = transverse pressure acting in global Cartesian Y direction) (input using face 3 on SFE command)



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(1–39)σdirx E

w

F F

a=

+

(1–40)σ σbendb o

r

CM r

I=

(1–41)σtorx oM r

J=

(1–42)σhi i o o i

o i

PD P D D

D D=

− +

−

2 2 2 2

2 2

( )

(1–43)σℓfsw

F

A=

2

where:

σdir = direct stress (output as SDIR)

Fx = axial force

FPD P D

Ei i o o=

−

π4

0 0

2 2( )

.

if KEYOPT(8) = 0

if KEYOPT(8) = 1

a d Dw o i= −π4

2 2( )

do = 2 ro

rD

too

c= −2

tc = corrosion allowance (input as TKCORR on RMORE command)

σbend = bending stress (output as SBEND)

Cσ = stress intensification factor, defined in Table 1.1: Stress Intensification Factors (p. 199)

M M Mb y z= = +bending moment2 2

I d Dr o i= −π

64

4 4( )

σtor = torsional shear stress (output as ST)

Mx = torsional moment

J = 2Irσh = hoop pressure stress at the outside surface of the pipe (output as SH)

RD

ii=

2



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te = tw - tc

σℓf = lateral force shear stress (output as SSF)

F F Fs y z= = +shear force2 2

Average values of Pi and Po are reported as first and fifth items of the output quantities ELEMENT PRESSUR

The outside surface is chosen as the bending stresses usually dominate over pressure induced stresses.

Figure 1.5 Elastic Pipe Direct Stress Output

J

σ

b e n d

σ

d i r

Figure 1.6 Elastic Pipe Shear Stress Output

M

F

J

x

s

h

σ

t o r

σ

d i r

σ ,

b e n d

σ

Stress intensification factors are given in Table 1.1: Stress Intensification Factors (p. 199).

Table 1.1 Stress Intensification Factors

CσKEYOPT(2)

at node Jat node I

C Jσ,C Iσ,0

1.0C Tσ,1

C Tσ,1.02


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C Tσ,C Tσ,3

Any entry in Table 1.1: Stress Intensification Factors (p. 199) either input as or computed to be less than 1.0 isset to 1.0. The entries are:

C Iσ, = stress intensification factor of end I of straight pipe (input as SIFI on R command)

C Jσ, = stress intensification factor of end J of straight pipe (input as SIFJ on R command)

C

t

D d

T

w

i o

σ =

+

=0 9

42 3

.

( )

"T" stess intensification factor (ASME(40))

σth (output as STH), which is in the postprocessing file, represents the stress due to the thermal gradient

thru the thickness. If the temperatures are given as nodal temperatures, σth = 0.0. But, if the temperatures

are input as element temperatures,

(1–44)σ α υth o aE T T= − −−( )1

where:

To = temperature at outside surface

Ta = temperature midway thru wall

Equation 1–44 (p. 200) is derived as a special case of Equation 2–8, Equation 2–9 and Equation 2–11 with y asthe hoop coordinate (h) and z as the radial coordinate (r). Specifically, these equations

1. are specialized to an isotropic material2. are premultiplied by [D] and -1

3. have all motions set to zero, hence εx = εh = εr = γxh = γhr = γxr = 0.0

4. have σr = τhr = τxr = 0.0 since r = Ro is a free surface.

This results in:

(1–45)

σ

σσ

ν

υ

ν ν

ν ν

xt

h

t

xht

E E

E E

G

=

−−

−−

− − − −−

1 10

1 1 0

0 0

2 2

2 2

α

α

∆

∆

T

T0

or



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(1–46)σ σ α

ν σx

tht

thE T

= = −−

=∆

1

and

(1–47)σxht = 0

Finally, the axial and shear stresses are combined with:

(1–48)σ σ σ σx dir bend thA= + +

(1–49)σ σ σxh tor fB= + ℓ

where:

A, B = sine and cosine functions at the appropriate angleσx = axial stress on outside surface (output as SAXL)

σxh = hoop stress on outside surface (output as SXH)

The maximum and minimum principal stresses, as well as the stress intensity and the equivalent stress, arebased on the stresses at two extreme points on opposite sides of the bending axis, as shown in Figure

1.7 (p. 202). If shear stresses due to lateral forces σℓf are greater than the bending stresses, the two pointsof maximum shearing stresses due to those forces are reported instead. The stresses are calculated from thtypical Mohr's circle approach in Figure 1.8 (p. 202).

The equivalent stress for Point 1 is based on the three principal stresses which are designated by small circin Figure 1.8 (p. 202). Note that one of the small circles is at the origin. This represents the radial stress onthe outside of the pipe, which is equal to zero (unless P o ≠ 0.0). Similarly, the points marked with an X

represent the principal stresses associated with Point 2, and a second equivalent stress is derived from the

Next, the program selects the largest of the four maximum principal stresses (σ1, output as S1MX), the

smallest of the four minimum principal stresses (σ3, output as S3MN), the largest of the four stress intensiti

(σI, output as SINTMX), and the largest of the four equivalent stresses (σe, output as SEQVMX). Finally, these

are also compared (and replaced as necessary) to the values at the right positions around the circumferencat each end. These four values are then printed out and put on the postprocessing file.


1.3.6. Stress Calculation

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Figure 1.7 Stress Point Locations

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x


































z

y

P o i n t 1

P o i n t 2

α

Figure 1.8 Mohr Circles

F o r p o i n t 1

F o r p o i n t 2

σ

τ

σ

x

σ

x

σ

x h

σ

x h

σ

3

σ

h

σ

1

Three additional items are put on the postdata file for use with certain code checking. These are:



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1.4.1. Other Applicable Sections

PIPE16 - Elastic Straight Pipe (p. 192) covers some of the applicable stress calculations.


The geometry in the plane of the element is given in Figure 1.9 (p. 204).

Figure 1.9 Plane Element

θ

R

The stiffness matrix is developed based on an approach similar to that of Chen. The flexibility of one endwith respect to the other is:

(1–53)[ ]f

f f f

f f f

f f f

f f f

f f

=

11 13 15

22 24 26

31 33 3542 44 46

51 5

0 0 0

0 0 0

0 0 0

0 0 0

0 33 55

62 64 66

0 0

0 0 0

f

f f f

where:

fR C

EI

R

EA

R

fiw11

3

2

3

2 2

2 1

= − +

+ +

+ +

θθ θ θ θ θ θ

ν

cos sin ( cos sin )

( )EEAw ( cos sin )θ θ θ−

f fR C

EIsin

R

EA

fiw13 31

3

12

5

22= − = − +

+ +

cos

sinθ

θθ

θ θ ν

f fR C

EIfi

15 51

2

= = −(sin )θ θ





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fR

EIsin

R

EIC sin

R

fo

22

3

3

1

21

4 1

= +

−

+ + + −

+ +

( )( )

( )( cos )

( ( )

νθ θ

ν θ θ θ

θ ν ))

EAw

f fR

EICfo24 42

2

21= = + + −( )( cos sin ) ν θ θ θ

f fR

EIcos Cfo26 62

2

1 12

1= − = + − + + +

( )( ( )) sin ( ) ν θ

θθ ν

fR C

EI

R

EA

cos sin

fiw33

3

2

1

2

2

1

2

= −

+

+ +

θθ θ

θθ θ

cos sin

+

4 1R

EAw

( ) ν

f fR C

EIfi

35 53

2

1= − = −(cos )θ

fR

EIC

R

EIC sinfo fo44

21

21= + + + + −( ) cos ( ) ν θ θ ν θ

f fR

EICfo46 64

21= − = + +( ) sin ν θ θ

fRC

EIfi

55 = θ

f REI

C Cfo fo662

1 1= + + − + −(( ) cos ( )sin ) ν θ θ ν θ

and where:

R = radius of curvature (input as RADCUR on R command) (see Figure 1.9 (p. 204))θ = included angle of element (see Figure 1.9 (p. 204))E = Young's modulus (input as EX on MP command)ν = Poisson's ratio (input as PRXY or NUXY on MP command)

I D Do i= = −moment of inertia ofcross-section π64

4 4( )

A D Dwo i= = −area of cross-section π

4

2 2( )

Do = outside diameter (input as OD on R command)

Di = Do - 2t = inside diameter

t = wall thickness (input as TKWALL on R command)



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C

C C

h C

fi

fi fi

fi

=

′ ′ >if 0.0

whichever is greater if

or 1.0,1 65.

′′ = 0.0 and KEYOPT(3) = 0

(ASME flexibility factor, ASME Coode(40))

whichever is greater ifor1 651

1 0. .h

PrX

tECK+

ffi

′ = 0.0 and KEYOPT(3) = 1

(ASME flexibility factor, ASME Code(40))

if = 0.0 and KEYOPT(3) = 2

(K

10 12

1 12

2

2

+

+

′h

h

Cfiaarman flexibility factor)

Cfi′ = in-plane flexibility (input as FLXI on command)R

htR

r=

2

r D to= −average radius ( )2

PP P P P

P P

o i o

i o

= − − >

− ≤

1 0 0

0 0 0 0

if

if

.

. .

Pi = internal pressure (input on SFE command)

Po = external pressure (input on SFE command)

X

r

t

R

rif

R

r

if Rr

K =

≥

<

6 1 7

0 0 1 7

4

3

1

3.

. .

′ = ′ ′ >

′ =

Cif

iffo

C C

C C

fo fo

fi fo

0 0

0 0

.

.

′ =Cfo out-of-plane flexibility (output as FLXO on comRMORE mmand)

The user should not use the KEYOPT(3) = 1 option if:

(1–54)θcR r< 2

where:

θc = included angle of the complete elbow, not just the included angle for this element ( θ)

Next, the 6 x 6 stiffness matrix is derived from the flexibility matrix by inversion:



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(1–55)[ ] [ ]K fo = −1

The full 12 x 12 stiffness matrix (in element coordinates) is derived by expanding the 6 x 6 matrix derivedabove and transforming to the global coordinate system.

1.4.3. Mass Matrix

The element mass matrix is a diagonal (lumped) matrix with each translation term being defined as:

(1–56)mm

te=

2

where:

mt = mass at each node in each translation direction

me= (ρAw + ρflAfl + ρinAin)Rθ = total mass of element

ρ = pipe wall density (input as DENS on MP command)ρfl = internal fluid density (input as DENSFL on RMORE command)

A Dfli=

π4

2

ρin = insulation density (input as DENSIN on RMORE command)

A D Din o o= − =+π4

2 2( ) insulation cross-section area

Do+ = Do + 2 tin

tin = insulation thickness (input as TKIN on RMORE command)

1.4.4. Load Vector

The load vector in element coordinates due to thermal and pressure effects is:

(1–57) [ ] , ,

F F R K A Fth pr ix e

pr tℓ ℓ ℓ

+ = +ε

where:

εx = strain caused by thermal as well as internal and external pressure effects (see Equation 1–38 (p. 197

)[K e] = element stiffness matrix in global coordinates

AT= 0 0 1 0 0 0 0 0 1 0 0 0⋮

,Fpr tℓ

= element load vector due to transverse pressure

,Fpr tℓ is computed based on the transverse pressures acting in the global Cartesian directions (input usin

face 2, 3, and 4 on SFE command) and curved beam formulas from Roark . Table 18, reference no. (loading)


1.4.4. Load Vecto

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Integration PointsShape FunctionsGeometryMatrix or Vector

2 x 2

Equation 12–117 and Equa-tion 12–118 and, if modified extra

Quad

Stiffness Matrix

shapes are included (KEYOPT(2)≠ 1) and element has 4 uniquenodes, Equation 12–129 andEquation 12–130

3 if axisymmetric1 if plane

Equation 12–98 and Equa-tion 12–99

Triangle

Same as stiffnessmatrix

Equation 12–117 and Equa-tion 12–118

QuadMass and Stress StiffnessMatrices Equation 12–98 and Equa-

tion 12–99 Triangle

2Same as mass matrix, specialized to facePressure Load Vector


Bilinear across element, constant thru thickness or around circumfer-ence

Element Temperature

Same as element temperature distributionNodal Temperature

Linear along each facePressure

References: Wilson, Taylor


"Structures" describes the derivation of structural element matrices and load vectors as well as stress evaluations.

1.6. SOLID45 - 3-D Structural Solid

J

K

O

P

M

I

L

r

N

s

t

Z , w

Y , v

X , u


1.6. SOLID45 - 3-D Structural Solid






































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2 x 2 x 2 if KEYOPT(2) = 01 if KEYOPT(2) = 1

Equation 12–215, Equation 12–216, andEquation 12–217 or, if modified extrashape functions are included (KEYOPT(1)Stiffness Matrix and

Thermal Load Vector = 0) and element has 8 unique nodes,Equation 12–230, Equation 12–231, andEquation 12–232

Same as stiffness matrixEquation 12–215, Equation 12–216, andEquation 12–217

Mass and Stress StiffnessMatrices

2 x 2Equation 12–68 and Equa-tion 12–69

Quad

Pressure Load Vector

3Equation 12–49 and Equa-tion 12–50

Triangle


Trilinear thru elementElement Temperature

Trilinear thru elementNodal Temperature

Bilinear across each facePressure

Reference: Wilson, Taylor et al.


"Structures" describes the derivation of structural element matrices and load vectors as well as stress evalu-ations. Uniform reduced integration technique (Flanagan and Belytschko) can be chosen by using KEYOPT(2)= 1.

1.7. CONTAC52 - 3-D Point-to-Point Contact

x

y

z

I

J

Y

X

Z

Integration PointsShape FunctionsGeometryMatrix or Vector

NoneNoneNormal DirectionStiffness Matrix

NoneNoneSliding Direction


None - average used for material property evaluationElement Temperature













































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(1–63)[ ]K

k k

k k

n n

n nℓ =

−

−

0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

and the Newton-Raphson load vector is the same as in Equation 1–62 (p. 211). For details on the unsymmetricoption (NROPT,UNSYM), see CONTAC12 - 2-D Point-to-Point Contact (p. 189)

If the element is open, there is no stiffness matrix or load vector.

1.7.3. Orientation of Element

For both small and large deformation analysis, the orientation of the element is unchanged. The element isoriented so that the normal force is in line with the original position of the two nodes.

1.8. PIPE59 - Immersed Pipe or Cable

I

z,w

y,vx,u

J

ZY

R

Xθ

Integration

Points

Shape FunctionsOptionsMatrix or Vector

NoneEquation 12–15, Equa-tion 12–16, Equa-

Pipe Option (KEYOPT(1)≠1)

Stiffness Matrix; and Thermal, Pressure, andHydrostatic Load Vectors tion 12–17, and Equa-

tion 12–18

NoneEquation 12–6, Equa-tion 12–7, and Equa-tion 12–8

Cable Option (KEYOPT(1)= 1)

NoneEquation 12–16 andEquation 12–17

Pipe Option (KEYOPT(1)≠1)

Stress Stiffness Matrix



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Integration

Points

Shape FunctionsOptionsMatrix or Vector

NoneEquation 12–7 and Equa-tion 12–8

Cable Option (KEYOPT(1)= 1)


Pipe Option (KEYOPT(1)≠1) with consistent massmatrix (KEYOPT(2) = 0)

Mass Matrix


Cable Option (KEYOPT(1)= 1) or reduced massmatrix (KEYOPT(2) = 1)

2Same as stiffness matrixHydrodynamic Load Vec-tor


Linear thru thickness or across diameter, and along lengthElement Temperature*

Constant across cross-section, linear along lengthNodal Temperature*

Linearly varying (in Z direction) internal and external pressure causedby hydrostatic effects. Exponentially varying external overpressure(in Z direction) caused by hydrodynamic effects

Pressure

Note

* Immersed elements with no internal diameter assume the temperatures of the water.

1.8.1. Overview of the Element

PIPE59 is similar to PIPE16. The principal differences are that the mass matrix includes the:

1. Outside mass of the fluid (“added mass”) (acts only normal to the axis of the element),

2. Internal structural components (pipe option only), and the load vector includes:

a. Hydrostatic effects

b. Hydrodynamic effects

1.8.2. Location of the Element

The origin for any problem containing PIPE59 must be at the free surface (mean sea level). Further, the Zaxis is always the vertical axis, pointing away from the center of the earth.

The element may be located in the fluid, above the fluid, or in both regimes simultaneously. There is a tol-

erance of only

De

8 below the mud line, for which

(1–64)D D te o i= + 2

where:


1.8.2. Location of the Element































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1.8.6. Hydrostatic Effects

Hydrostatic effects may affect the outside and the inside of the pipe. Pressure on the outside crushes thepipe and buoyant forces on the outside tend to raise the pipe to the water surface. Pressure on the insidetends to stabilize the pipe cross-section.

The buoyant force for a totally submerged element acting in the positive z direction is:

(1–70) / F L C D gb b w e= ρ π

4

2

where: F/Lb = vector of loads per unit length due to buoyancy

Cb = coefficient of buoyancy (input as CB on RMORE command)

g = acceleration vector

Also, an adjustment for the added mass term is made.

The crushing pressure at a node is:

(1–71)P gz Pos

w oa= − +ρ

where:

Pos

= crushing pressure due to hydrostatic effectsg = acceleration due to gravityz = vertical coordinate of the node

Poa

= input external pressure (input on SFE command)

The internal (bursting) pressure is:

(1–72)P g z S Pi o fo ia= − − +ρ ( )

where:

Pi = internal pressure

ρo = internal fluid density (input as DENSO on R command)

Sfo = z coordinate of free surface of fluid (input as FSO on R command)

Pia

= input internal pressure (input as SFE command)

To ensure that the problem is physically possible as input, a check is made at the element midpoint to seeif the cross-section collapses under the hydrostatic effects. The cross-section is assumed to be unstable if:



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(1–73)P PE t

Dos

iw

o

− >−

4 1

22

3

( ) ν

where:

E = Young's modulus (input as EX on MP command)ν = Poisson's ratio (input as PRXY or NUXY on MP command)

The axial force correction term (Fx) is computed as

(1–74)F AEx x= ε

where εx, the axial strain (see Equation 2–12) is:

(1–75)ε α σ ν σ σx x h rTE

= + − +∆1

( ( ))

where:

α = coefficient of thermal expansion (input as ALPX on MP command)∆ T = Ta - TREF

Ta = average element temperature

TREF = reference temperature (input on TREF command)

σx = axial stress, computed below

σh = hoop stress, computed below

σr = radial stress, computed below

The axial stress is:

(1–76)σx

i i o o

o i

P D P D

D D=−

−

2 2

2 2

0 0

if KEYOPT(8) = 0

if KEYOPT(8) = 1.

and using the Lamé stress distribution,


1.8.6. Hydrostatic Effects

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(1–77)σh

i i o oi o

i o

o i

P D P DD D

DP P

D D=

− + −

−

2 22 2

2

2 2

( )

(1–78)σri i o o

i o

i o

o i

P D P DD D

DP P

D D=

− − −

−

2 22 2

22 2

( )

where:

P P Po os

od= +

Pod

= hydrodynamic pressure, described belowD = diameter being studied

Pi and Po are taken as average values along each element. Combining Equation 1–75 (p. 217) thru Equa-

tion 1–78 (p. 218).

(1–79)ε α ν

xE i i o o

o i

Tf

E

P D P D

D D= +

− −

−∆

2 2 2

2 2

Note:

fE =

1 0

0 0

.

.

if KEYOPT(8) = 0

if KEYOPT(8) = 1

Note that if the cross-section is solid (Di = 0.), Equation 1–77 (p. 218) reduces to:

(1–80)ε α ν

xE

oTf

EP= −

−∆

2

1.8.7. Hydrodynamic Effects

See Hydrodynamic Loads on Line Elements in the Element Tools section of this document for information

about this subject.

1.8.8. Stress Output

The below two equations are specialized either to end I or to end J.

The stress output for the pipe format (KEYOPT(1) ≠ 1), is similar to PIPE16. The average axial stress is:





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(1–81)σxn EF F

A=

+

where:

σx = average axial stress (output as SAXL)

Fn = axial element reaction force (output as FX, adjusted for sign)

FPD P D

Ei i o o=

−

π4

0 0

2 2( )

.

if KEYOPT(8) = 0

if KEYOPT(8) = 1

Pi = internal pressure (output as the first term of ELEMENT PRESSURES)

Po = external pressure = P Pos

od+ (output as the fifth term of the ELEMENT PRESSURES)

and the hoop stress is:

(1–82)σh i i o o i

o i

P D P D DD D

= − +−

2

2 2 2

2 2( )

where:

σh = hoop stress at the outside surface of the pipe (output as SH)

Equation 1–82 (p. 219) is a specialization of Equation 1–77 (p. 218). The outside surface is chosen as the benstresses usually dominate over pressure induced stresses.

All stress results are given at the nodes of the element. However, the hydrodynamic pressure had been

computed only at the two integration points. These two values are then used to compute hydrodynamicpressures at the two nodes of the element by extrapolation.

For the stress output for the cable format (KEYOPT(1) = 1 with D i = 0.0), the stress is given with and withou

the external pressure applied:

(1–83)σxIF

AP= +ℓ

(1–84)σ

eI

F

A= ℓ

(1–85)F Aa xI= σ

where:

σxI = axial stress (output as SAXL)


1.8.8. Stress Output

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PP

Eo=

if KEYOPT(8) = 0

if KEYOPT(8) = 10 0.

σeI = equivalent stress (output as SEQV)

Fℓ = axial force on node (output as FX)Fa = axial force in the element (output as FAXL)

1.9. SHELL63 - Elastic Shell

L

K

J

I

y , v

s

t

z , w

t

x , u

Y

X

Z


2 x 2

Equation 12–92 and Equa-tion 12–93 (and, if modified

Membrane / Quad

Stiffness Matrix and Thermal Load Vector

extra shape functions areincluded (KEYOPT(3) = 0)

and element has 4 uniquenodes, Equation 12–95,Equation 12–96, and Equa-tion 12–97

1Equation 12–65, Equa-tion 12–66, and Equa-tion 12–67

Membrane / Tri-angle

3 (for each triangle)

Four triangles that areoverlaid are used.These

Bendingsubtriangles refer to Equa-tion 12–67

2 x 2Equation 12–68, Equa-tion 12–69, and Equa-tion 12–70

Membrane / Quad

Mass, Foundation Stiff-ness and Stress StiffnessMatrices

1Equation 12–49, Equa-tion 12–50, and Equa-tion 12–51

Membrane / Tri-angle

3 (for each triangle)Four triangles that areoverlaid are used.These tri-Bendingangles connect nodes IJK,





















































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IJL, KLI, and KLJ. w isdefined as given in Zien-kiewicz()

None

One-sixth (one- third fortriangles) of the total pres-

Reduced shellpressure loading

Transverse Pressure LoadVector

sure times the area is ap-

(KEYOPT(6) = 0) plied to each node normal(Load vector ex-cludes moments)

of each subtriangle of theelement

Same as mass matrixSame as mass matrix

Consistent shellpressure loading(KEYOPT(6) = 2)(Load vector in-cludes moments)

2Equation 12–68 and Equa-tion 12–69 specialized tothe edge

Quad

Edge Pressure Load Vec-tor

2Equation 12–49 and Equa-tion 12–50 specialized tothe edge

Triangle


Bilinear in plane of element, linear thru thicknessElement Temperature

Bilinear in plane of element, constant thru thicknessNodal Temperature

Bilinear in plane of element, linear along each edgePressure

1.9.1. Other Applicable Sections"Structures" describes the derivation of structural element matrices and load vectors as well as stress evaluations.

1.9.2. Foundation Stiffness

If K f , the foundation stiffness, is input, the out-of-plane stiffness matrix is augmented by three or four spring

to ground. The number of springs is equal to the number of distinct nodes, and their direction is normal tothe plane of the element. The value of each spring is:

(1–86)K

K

Nf i

f

d, =

∆

where:

K f,i = normal stiffness at node i

∆ = element areaK f = foundation stiffness (input as EFS on R command)

Nd = number of distinct nodes


1.9.2. Foundation Stiffness









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The output includes the foundation pressure, computed as:

(1–87)σpf

I J K LK

w w w w= + + +4

( )

where:

σp = foundation pressure (output as FOUND, PRESS)

wI, etc. = lateral deflection at node I, etc.

1.9.3. In-Plane Rotational Stiffness

The in-plane rotational (drilling) DOF has no stiffness associated with it, based on the shape functions. Asmall stiffness is added to prevent a numerical instability following the approach presented by Kanok-Nukulchaifor nonwarped elements if KEYOPT(1) = 0. KEYOPT(3) = 2 is used to include the Allman-type rota-tional DOFs.

1.9.4.Warping

If all four nodes are not defined to be in the same flat plane (or if an initially flat element loses its flatnessdue to large displacements (using NLGEOM,ON)), additional calculations are performed in SHELL63. Thepurpose of the additional calculations is to convert the matrices and load vectors of the element from thepoints on the flat plane in which the element is derived to the actual nodes. Physically, this may be thoughtof as adding short rigid offsets between the flat plane of the element and the actual nodes. (For the membranestiffness only case (KEYOPT(1) = 1), the limits given with SHELL41 are used). When these offsets are required,it implies that the element is not flat, but rather it is “warped”. To account for the warping, the followingprocedure is used: First, the normal to element is computed by taking the vector cross-product (the commonnormal) between the vector from node I to node K and the vector from node J to node L. Then, the check can be made to see if extra calculations are needed to account for warped elements. This check consists of

comparing the normal to each of the four element corners with the element normal as defined above. Thecorner normals are computed by taking the vector cross-product of vectors representing the two adjacentedges. All vectors are normalized to 1.0. If any of the three global Cartesian components of each cornernormal differs from the equivalent component of the element normal by more than .00001, then the elementis considered to be warped.

A warping factor is computed as:

(1–88)φ =D

t

where:

D = component of the vector from the first node to the fourth node parallel to the element normalt = average thickness of the element

If:

φ ≤ 0.1 no warning message is printed.10 ≤ φ ≤ 1.0 a warning message is printed1.0 < φ a message suggesting the use of triangles is printed and the run terminates





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Mx = moment per unit length

νxy = Poisson's ratio (input as PRXY on MP command)

κx = curvature in x direction

A nonuniform material may be represented with Equation 1–93 as:

(1–94)M C

t E

E

E

x r

x

xyy

x

x= − −

3

212 1 ν κ

where:

Cr = bending moment multiplier (input as RMI on RMORE command)

The above discussion relates only to the formulation of the stiffness matrix.

Similarly, stresses for uniform materials are determined by:

(1–95)σ ε κ xtop

x xEt

= +

2

(1–96)σ ε κ xbot

x xEt

= −

2

where:

σxtop = x direction stress at top fiber

σxbot = x direction stress at bottom fiber

For nonuniform materials, the stresses are determined by:

(1–97)σ ε κ xtop

x t xE c= +( )

(1–98)σ ε κ xbot

x b xE c= −( )

where:

ct = top bending stress multiplier (input as CTOP, RMORE command)

cb = bottom bending stress multiplier (input as CBOT, RMORE command)

The resultant moments (output as MX, MY, MXY) are determined from the output stresses rather than fromEquation 1–94.



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1.11. SOLID92 - 3-D 10-Node Tetrahedral Structural Solid

K

R

L

Q

O

P

M

N

J

I

Y , v

X , u

Z , w


4Equation 12–182, Equation 12–183, and Equa-tion 12–184

Stiffness, Mass, and StressStiffness Matrices; and Thermal Load Vector

6Equation 12–182, Equation 12–183, and Equa-tion 12–184 specialized to the face

Pressure Load Vector


Same as shape functionsElement Temperature

Same as shape functionsNodal Temperature

Linear over each facePressure

Reference: Zienkiewicz


"Structures" describes the derivation of structural element matrices and load vectors as well as stress evalu-ations.

























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Chapter 2: Hydrodynamic Loads on Line Elements

Hydrodynamic effects may occur because the structure moves in a motionless fluid, the structure is fixedbut there is fluid motion, or both the structure and fluid are moving. The fluid motion consists of two partscurrent and wave motions. The current is input by giving the current velocity and direction (input as W(i)and θ(i)) at up to eight different vertical stations (input as Z(i)). (All input quantities referred to in this sectionot otherwise identified come from the TBDATA commands used with TB,WATER). The velocity and directiare interpolated linearly between stations. The current is assumed to flow horizontally only.

The information in this section applies to the legacy PIPE59 element.

The following topic is available:2.1.Wave Theory

2.1.Wave Theory

The wave may be input using one of four wave theories in the following table (input as KWAVE via TB,WAT

Table 2.1 Wave Theory Table

KWAVE TB,WATER In-

putDescription of Wave Theory

1Small amplitude wave theory, unmodified (Airy wave theory), (Wheeler())

0Small amplitude wave theory, modified with empirical depth decay function,(Wheeler())

2Stokes fifth order wave theory, (Skjelbreia et al.())

3Stream function wave theory, (Dean())

The free surface of the wave is defined by

(2–1)η η βs ii

Ni

i

N

iw w H

cos= ∑ = ∑= =1 1 2

where:

ηs = total wave height

Nw = = ≠

number of wave componentsnumber of waves K 2

5

if w

K 2if w =

K w = wave theory key (input as KWAVE with TB,WATER)

ηi = wave height of component i

Hi = = =

surface coefficientinput quantity A(i) if K 0 or 1

deri

w

vved from other input if K 2w =


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β

πλ τ

φ

πλ τ

i

i i

i

i

R t

R t

=

− +

−

2360

2

if L = 0 and K = 0 or 1w w

ii

i i+

φ

π

360

2

( ) if L = 0 and K = 2 or 3

if L = 1

i

w w

w

0.0

ff L = 2

if L = 3

if L = 4

w

w

w

−

π

π2

R = radial distance to point on element from origin in the X-Y plane in the direction of the waveλi = wave length = input as WL(i) if WL(i) > 0.0 and if K w = 0 or 1 otherwise derived from Equa-

tion 2–2 (p. 230)t = time elapsed (input as TIME on TIME command) (Note that the default value of TIME is usually notdesired. If zero is desired, 10-12 can be used).

τ τ

i = = ≠

wave period

input as (i) if K 3

derived from other inp

w

uut if K 3w =

φi = phase shift = input as φ(i)

If λi is not input (set to zero) and K w < 2, λi is computed iteratively from:

(2–2)λ λ π

λi id

i

d=

tanh

2

where:

λi = output quantity small amplitude wave length

λ τ

πid ig

= =( )2

2output quantity deep water wave length

g = acceleration due to gravity (Z direction) (input on ACEL command)d = water depth (input as DEPTH via TB,WATER)

Each component of wave height is checked that it satisfies the “Miche criterion” if Kw ≠3. This is to ensurethat the wave is not a breaking wave, which the included wave theories do not cover. A breaking wave isone that spills over its crest, normally in shallow water. A warning message is issued if:

(2–3)H Hi b>

where:

Hd

b ii

=

=0 142

2. tanhλ

πλ

height of breaking wave


Chapter 2: Hydrodynamic Loads on Line Elements

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When using wave loading, there is an error check to ensure that the input acceleration does not changeafter the first load step, as this would imply a change in the wave behavior between load steps.

For K w = 0 or 1, the particle velocities at integration points are computed as a function of depth from:

(2–4)vcosh k Zf

sinh k dvR

i

ii

N

ii D

w = ∑ +

=

( )

( )1

2πτ

η

(2–5)vsinh k Zf

sinh k dZ

i

ii

N

iw

ɺ= ∑=

( )

( )1η

where:

vR

= radial particle velocity

vZ

= vertical particle velocity

k i = 2π /λi

Z = height of integration point above the ocean floor = d+Z

ɺηi = time derivative of ηi

vD

= drift velocity (input via TB,WATER)

f d

d s

=+

=

=

1.0 if K 0 (small amplitude wave theory)

if K 1

w

wη (Wheeler(35))

The particle accelerations are computed by differentiating vR

and vZ

with respect to time. Thus:

(2–6)ɺ

ɺvcosh k Zf

sinh k dCR

i

ii

N

ii i

w= ∑

−

=

( )

( )( )

1

2πτ

η η

(2–7)ɺ

ɺvsinh k Zf

sinh k dCZ

i

ii

N

i ii i

w= ∑

− −

=

( )

( )1

2 2

2

πτ

πτ

η η τ

π

where:

C

Zd

ds

i s= +

=ɺηλ η

2

0 0

2

Π

( )

.

i fK 0 (small amplitude wave theory)

i

w

ff K 1 (W heeler(35))w =

Expanding equation 2.29 of the Shore Protection Manual() for a multiple component wave, the wave hydrodynamic pressure is:


2.1.Wave Theory

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For K cr = 2, the same adjustment as for K cr = 1 is used, as well as a second change that accounts for “con-

tinuity.” That is,

(2–12)W j W jd

d s

′ =+

( ) ( )η

where:

W(j) = velocity of current at this location (input as W(j))

′W j( ) = adjusted value of W(j)

These three options are shown pictorially in Figure 2.1 (p. 233).

Figure 2.1 Velocity Profiles for Wave-Current Interactions

Horizontal arrows represent

input velocities

Mean Water

Surface

Mud Line

Constant (K = 0)

Stretch (K = 1)

Continuity (K = 2)

Water Surface

Z

Nonlinear Stretch (K = 3)

CR

CR

CR

CR

To compute the relative velocities ( ɺun , ɺut ), both the fluid particle velocity and the structure velocitymust be available so that one can be subtracted from the other. The fluid particle velocity is computed usirelationships such as Equation 2–4 (p. 231) and Equation 2–5 (p. 231) as well as current effects. The structurevelocity is available through the Newmark time integration logic (see Transient Analysis).

Finally, a generalized Morison's equation is used to compute a distributed load on the element to accountfor the hydrodynamic effects:

(2–13)

/

F L CD

u u C D v

CD

u u

d D we

n n M w e n

T we

t t

= +

+

ρ ρ π

ρ2 4

2

2ɺ ɺ ɺ

ɺ ɺ

where:

F/Ld = vector of loads per unit length due to hydrodynamic effects

CD = coefficient of normal drag (see below)


2.1.Wave Theory



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′ =′[ ] ′[ ]

C C x

J x Y xm m

22

12

12

π

( ) ( )

where:

x De= πλ1

′ = −J x J xJ x

xo1

1( ) ( )( )

′ = −Y x Y xY x

xo1

1( ) ( )( )

J0 = zero order Bessel function of the first kind

J1 = first-order Bessel function of the first kind

Y0 = zero order Bessel function of the second kind

Y1 = first-order Bessel function of the second kind2. The phase shift is added to φi (before the Wc correction, if used):

ϕ′ ϕi iJ x

Y x= +

′′

arctan( )

( )


2.1.Wave Theory

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