104 - understand large deformation analyses.pdf

8/14/2019 104 - Understand Large Deformation Analyses.pdf

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Structural Analysis I

Understand Large Deformation Analyses Lecture

UnderstandingLargeDeformationAnalyses.mp3

Understanding Large Deformation AnalysesA Large Deformation Static Analysis can be used to calculategeometrically nonlinear static results for a Mechanica simulationmodel. These results can be stresses, deformations, and strains.

Geometrical NonLinearities

Material (Nonlinear elastics, viscosoty) Geometrical (Large Deformation, Post-Buckling) Boundary (Contact)

Large Deformation Analysis Inputs:

No Bearing Loads Distribution limited to Total Load or Total Load at Point No temperature dependent material No Beam/Shell Idealizations

Large Deformation Analysis Outputs:

Stresses Deformations Almansi strains (no measures)


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Elastic material undergoing large deformation

Hyperelastic material undergoing large deformation

Lecture Notes

Geometrical Nonlinearities


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There are three types of nonlinearities:

Material nonlinearity (nonlinear elastic behavior, viscosity, and so on) Geometrical nonlinearity (large deformations, post-buckling behavior) Boundary nonlinearity (contact)

When using a software program that is based on a linear assumption, you will find thatdoubling a load causes displacements and stresses to double. This technique workswell for a cantilevered beam that displaces very little in comparison to its length. Onthe other hand, if you consider a strongly bent fishing rod, the bent rod responds to anincremental load much differently than the originally straight rod responds. Paper clipsare also subjected to back and forth bending as well as soda cans that are subjected tocompressive forces (buckling). In all these cases the models exhibit largedeformations.

In reality there is not a specific state of nonlinearity, but rather a combination of any

of these types. Ultimately, based on the investigation carried out in the field or lab(dramatic distortions, extreme thinning of the part features, cracks, fissures, and soon) and with help from Mechanica you should be able to identify the type ofnonlinearity.

Mechanica supports linear elastic and hyperelastic materials for Large DeformationAnalysis. When using linear elastic materials for a Large Deformation Analysis,Mechanica interprets material properties according to a natural generalization of linearelasticity. E and are converted to the Lame constants and , using the sameformulas as used in linear elasticity. Stresses are calculated by using the neo-Hookeanmaterial law, which depends linearly on and .

For more information on neo-Hookean material, see Nonlinear Continuumfor Finite Element Analysis, Javier Bonet and Richard D. Wood (CambridgeUniversity Press: 1997).

Large Deformation Static Analysis Input.

The input for a Large Deformation Analysis can be any combination of loads andboundary constraints. However, no Bearing loads are allowed and the distribution formost other loads (Pressure, Surface/Edge/Curve/Point, and so on) is restricted to TotalLoad or Total Load at a Point. No temperature dependent materials are allowed andthe Beam and Shell elements are not supported for this type of analysis.

Large Deformation Static Analysis Output.

You can evaluate stresses and deformations with a Large Deformation Static Analysis.Mechanica reports Almansi strains but, the resultant measures are not currently


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available for this analysis type.

Best Practices You may want to perform a linear Static Analysis first to determine whether

geometrically nonlinear results are required. You may also want to perform alinear Buckling Analysis. If the load factor is greater than the critical buckling

load factor for your model, the Large Deformation Static Analysis may eithertake long time to converge, or may not converge to a solution. If you run aBuckling Analysis that indicates your model will buckle, you can reduce run timefor a Large Deformation Static Analysis by using a load that is less than thelinear buckling load.

Be aware that in some cases the results of linear Static Analysis and BucklingAnalysis may not accurately predict what will actually occur in a LargeDeformation Static Analysis.

Understand Large Deformation Analyses Demonstration

UnderstandingLargeDeformationAnalyses_demo.mp4

Understand Large Deformation Analyses Procedure

Procedure: Creating Large Deformation Analyses

ScenarioIn this procedure, you will define a Static Analysis including the Calculation of large

deformations in a Pro/ENGINEER part model for which loads and constraints were alreadycreated and defined.

CreateLDA clip.prt

Task 1. Open the Mechanica Application and define a Static Analysis with LargeDeformations.

1. Click Applications > Mechanica .

2. Click Mechanica Analyses/Studies from the main toolbar.

3. Click File > New Static...

4. In the Name field type CLIP_LDA .


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5. Verify that the SUPPORT constraint is selected in the Constraints area of the dialogbox.

6. Verify that the FINGER load is selected in the Loads area of the dialog box.

7. Select the Nonlinear check box, then select the Calculate large deformations check box.

8. Select the Convergence tab and verify that the Method drop-down menu is set toSingle-Pass Adaptive .

Note: The Multi-Pass Adaptive convergence method is not available for LargeDeformation Static Analyses.


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9. Select the Output tab and verify that the Stresses , Rotations , and Reactions check boxes are selected, and that Plotting Grid is set to 4 .

10. Select the Load Intervals tab. Type 4 in the Number of Intervals field and clickSpace Equally .

For example, if the load is 5 N then, Mechanica will reportstress/deformations/strains at 25% of the load (1.25 N), 50% (i.e., 2.5 N),and so on. Using this Number of Intervals option enables you to detect thebehavior of the model as it deforms geometrically nonlinearly.Here, the load interval is being shown so you are familiar with the procedurefor defining the Number of Intervals. In real-life examples, this number mayvary depending on your application. Mechanica limits this option to 99intervals.As a handy tip, if you are concerned only with the stress and deformation ofyour model with the load fully applied, you should use the default of 1 for

the Number of Intervals.

11. The dialog box should now appear as shown in the figure. Click OK to completethe Static Analysis Definition and close the dialog box.


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Task 2. Save the model and erase it from memory.

1. Return to the Standard Pro/ENGINEER mode by clicking Applications > Standard .

2. Click Save from the main toolbar and click OK to save the model.

3. Click File > Erase > Current > Yes to erase the model from memory.

This completes the procedure.

Understand Large Deformation Analyses Exercise

Exercise: Large Deformation Analysis


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Objectives

After successfully completing this exercise, you will be able to:

Run a Large Deformation Analysis. Compare a Static versus a Large Deformation Analysis results for the same model.

Use a predefined hyper-elastic material.

ScenarioIn this exercise, you will use Mechanica to evaluate the stresses and deformations in a 3DPro/ENGINEER assembly model subjected to steady loads and constraints. Thecomponents of the assembly are bonded together by a piece of an elastomer. You areinterested in the effects on this bonding component when the pieces are pulled away fromeach other. This investigation will be carried out using a linear Static Analysis and thencompared to a Large Deformation Analysis.

The assembly model has two plates made out of steel which are bonded together by a

piece of rubber. The model is held in place at the end of one of the steel plates and pulledaway at the other. The loads and constraints are already defined in the model. Becausehyper-elastic materials (such as rubber) are nonlinear materials they will exhibitinstantaneous elastic response to large strains. You will examine the behavior of thiselastomer under the current loads and constraints.

LDAHanger hanger.asm

Task 1. Open the Mechanica application, explore the existing Mechanica simulationfeatures, and review the predefined URETHANE material.

1. Click Applications > Mechanica .

2. Explore and examine the model. From the top of the Model Tree, click Show >Expand All . Scroll to the bottom of the model tree and review the existingMechanica simulation features.


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Note that a number of Mechanica features have already been createdincluding:

The STEEL and URETHANE material definitions. Loads and Constraints.

3. Right-click the URETHANE material in the model tree and select Edit Definition .

Note that the material Sub Type is set to Hyperelastic and the Define ByTest check box is selected.

Since Hyperelastic Materials are beyond the scope of this course, thematerial has been created for you.


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4. In the Material Model area of the dialog box, click Edit to bring up the Hyperelastic

Material Definition dialog box so you can explore how the material behavior hasbeen defined.

5. Examine the Hyperelastic Material Definition dialog box.

Note that the left side of the dialog box contains a Strain-Stress table thatwas obtained from a physical test of the material. These test results aregraphed in the center of the section of the dialog box and Best Fit MaterialModel Curves are displayed with it. On the right side of the dialog box, youcan see that Select Material Model field is set to Automatic . As result of thissetting, the Mooney-Rivlin model has been selected as the best fit and itsBest Fit Coefficients are used to define the model.


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6. Click OK when you are done examining the Hyperelastic Material Definition dialogbox.

7. Click OK to close the Material Definition dialog box.

Task 2. Assign STEEL to the two steel plates (PLATE_2.PRT) components andURETHANE to the ELASTOMER_INSERT.PRT component.

1. Click Material Assignment from the Mechanica toolbar.

2. Press CTRL and select both of the PLATE_2.PRT components from the model tree asshown in the figure.

3. In the Properties area of the dialog box, verify that the Material drop-down menu isset to STEEL .

4. Type SOLID_PLATES in the Name field.5. The dialog box should now appear as shown in the figure. Click OK to complete the

Material Assignment and close the dialog box.


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6. Click Material Assignment from the Mechanica toolbar.

7. Select the ELASTOMER_INSERT.PRT components from the model tree.

8. In the Properties area of the dialog box, select URETHANE from the Material drop-down menu.

9. The dialog box should now appear as shown in the figure. Click OK to complete theMaterial Assignment and close the dialog box.

Task 3. Define Static and Large Deformation Analyses for the assembly.

1. From the Main toolbar, click Mechanica Analyses/Studies .


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2. Click File > New Static...

3. In the Name field, type HANGER_LINEAR .

4. Verify that the HOLD Constraint is selected in the Constraints area of the dialogbox.

5. Verify that the PULL Load is selected in the Loads area of the dialog box.

6. The dialog box should appear as shown in the figure. Click OK to complete theStatic Analysis Definition and close the dialog box.

7. Verify that HANGER_LINEAR is selected from the Analyses and Design Studiesdialog box.

8. Click Copy to copy the analysis.

9. Right-click Copy_of_HANGER_LINEAR and select Edit...

10. In the Name field, type HANGER_LDA .


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11. Verify that the HOLD Constraint is selected in the Constraints area of the dialogbox.

12. Verify that the PULL Load is selected in the Loads area of the dialog box.

13. Select the Nonlinear check box, then select the Calculate large deformations check box.

14. Select the Load Intervals tab if necessary.

15. Type 4 in the scroll box for Number of Intervals and click Space Equally .

16. The dialog box should appear as shown in the figure. Click OK to finish the StaticAnalysis Definition and close dialog box.

Task 4. Run the HANGER_LINEAR and HANGER_LDA analyses and compare theirresults.

1. Select HANGER_LINEAR from the Analyses and Design Studies dialog box and

click Start Run > Yes . Click Confirm in the Confirmation dialog box to run the


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analysis for the non-linear material with small strain properties of the material asshown in the figure.

2. Click Display Study Status once the analysis is started.

The analysis should complete in less than one minute.

3. When the analysis is complete, make note of the max_disp_mag andmax_stress_vm measures.

max_disp_mag 15.8 mm and max_stress_vm 285 MPa

4. Select HANGER_LDA from the Analyses and Design Studies dialog box and click

Start Run > Yes to start the design study.

5. Click Display Study Status once the analysis is started.


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The analysis should complete in 10-15 minutes. If you do not have time towait for this analysis to complete, consider using the results in theComplete directory for comparison with the HANGER_LINEAR results.

6. When the analysis is complete, make note of the max_disp_mag and

max_stress_vm measures.

max_disp_mag 8.8 mm and max_stress_vm 226 MPa

Note that the results for the same model when Calculating LargeDeformations is about 40% less for displacement and 25% less formaximum von Mises Stress.You can observe that the model maximum deformation and von Misesstresses appreciably between the Static Analysis and the Calculate LargeDeformations analysis. In this case, the correct results are from the LargeDeformation Analysis due to the fact the deformation in the elastomerdoesn't vary linearly with the load. This type of analysis is also know as ageometrically non-linear analysis.

7. Click Close to close all open Run Status windows and click Close to close all openDiagnostics windows.

8. Select HANGER_LINEAR from the Analyses and Design Studies dialog box andclick Results to enter results mode.

9. Type LINEAR in the Name field and Static Linear in the Title field.


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10. Verify that the Display Type drop-down menu is set to Fringe .

11. Select Displacement from the first drop-down menu on the Quantity tab andverify that the Unit drop-down menu is set to mm and that the Component drop-down menu is set to Magnitude .

12. Select the Display Options tab and select the Deformed and Animate checkboxes.

13. Click OK and Show to finish the Results Window Definition and show the results.

14. Click Copy from the main toolbar in the Results Window.

15. Type LDA in the Name field and Static LDA in the Title field.

16. Click Open Results , select HANGER_LDA and click Open .

17. If necessary, select the % check box next to the Scaling field.

18. Select step 4 from the Steps area.19. Verify that the Display Type drop-down menu is set to Fringe .

20. Select the Quantity tab.

21. Select Displacement from the first drop-down menu on the Quantity tab andverify that the Unit drop-down menu is set to mm and that the Component drop-down menu is set to Magnitude .

22. Click OK and Show to finish the Results Window Definition and show the results.

23. When you are finished reviewing the results, click File > Exit Results > No toexit the Result Window without saving any results.


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Task 5. Save the model and erase it from memory.

1. Click Save from the main toolbar and click OK to save the model.

2. Click File > Close Window .

3. Click File > Erase > Not Displayed > OK to erase the model from memory.

4. If necessary, click Close from the Summary window and click Close to close theDiagnostics window.

This completes the exercise.

104 - understand large deformation analyses.pdf

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