Shell element performance: Orthotropic, Isotropic and Laminate

disla

Hi,

I have spent some time comparing our shell elements with other formulations and analytical results. Attached is a sample of one of the tests I have done with Cylindrical shells (Static).
I will be posting some more results.The aim of the analysis is not to criticize ccx or Mecway.I really love these priceless products. My main interest is to have clear which are the limitations of the Shells and how to sort them to achieve the best possible results. I would appreciate If you would like to share your experience and comment to help me and other users to get the best from MECWAY and Calculix.

This are some of my findings at this moment.

-Using the same mesh density, the overall results are irregular for strains and bad for stresses compared with other more advanced formulations. Strains converge to the expected results but with a higher computational cost. For the stresses, I still need some more time to find a response.

-Thin shells shows big locking for low mesh densities. This is most of the times solved with refinement of the mesh. Reduced integration do not solve the problem as much as I thought. I have some example file showing this.
I needed one or (normally) two additional refinements to achieve a comparable accuracy to elements designed specifically for the job (Composites for example).

-Surprisingly to me, shell elements in ccx and Internal solver seems to give better results for thick plates than for thin ones when talking about strains. That’s probably because they are expanded to 3D-brick elements.

-Mecway solves Laminates by transforming the composite layers into the equivalent orthotropic material by means of the ABD Matrix.
Ccx expands the composite shell element into a unique 3-D Brick element to solve and then, the stresses are computed using each layer property. This is possible because there are more integration points, and they are assigned the material properties appropriate for the layer they belong to. Slightly different than MECWAY Internal.

-One must be very careful using symmetry BC on Laminates. When going to the full model, one can verify that, that approach is risky for arbitrary directions of the plies and give incorrect results. I have some example file showing this but I just keep it for comparison.

-One must pay attention with the Orthotropic or Laminated element orientations which can be difficult to set up specially in curved surfaces.

-As Victor warn on a previous post, there are two indexing conventions around for Poisson Ratios that can be a source of errors when looking material databases.

-The E3 in Orthotropic and Laminates can mess the convergence if it is not high enough. 10*Max(E1,E2) seems to work well.

-Quadratic and reduced integration shells seems the safest combination for Calculix/Internal solver (sometimes it is the only option).


Regards

prop_design

hi disla,

i did tests along these lines as well, when i first started testing the composite capabilities of mecway. to your point here:

"-Surprisingly to me, shell elements in ccx and Internal solver seems to give better results for thick plates than for thin ones when talking about strains. That’s probably because they are expanded to 3D-brick elements. "

this doesn't surprise me at all. the aspect ratio of thin elements is far from the ideal 'cube' shape of quality factor 1.0

i tried to look into that myself but was seeing no difference. i was surprised that i didn't. so you found a way to see the issue. in my tests, a shell, laminate of 1 element thick, or laminate of say 8 elements thick, there wasn't much difference . the only thing better was more resolution through the thickness.

for your element orientation issues. it took me a long time and a lot of testing to get familiar with how to set them up. it actually ends up being very easy. however, it's a confusing thing. the element normals being aligned to local z gives unexpected orientations. so if you define you want the lams along x but the surface is curved. x ends up changing throughout the object. however, this is right if z is normal to the surface. in my case, i want that. so even though the program is doing the right thing, it looks weird and takes awhile to grasp.

not sure if it's useful to anyone, but, these were the issues i had:

1) mecway shell formulation won't work on the objects i have to analyze. mecway's shells seem to work more like plate elements than shells. i suggested to victor to have a better shell implementation. however, back then, mecway had it's nonlinear capability. so now it would do no good. i need composite laminates for nonlinear and nonlinear modal analysis. with cyclic symmetry too.

2) calculix has no actual shell element. at least when i tested. i think they introduced something recently. calculix expands shells to solids. this wastes tons of compute time and defeats the purpose of using a shell mesh in the first place. it also causes me a lot of modeling problems. often things will fail and i have to try making the cad model a different way. so a lot of trial and error and slow solves. i truly hate this about ccx.

3) can't define element orientation for solids. it's locked to global xyz. so even though ccx uses solids for composites, you can't actually make and run a solid model yourself. so it's frustrating. i suggested to victor to try making something that assigned element orientation based off the curvature of user selected model surfaces and worked inward. but i doubt this would get made. it would be a useful feature though. you would use quasi-isotropic coupon properties to handle laminates. they get input the same was as shells.

4) can't view the results of internal laminate layers of ccx models. about all you can do is use open cracks and peak in a little. it would be nice if you could see each layer to know which is failing. all you can do is look at the legend and know somewhere one or more layers are over stressed. then change the layup until you fix the problem. it's not too hard to work around but certainly not ideal.

anthony

disla

Thanks for your comments @prop-design

“3) can't define element orientation for solids. it's locked to global xyz. so even though ccx uses solids for composites, you can't actually make and run a solid model yourself “

Solid Element orientation accepts formulas. You are not forced to align it with the general axis. You could orient at least radially and tangentially.

“4) can't view the results of internal laminate layers of ccx models.”

I have been able to see inside the laminate with the cut tool bar on flat surfaces after opening cracks, but I recognize it is not the best solution.
I asked Victor to see if Open Cracks could be user adjusted.

prop_design

maybe something was updated wrt solid element orientation. i did my testing a long time ago. back then, even if you defined an element orientation for a solid, it was ignored. you can view the element orientation by clicking on an icon in the toolbar. i would check to see if it was actually applied.

disla

Problem 8 Nonlinear Bending of an Isotropic Plate. Validation File.

Thin shells shows important Locking for small mesh density (4x4).
Acceptable results for displacements starts after the first refinements.
Compared with the Analytical solution and reference element.
Ploted 8x8 mesh S8 Element.
Linear analysis in this case (Thin Plate) would give wrong results even for such an small displacement (comparable to the thickness of the shell - 2mm ).

disla

EDITED. 23/05/2022

Another Validation File.
Static and Nonlinear Quasi-Static Analysis of Cantilever Plate.

I’m looking at Stresses and through thickness Shear Stress in the shell.

To obtain through thickness stress and shear detail in the shell elements I have created a Isotropic/laminated material with two exactly the same material properties.
This forces Ccx to generate additional through thickness integration points. See ccx manual v.2.19 pag 106. It is also interesting as the Laminate should theoretically approximate to the isotropic behavior under this conditions. Isotropic is also included in the comparison.
E1=E2 , E3=10Max(E1,E2) and G12=G23=G31=E/2(1+Nu)

Some preliminary conclusions:

-CalculiX shell element provides uniform shear stress through thickness that agrees perfectly with FSDT theory (could be nonconservative)
-The "Isotropic/Laminated" aproach behaves as spected.
-Shear results for the Static Analysis and ISOTROPIC agrees perfectly for S8R but give wrong results when using full integration S8.
-Shear Stress for large deflections can't be postprocesed correctly as Mecway nor ccx can't plot out of plane Shear Stress in element coordinates.

See post for details:

https://calculix.discourse.group/t/orthotropic-shell-plate-analysis/1086

Victor

I'm now replacing the internal solver's quad4 shell element with an improved formulation (MITC4). It was already something like a flat-plate equivalent but the new one works better with non-planar and non-rectangular elements. It will also have more solution variables such as out-of-plane shear stresses and forces.

prop_design

Is there a way to apply the new formulation to tets and quads with midside nodes? Will it work with laminates?

Victor

Tet, I'm not sure, but yes, there's a similar formulation for quad8 and tri6. I just haven't worked on that yet and don't want to overpromise. Yes, it will work with laminates.

prop_design

thanks. sounds exciting. i may be using the wrong terminology when i said tet. i think when you said tri6, that is probably what i meant. basically a triangular surface element with midside nodes. it seems like netgen is best at making those. the quad dominant option sometimes produces nodes that aren't connected to anything. although i had netgen do that with triangles once too. anyways, looking forward to this. thanks for continuing to make improvements.