Supported suctural elements in FSI CalculiX OpenFOAM

Dear all,

I have a question regarding the element types I can use in FSI coupling between OpenFOAM and CalculiX. I recently run some tests with linear and second FE elements. The cases converge but the results seem different and I wonder if second order elements can be used in the coupling at all:

Typically, in FEA second order (Tet) elements are used, as they give more accurate results compared to linear elements (in particular linear Tets) and are more flexible in meshing complex geometries. In a FSI analysis in most cases the deformation of the structure takes place by the fluid pressure. If I would like to transfer the (fluid) pressure to forces for second order elements, as far as understood care has to be taken regarding the force distribution on the different nodes (distinguish between corner node and node on edge).

http://web.mit.edu/calculix_v2.7/CalculiX/ccx_2.7/doc/ccx/node147.html

I wonder if this kind of weighting (to distinguish between corner nodes and edge-nodes) is considered in preCICE for second order FE-elements or if there is no need to consider this (e.g. in a conservative nearest-projection coupling).
Thanks
Best regards

Ulrich

Hi Ulrich,

at the moment, there is no consideration for how the forces are applied to the nodes depending on their position in the mesh (corner or edge nodes). This is something that can be looked into, but we need to look at the coupling.

By modifying the value of a force on a node after reading in the forces from preCICE, preCICE will not know this. This can influence the stability and convergence of the Quasi-Newton schemes. preCICE thinks it is applying a specific load, but it actually is not, and therefore the results of the simulation are not due to the forces it sent to CalculiX.

However, I think this raises a good point and does need to be looked at. I think this should be tested after trying out with DLOAD instead.

Regards
Kyle

Dear Kyle,

thanks for your reply. Good to know this. This might be a general issue (not CalculiX only). I think the equivalent nodal force is caused by the shape function of the element. Please see the details here, in particular 3d quadratic isoparametric element:

http://rickbradford.co.uk/NodalForcesEquivalenttoPressure.pdf

So this might affect all second order elements in almost every FE-code. Or what do you think?

For the second order tetrahedral elements a pragmatic approach might be to use two different node groups in the mapping, one for displacement (with all nodes to preserve the spatial resolution) and the other one for forces using the mid-nodes only. For the tetrahedral second order element the corner nodes don’t carry any forces, the forces are distributed uniformly on the mid-nodes (each 1/3 of the pressure load). So if preCICE does only see element the mid-nodes for a conservative force mapping in case of second order tetrahedral element, the nodal load onto the individual nodes might be correct. Do you think this makes sense and is feasible?

Best regards

Ulrich

Dear Kyle,

I followed your suggestion and compared the DLoad in CalculiX with the CLoad on different node groups. I performed the test for tetrahedral second order elements. In one case I applied the corresponding force on all surface nodes (as preCICE seems to do for now), in the other case only on the mid-nodes of the elements to consider the theory for equivalent forces on second order elements. At least for displacement response (what is the most important outcome for me), I didn’t see a different between these conditions. Also the resulting displacement matches very well with the analytical solution. So far for me it seems the preCICE approach should be okay to use a uniform distribution on all nodes.

Best regards

Ulrich

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