Global System matrix assembly with different elements.

[Ronankeating]

Hi all,

I would like to know if its possible and consistent to compose the global system matrix with different FEM elements such as frame, plane, shell solid etc... Theoritically all of them will have the same DOF per node just only comprising the local matrix will differ. And as long as we solve the linear algebraic systems with any methods that shouldnit do any harm at all.

Your comments will be appreciated.

Regards,

 

[AlephZero]

There is no mathematical or numerical problems with this. The problem is what the results of the model mean. The issue is not so much different degrees of freedom but different shape functions at the faces or edges of the elements that are joined.

If the shape functions are different, the assembled structure will have cracks or overlaps when it deforms. That means the load transfer between the elements is inconsistent in some way.

Elements with different DOFs at the nodes will have different shape functions almost by definition, but doing something like joining several low-order elements to one higher-order element is also inconsistent.

Sometimes the results will still converge to the continuum mechanics solution in spite of the inconsistencies, but that is not guaranteed. You can sometimes make an arm-waving argument using St Venant's principle and say the errors are only local to where the incompatible elements join and don't affect the results elsewhere, but IMO you really need to do a numerical study to confirm that before you believe it.

 

[Ronankeating]

Thanks for that valuable post, as usual.

The thing you said really has made me pondered for a while, because I almost thought that I'm at "voila". What you said is really coherent and absolutely makes sense.
So, does that mean that I have no option left other than sub-structuring the whole structure, compound etcc ?

I also wonder, what kind of techniques are using nowadays s/w(Catia, Solid, etcc) for that discretization phase? Could you shed some light on that, as well?

Best Regards,

 

[AlephZero]

So, does that mean that I have no option left other than sub-structuring the whole structure, compound etcc ?

No, people make models joining incompatible elements quite often. You just have to think whether the way you are using the model is sensible.

For eaxmple, think about an object modeled with elements with only translation variables, and mounted on some pillars modeled with beams including rotation variables.

When you assemble the complete model, the joints are effectively pinned not built-in, because the rotation variable at the end of the each pillar isn't connected to anything else and can take any value it wants.

If that is a reasonable (conservative) assumption, you don't have a problem. If not, you need to add something to the model to constrain the rotation somehow.

 

[alphy]

I would like to address this question by saying that it is indeed possible to compose a global system matrix with different FEM elements. Theoretically, as long as the elements have the same degrees of freedom per node, the global matrix can be assembled without any issues. The local matrices for each element may differ, but as long as the linear algebraic systems are solved correctly, there should be no problems. This approach can actually provide more flexibility in modeling complex structures and can be a useful tool in many engineering and scientific applications. Of course, it is important to carefully consider the compatibility and consistency of the different elements used in order to ensure accurate results. Overall, the use of different FEM elements in the global system matrix assembly can be a valuable technique in the field of numerical analysis.