structure frequency responses under vibration forces

Numerical methods and mathematical models of Elmer
alexbrown
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Re: structure frequency responses under vibration forces

Post by alexbrown »

Thanks, Mika!

For the Shell Solver, as discussed before, it gave out incorrect eigen results for box-type structures. The case you metnioned below regarding eigen analysises dones't have right corners so it might be correct.

As you may understanding, right corner cases are quite common for shell structures. If the shell solver can not deal with this kind of cases, it is very difficult to use for many analysises.
mika wrote: 09 Sep 2020, 17:17
alexbrown wrote: 04 Sep 2020, 17:55 Another question, how to set the damping value of the harmonic analysis?
I just updated the source codes of both shell solvers in order to enable mass-proportional damping. If the material section has the command

Rayleigh Damping Alpha = Real ...

the solver should now create a damping matrix D = alpha * M, with M being the mass matrix. I didn't have time to run any shell case with damping, but in principle this should work after recompilation.

I nevertheless hesitate over how much time I'm willing to spend developing the facet shell solver, since the analysis presented in the article

Bernadou, M, Trouve, P. Approximation of general shell problems by flat plate elements. Part 2: Addition of a drilling degree of freedom. Comput. Mech., 6 , 359–378 (1990)

gives a good reason to think that for general shells the facet finite element approach gives curvature-dependent errors which cannot be reduced by refining the mesh. The article proposes a perturbation term and a way to estimate the shell curvatures to get rid of this error, but the facet shell solver of Elmer doesn't try to add such a modification. Moreover, the plate formulation used in Elmer is different from that used in the article, so one should perhaps do some maths to find an appropriate perturbation term for the Reissner-Mindlin model. I believe there are better approaches to general shell problems.
alexbrown wrote: 04 Sep 2020, 17:55 As the shell solver doens't seems to give correct results for eigen analysis
What makes you think that switching to eigenanalysis makes the solution obtained with the shell solver incorrect? There are some verification cases where the results of shell eigenanalysis has been compared with results given in literature, obtained with commercial software or given by other models of the same problem

https://github.com/ElmerCSC/elmerfem/tr ... s_Cylinder
https://github.com/ElmerCSC/elmerfem/tr ... _Spherical
https://github.com/ElmerCSC/elmerfem/tr ... enanalysis

If wrong results are obtained, I doubt the root reason may not be that the solution type is selected to be eigenanalysis, but something else.

A non-traditional feature of the (newer) shell solver of Elmer is that it models the straining in the normal direction. Unfortunately the normal strain is a difficult concept when the director data makes large jumps. It has now become known that the discontinuities in the director data would need some special treatment to get the equations right. Hopefully we can improve this somehow in future, so that this wouldn't be a cause for opting for the otherwise doubtful facet shell model.

On the other hand, the ability of the shell solver to model normal strain makes the coupling with solid elements more straightforward and we have recently developed some functionality related to such coupling. In addition to the test Shell_with_Solid_Eigenanalysis, other tests related to this option are

https://github.com/ElmerCSC/elmerfem/tr ... hmarkCase1
https://github.com/ElmerCSC/elmerfem/tr ... hmarkCase2
https://github.com/ElmerCSC/elmerfem/tr ... Solid_Beam
https://github.com/ElmerCSC/elmerfem/tr ... Beam_Eigen

I'm afraid trying to repeat these coupling tests with the facet shell solver would require more than a quick modification of the code. Adding beam sections would be an easier task by making some additional modularization. Nevertheless, with very limited resources it would be ideal to put efforts to developing one shell solver rather than sharing the work between two solvers. Perhaps this is an ideal thought as in some cases it might be nice to have an option to use solid shell elements (very special 3-D finite elements) and this would be a third approach.

-- Mika
mika
Posts: 236
Joined: 15 Sep 2009, 07:44

Re: structure frequency responses under vibration forces

Post by mika »

As it seems that a drilling rotation formulation may have a relative merit when the middle-surface is not smooth and the normal strain in the thickness direction is not of a primary interest, I updated the shell solver (in the devel branch) today to enable drilling degrees of freedom. With the new version the eigenanalysis results of the L-shaped beam case seem to be in agreement with the results obtained by other models. With a default stabilization parameter (the unity as in the facet shell solver) the eigenvalues are (compare with the results I sent earlier)

EigenSolve: Computed 10 Eigen Values
EigenSolve: --------------------------------
EigenSolve: 1: 1.243924E+03 0.000000E+00
EigenSolve: 2: 4.451749E+03 0.000000E+00
EigenSolve: 3: 4.789578E+04 0.000000E+00
EigenSolve: 4: 5.222013E+04 0.000000E+00
EigenSolve: 5: 1.465874E+05 0.000000E+00
EigenSolve: 6: 3.625226E+05 0.000000E+00
EigenSolve: 7: 4.757157E+05 0.000000E+00
EigenSolve: 8: 8.106630E+05 0.000000E+00
EigenSolve: 9: 1.314478E+06 0.000000E+00
EigenSolve: 10: 1.404925E+06 0.000000E+00
EigenSolve: --------------------------------

Now, if the command "Drilling DOFs = True" is given for the shell solver, the sixth field variable is taken to be a drilling rotation instead of the normal strain in the direction of the shell director. The implementation of drilling rotation formulation does not yet support all options and alters the meaning of all rotational DOFs/BCs, since the rotation variables used locally are related to the corresponding global variables via a rotation (by applying a cross product with the director vector). Therefore a sif generated for the normal strain formulation may not work with drilling DOFs without reconsidering BCs. Moreover, the drilling rotation implementation is still preliminary, so using drilling DOFs also breaks current coupling procedures for more advanced simulations.

The drilling rotation formulation comes with an adjustable stabilization parameter (a shell solver parameter "Drilling Stabilization Parameter"). Performing static analyses of the L-shaped beam case indicates that the results can be very sensitive with respect to the value of this parameter if it's too large. The default value (1.0) seems to give good results in this case.

-- Mika
mika
Posts: 236
Joined: 15 Sep 2009, 07:44

Re: structure frequency responses under vibration forces

Post by mika »

The issue with giving the imaginary part of a point load should now be resolved in the devel branch of the code repository. For example, if there exists a component variable "U Im 2", then the command "U 2 Load Im = Real ..." should define the imaginary part of the corresponding point load. Note the place of "Im" in the two expressions.

-- Mika
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