Linear convergence with Lysmer element

[wklausler]

Hello FEAP community,

I am attempting to run dynamic mechanical simulations considering an arbitrarily large (ie. infinite) domain. For the solid quasi-static elastic part, use of a self-programmed infinite domain element on the structure boundary produces good results and converges quadratically. To handle boundary reflections, I have applied a FEAP Lysmer element (LABC) to the boundary of the finite region (between the finite domain elements and the infinite domain elements), and again the results are favorable. However, using the Lysmer surface element causes the each time step to converge linearly. Is this expected behavior? Could someone point me to literature on the matter?

Thanks and best regards,
wklausler

[Prof. R.L. Taylor]

Reference was:
!     Reference: "Finite dynamic model for infinite media", by
!                J. Lysmer and R.L. Kuhlemeyer, J. Eng. Mech, ASCE,
!                EM 4, August 1969, 859-877.

If convergence is only linear then there may be a "bug" in the coding.  Are you doing 2-d or 3-d?

[Prof. S. Govindjee]

My recollection is that the LysmerKuhlenmeyer element is linear so it should not create a problem with convergence.  Can you try a mesh without your infinite element to see what happens with the convergence?

[wklausler]

Dear Professors,

Thank you for your responses. I am doing 3D simulations with FEAP 8.6. The test case is a rod that is completely fixed in the transverse directions. With the infinite elements at the non-loaded end, there are no longitudinal Dirichlet boundary conditions. The infinite element formulation enforces zero displacements at infinity. Without the infinite domain element and with only the Lysmer element, the simulation quickly fails to converge. The loading conditions I've tested - all force based - do not yield large deformations.

Best regards,
wklausler

[Prof. S. Govindjee]

Can you post this last input file, the one with just the rod and the Lysmer element?

[wklausler]

Prof. Govindjee,

Please find attached the input file. When I run this file, the simulation fails to converge after a few time steps.

Best regards,
wklausler

[wklausler]

I also modified lysmerabc.f to bypass the checks of ctan(2)

[Prof. R.L. Taylor]

There is a missing 'xsj' in lysmerabc.f for the 3-d tangent.  At line 404 of the file add a multiply by 'xsj' on  the definition of 'shpab'.

I hope this helps correct the problem.   Please let us know.

[wklausler]

Yes, this has resolved the problem, thank you very much