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solidDisplacementFoam linear? nonlinear?

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Old   November 6, 2016, 09:24
Default solidDisplacementFoam linear? nonlinear?
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Xiaoxue Shen
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Hi everyone,

I applied the solidDisplacementFoam to analyse a simple case, a plate (1m*1m*3mm) with four edges fixed ,and put a constant 10 Pa force on one of the remainder face, the other with 0 Pa(using tractionDisplacement BC). The geometry is in like picture "Selection_016.png". and I set the d2dt2Schemes under the fvSchemes dictionary Euler. The displacement of the point at center of the plate is like the "Selection_017.png". It seems that there is nonlinear factors in it.

But the solidDisplacementFoam solver is a linear solver, I was really confused about this. Anybody can help me with this... I would appreciate it very much.



The D dictionary is

version 2.0;
format ascii;
class volVectorField;
object D;
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions [0 1 0 0 0 0 0];

internalField uniform (0 0 0);

type fixedValue;
value uniform (0 0 0);
type tractionDisplacement;
traction uniform (0 0 0);
pressure uniform 0;
value uniform (0 0 0);
type tractionDisplacement;
traction uniform (0 0 0);
pressure uniform 10;
value uniform (0 0 0);

// ************************************************** *********************** //
Attached Images
File Type: png Selection_016.png (55.9 KB, 6 views)
File Type: png Selection_017.png (37.1 KB, 6 views)
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Old   November 30, 2016, 14:02
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Philip Cardiff
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Hi Xiaoxue Shen,

You are correct, solidDisplacementFoam assumes a linear analysis:
  • Linear geometry: small strains and rotations
  • Linear material: stress is linearly proportional to strain
  • Linear loading conditions: the standard boundary conditions are linear functions of displacement

Why do you think you are getting nonlinear results?

From your results for the displacement vs. time at the centre of the plate, the decay in the displacement amplitude suggests numerical dissipation: this is consistent with the use of a 1st order time integration scheme (backward Euler).

If you would like to reduce this numerical dissipation, you can try the following:
  • a smaller time-step
  • a higher order time differencing scheme e.g. "backward" is second order; though finite element methods typically use Newmark-beta schemes.

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Old   December 4, 2016, 21:37
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Xiaoxue Shen
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Hi Philip,

Sorry to say thanks to you so late. Yes, as you say, after changing a smaller time-step,the dissipation disappeared. And I have to learn more about theories and methods, thanks for your work of solid mechanics and your helpful papers.

Best wishes,

Xiaoxue Shen
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