mechanical nonlin 13.0 ws 09b singularities

8/12/2019 Mechanical Nonlin 13.0 WS 09B Singularities

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Customer Training Material

or s op

Sin ularities

Structural Nonlinearities

WS9B-1ANSYS, Inc. Proprietary

2010 ANSYS, Inc. All rights reserved.Release 13.0

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ANSYS Mechanical Structural Nonlinearities

Customer Training MaterialWorkshop 9B: Singularities

Goal

Diagnose convergence trouble related to large deflection of hyperelastic

material bonded to steel plate

ac groun

Large model representing a series of

rubber isolators glued to thin steel

plates fails to converge at about 30% of

total load when under a large deflection

dominated by shear deformation.

Material was tested extensively in all

modes of loading and test data

produced very good curve fit of 3rd

order Ogden hyperelasticity model.

Bonded contact defined between rubber



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isolator and steel plate. c ure use w perm ss onfrom Penn State University.


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Model Description

The same convergence failure was replicated with a simplified

representation using a 2D Plane Stress Model



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Steps to Follow:

Restore Archive browse for file W9b-singularities.wbpz

Save as

File name: W9b-singularities

Save as t e: Workbench Pro ect Files *.wb



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Customer Training Material Workshop 9B: Singularities

The project Schematic should look like the

picture to the right.

From this Schematic, you can see that the

Engineering (material) Data and Geometry have

already been defined (green check marks).

It remains to set up and run the FE model in

ec an ca

Highlight the Engineering Data Cell and open by

(RMB)=>Edit to verify the predefined 3rd Order

Ogden material properties.

Verif that the units are in Metric Tonne mm ..

system. If not, fix this by clicking on

Utility Menu=>Units=>Metric(Tonne, mm,..)



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e urn o e ro ec c ema c.

Double click on the Model Cell to open the FE Model (Mechanical

Session) (or RMB=>Edit)



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nce ns e e ec an ca app ca on, ver y e wor ng un sys em

Unit > Metric (mm,kg,N,s,mV,mA)

The model is already set up with a bonded contact region, a fixed

the rubber body. Highlight the entities beneath each folder to become familiar with the

model and to confirm that it is ro erl su orted and loaded and read

to solve.

Review the Analysis Settings

Execute a Solve



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After solution run is complete, highlight the Solution Information

folder and inspect the Force Convergence Graph.

After a number of bisections, the solution fails to converge at 30% ofoa



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Review the Total Deformation results.

Notice the element deformation in lower right corner of isolator/steel

interface



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Review the Newton Raphson Force residual plot.

Notice the concentration of strain energy in this corner.

The source of trouble is a eometric sin ularit at this location.



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To test this theory, we will introduce a very small radius at this corner

and rerun the analysis

Return to the Project Schematic.

Highlight the Geometry Cell

RMB > Replace Geometry > Browse for radius.agdb

radius.agdb represents a

modified geometry (with small

radius already incorporated)

Highlight the Model Cell

From Utility Menu > Refresh Project



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Return to Mechanical Interface

The small radius should be visible in lower right hand corner



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Execute another SOLVE

After a few bisections, the solution now converges successfully.



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Post Process the results.



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Conclusions:

This exercise underscores the importance of considering the influence

that singularities can have on convergence stability and quality of results

.

In this example: The hyperelastic material model was correct.

.

The bonded contact had been properly defined but was insufficient to

deal with the inherent instability at the sharp corner and the eventualen a ement of the side face with the lower boundar .

The mesh was sufficient for the problem. No amount of further mesh

refinement at the sharp corner would improve the convergence.

No Analysis Settings (more substeps, different solver) could

overcome the problem.



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mechanical nonlin 13.0 ws 09b singularities

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