Computational Mechanics and Signatures

Presented to the National AcademySept. 30, 2009

Luise CouchmanCode 331

Office of Naval Research

6.1 Computational MechanicsCode 331, Ship Systems & Engineering DivisionCode 331, Ship Systems & Engineering Division

34AX Couchman

Program Objective/Goal:Develop fundamental advances in the state of the art of physics-based modeling of mechanical structures. Via experiments and simulations obtain improved understanding of the linear and nonlinear mechanical behavior of complex structures. Apply the enhanced understanding to develop approaches for predicting the behavior. Develop physics- based models and evaluate their predictive capability against measurement. Develop methods for increasing the speed of input model generation.

Rationale:• Requirement for much more efficient, accurate modeling

of highly complex structures• Currently months-long input model generation times

S&T Products/Deliverables:• Advanced techniques for structural modeling

• Advanced techniques for speeding input model generation

Major Accomplishments:• XFEM, Extended Finite Element Method (Ted

Belytschko, Northwestern U) Fields Medal• Isogeometric Analysis (Thomas R. Hughes, Stanford/U.

Texas)• LOGOS Fast Linear Equation Solver (Robert Adams, U.

Kentucky)• Ghost Fluid Stabilized Method (Charbel Farhat,

Stanford)• FETI Substructuring Method for Shells (Charbel Farhat,

U. Colorado/Stanford)• DEM Finite Element Approach (Charbel Farhat, U.

Colorado/Stanford)

Description of work in FRC: Improve the accuracy and efficiency of the modeling of the linear and nonlinear mechanical behavior of complex structures

Primary S&T Focus Area /Sub Area: Survivability and Self-Defense

Secondary S&T Focus Area(s) /Sub Area(s): Affordability, Maintainability, and Reliability

Customers: Navy Shipbuilders, Navy Ship Acquisition Programs, NAVSEA Warrant Holders and their SME’s

Current Focus:• Fundamental Computational Mechanics• Residual Strength of Structures in Fire• Air Blast• Rapid Input Model Generation

Interelement crack method

XFEM

Results for Kalthoff Experiment

ExperimentElement Deletion

Displacement field is decomposed into continuous and discontinuous parts

Level sets are used to describe the topology of the discontinuity (crack)

cont disc enrich

continuous discontinuous

enrichment

, , , ,

, ,

, , ,

I I J JI J

K KK

t t t t

N t N H t t t

N t t t

u X u X u X u X

X u X X X q

X X X r

ε

XFEMT. Belytschko

Northwestern U.

New Method for Treating Fluid Structure Interaction and Two-phase Flows: GFSMP - FSI

Log

(rela

tive

erro

r)

‐12 ‐10 ‐8 ‐6 ‐4 ‐2 0‐14

‐12

‐10

‐8

‐6

‐4

‐2

0

Log (t)

2.01

Previous GFSM – FSI New Stanford GFSMP - FSI

Structure surface mesh (S)

Fluid mesh with ghost domain (F)

Real nodes Ghost nodes

fluid sidestructure

side

FSI

Theoretical justification or analysis -

NONE

Extensive numerical experiments -

only 1st-order accuracy exhibited in all cases

Stanford Analysis-

At the fluid-structure interface

GFSM is unconditionally inconsistent at the FSI!

This reduces its accuracy elsewhere from 2nd-orderto 1st-order

c2tcut

= ( )ux

+ O(t) + O(x)4x2

• Fundamentally new approach to structural modeling

• Based on technologies (e.g., NURBS) from computational geometry used in:

– Design (CAD) – Animation– Graphic art– Visualization

• Includes standard FEA as a special case, but offers other possibilities:

– Integration of design and analysis– Superior approximation properties– More robust analysis– Precise and efficient geometric

modeling

N

nnn xPaxu

1)()(

Isogeometric

Analysis: A New Finite Element Method

Thomas J. R. Hughes

University of Texas at Austin

NURBS Have Better Approximation Properties

Lagrange polynomials

p=7p=5p=3

NURBS

p=7p=5p=3

NURBS Give Lower Frequency Errors:

Comparison of FEM and NURBS Frequency

Errors for Vibration of a Finite Elastic Rod with Fixed

Ends

FEM

NURBS

h

h / n / N

Acoustic branch

Optical branch

Variation Diminishing Property

Fire on Naval Composite Structures (BA1, NICOP, SBIRs)Vision:• Understanding of heat conduction, charring, buckling, and residual strength of composites under simultaneous heat and load• Models to predict failure timesCritical Scientific IssueThe failure of composites during a fire involves a wide range of physical and chemical effects which are still poorly understood, and thus cannot be predicted when applying them in a design.Approach:

Via testing and analysis determine the significant physical effects and develop the ability to model them

Debonding

Microcracking

Multi-layerLaminate

Fire-protection

Burning

Outgassing

Bal

sa c

ore

Load

Load

Bur

ner

0 500 1000 1500 20000

50

100

150

200

250

Edg

ewis

e C

ompr

essi

ve S

treng

th (M

Pa)

Exposure Time (s)

Skin Failure

Buckling Failure

Sam

ple

Modeling of Blast Failure of FRP Composite Ship Structures:

UCSD

• Objective:–develop an understanding and predictive capability for

the failure of naval composites under blast.• Approach:

–Via small and large-scale testing develop the understanding and material parameters required to develop a predictive model

–DDG1000 is providing the Quarter-Scale Deckhouse to UCSD for sample extraction

–DDG1000 is sending funding to conduct tests on the quarter-scale deckhouse specimens

Nose Geometry

Elastomer Foam

Computational SignaturesCode 331, Ship Systems & Engineering DivisionCode 331, Ship Systems & Engineering Division

34AR Couchman

Technical Approach:Develop fundamental advances in the state of the art of signature modeling

Recent Breakthroughs• Sub-grid Modeling was developed under this

program• Energy Finite Element Analysis (EFEA) developed

under this program is replacing the conventional Statistical Energy Analysis (SEA)

S&T Products/Deliverables:• Ability to analyze whole-ship models• Rapid transition between disciplines, eg. acoustic,

magnetic, radar• Rapid turn-around of predictions

Description of work in FRC: Develop improved understanding and predictive capabilities for ship and submarine acoustic and electromagnetic signatures. Develop algorithms and methods that will enable the development of improved design, analysis, and prediction tools.

Primary S&T Focus Area /Sub Area: Survivability and Self-Defense

Secondary S&T Focus Area(s) /Sub Area(s): Affordability, Maintainability, and Reliability

Program Objective/Goal:• Increased reliability and efficiency of signatures

prediction• Early integration of signatures effects into the design• Multi-disciplinary optimization of the early concept

design over signatures, structures, and hydrodynamics• Rapid re-evaluation of effects of design changes on

signatures• Decreased need for re-design due to failure to meet

signature requirements

S&T Technical Challenges/Issues:• More accurate and efficient modeling of acoustic and

EM signatures of highly complex platforms and systems

• Greatly decreased input model generation times

Energy Finite Element MethodVlahopoulos, Univ. of Michigan

Validation

6

4

2

5

3

1

7

Finite Element Analysis• Take pressure or displacement as the

unknown quantity• Approximate the unknown as a sum over a

basis set• Find an approximate solution to the

differential equation by a variational approach

Energy Finite Element Analysis• Take energy as the unknown quantity

EFEA Model

n

n xcxu )()(

Displacement continuous across a joint

Energy density discontinuous across a joint

uuu )(2

022 pk

Energy Finite Element Analysis on CVN78 (Collaboration of U. Mich. with Northrop Grumman Newport News)

• CVN 78 is the first CVN to have radiated noise goals

• Meeting those goals within the Program’s cost and weight limits requires detailed knowledge of the hull’s noise transmission properties

– Very little test data exists from previous CVN’s– Data from other surface combatants does not apply due to large

differences in plate thickness

• Existing noise prediction tools were not suited to the extremely large size of the CVN

• Developed under ONR sponsorship, the Energy Finite Element Analysis method meets the program’s needs

– Geometry taken directly from existing hull structural models →

No new geometry creation required

– Coarse computational mesh means smaller models than conventional FEA approaches → Faster run times

– EFEA code operates on a PC in Windows environment → No special hardware / software required

– Substructuring feature allows tradeoff between model size, run times, and available PC memory

– Previous code validation ensures confidence and reduces risk

Conventiona l FEA

Energy Finite Element Model

A Technology Transition SuccessA Technology Transition Success

Implosion: Integrated BA1-FNC Program Multidisciplinary University Research Initiative:Develop improved methods for modeling both

the failure of the structure and the resulting two-phase flow.

In addition, due to the complexity and multidisciplinary nature of the physics, significant effort is required in order to produce highly efficient numerical methods to evaluate the physical model.

FNC EPE-FY08-06:• Develop validated, user-friendly tools

enabling the designer to predict the implosion of payloads of all sizes, implosion effects, and mitigation techniques:

1)

a payload design tool, and 2)

a physics-based model for complex analyses.

• Develop the relevant materials data base• Validate against small and large scale data

Other BA1 Base Programs Leveraged:• Computational Mechanics base program

(Couchman)• Solid Mechanics base program (Barsoum)• National Naval Responsibility in Naval

Engineering (Cooper)

NAVSEA Small Business Program (SBIR):Conduct large-scale at-sea implosion tests

Background:

NAVSEA 05P and NAVSEA 05U approached ONR to request assistance on the issue of implosion.

Inability to predict accurately enough the magnitude of shock waves produced by the implosion of underwater structures is resulting in extremely conservative designs, and in some cases obviating the approval of desired systems and functions. Thkl;atlakehtlaksetjl;askjtlkasetjBA1/BA2 Base Program Dedicated to Implosion:

develop an improved understanding of the process of implosion, including the precise mode of failure, the mechanism of production of the shock wave, the importance of fluid jets through fractures in the structure, the onset and rate of structural collapse, cavitation, and the two-phase fluid dynamics of the shock wave.

Aluminum

6.1 Program Tank Tests NAVSEA SBIR: Large-scale At-sea Tests

Description: Develop the capability to design and qualify external payloads for implosion avoidance and platform survivability. Current inability to predict implosion effects requires severe conservatism in payload design, limiting payload capability and impacting cost and schedule.

FNC Product: Payload Implosion and Platform Damage AvoidanceCode 331, Ship Systems & Engineering DivisionCode 331, Ship Systems & Engineering Division

3DA2 Couchman

Program Objective/Goal:The affordable introduction of new underwater vehicles capabilities using external payloads requires the development of design tools for modeling payload implosion and its effects on the platform. This would remove the most significant obstacle to the Navy’s goal of affordably enhancing warfighting capability using external payloads, without restricting operating depth or payload capability.

S&T Technical Challenges/Issues:• Inadequate ability to predict the implosion

pressure pulse• Difficulty of conducting validation experiments• Unavailability of material-parameters data

Technical Approach:• Develop a physics-based tool to model the

implosion pressure pulse and platform damage• Validate via small and large-scale tests• Develop the relevant materials data base• Develop a rapid design tool based on the

experiments and physics-based model results.

S&T Products/Deliverables:Validated, user-friendly tools enabling the designer to predict the implosion of payloads of all sizes, the magnitude of the implosion pressure pulse, and the efficacy of mitigation techniques:

1) a payload design tool for conventional geometries, and

2) a physics-based model for complex analyses

Task E’Test Series

Plan Task A – Weidlinger United KingdomAt-Sea Testing

Task BFabrication

Task C – UT AustinMaterial Characterization

Task D – Stanford/NorthwesternPhysics-Based Model Development

Task E - WeidlingerDesign/Assessment Tool Development

Task D – Navy LabsPre-test Calculations

Task D – Navy LabsCode Validation Against At-Sea Data

FY08 FY09 FY10 FY11 FY12

Task FPressure Tank Testing

Time (msec)

Pre

ssur

e (p

si)

TASK D – PHYSICS BASED COMPUTATIONAL MODEL DEVELOPMENT

100

150

200

250

300

350

400

0.0004 0.0009 0.0014 0.0019 0.0024 0.0029 0.0034

Experimental

AERO-F/XFEM(coarse mesh inside)