Stiffness of tri and tet elements 3

[Tunalover]

I took an FEA methods course one time that went over element types. The course said that quad and hex element meshes were the best provided certain aspect ratios were not exceeded, and that tri and tet element meshes were "stiff" and tended to overestimate stresses. This was in the 80's. Have the software programs progressed to overcome this one-time weakness of tri and tet elements? The reason I ask is that I recently used an FEA code that meshes only in tet elements. The code, however, was a CFD code. When solving CFD problems is there an inherent weakness with tet elements like there once was with stress problems? TIA for your thoughts.



Tunalover

 

[Tunalover]

Of all the FEA gurus in this forum, does no one have this knowledge that seems so fundamental?


Tunalover

 

[GregLocock]

no guru me, but

http://www.colorado.edu/engineering...AFEM.pr.06.CMM.d/CarlMullerMeadows.report.pdf

Cheers

Greg Locock


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[inline6]

in ansys they recommend inflation on the boundary/walls for a CFD tet mesh but a fine enough tet mesh still works. CFD and FEA are not the same as far as limitations with elements are concerned.

 

[Tunalover]

inline6:
ANSYS CFD consists of Fluent and Icepak, both of which are Finite Difference Method programs where element types and aspect ratios are not as important as with FEA software. Am I just refining your statement?




Tunalover

 

[Tunalover]

Greg,
Thanks for the link. That's a pretty thorough and lengthy paper so I just read the conclusion. The conclusion said basically "brick elements are better than tetrahedron elements" but didn't really explain why. But in the body of the paper it said that tetrahedral elements are stiffer (as I was taught) but in the brief scan of the paper I didn't see anything in the way of validation of that statement.

Bruce Jackson
aka Tunalover


Tunalover

 

[csk62]

The paper does a very good job of explaining why hex elements are better than tets for the purpose of stress analysis.

Only looking at the case of linear elements, we see that the tetrahedron element has only one integration point in the entire element. I have seen some people even call these "constant strain" elements because there cannot be a strain/stress gradient throughout the element, if it only has one integration point.

Comparing this to the linear hexahedral (8 node element), there are two integration points in each orthogonal direction for the master element. Clearly, there can now be a strain/stress gradient in the element.

The way stress is computed in FEA requires that integration point value is mapped to the nodes on the elements, and then we acquire our nodal stresses.

The answer I think you are looking for is that tet elements are usually not considered sufficient for most analyses that require a reasonable level of accuracy for calculating stress. That being said, the computational cost is different.

I try to use tet elements in places where A) nice hex mapped meshes are not easy to create, and B) we don't care about high strains, etc.

That being said, what I just said applies only to structural FEA. I have very little experience with CFD, and I realize that the fundamental differential equations are different, but I would be willing to extend this analogy if you want a simple answer.

 

[hokhay]

I have used Fluent for two years and now I am using NX Nastran for structural simulation. Although the fundamental theory of fluid and structural analysis are different, their methodology are similar, finite element.
One thing in common in finite element is data is computed at the integration point and result between each element is computed by taking average from integration point of two elements.

Since hex element has more faces than tri element, a single hex element has more connections with other elements. Therefore hex element gives smoother result than tri. Also since tri provides a more discrete result, the structural result will look "stiffer". This is the stiffing effect when less elements are used in structural analysis

P.S. This conclusion is based on my education knowledge and experience. I have no mathematical prove, so please feel free to correct me

 

[Tunalover]

hokhav-
For my employer years ago I purchased Fluent and Icepak and attended the training. I also studied CFD in grad school and wrote my own programs. At both places it was clear that the codes were Finite Difference Method, not FEA. Unless they rewrote the codes when ANSYS purchased Fluent and Icepak (which is highly unlikely) these two programs are based on the Finite Difference Method. As for your reasoning as to why tet elements are stiffer than hex elements, I'm going to stick with csk62's explanation as it does agree with my understanding of FEA with regard to Gauss integration points and how they are used to compute stresses.


Tunalover

 

[rb1957]

TRIA3 elements are inherently unstable, read into any FEA text about the derivation of the internal results of a TRIA3; unlike a QUAD4 which you can solve. To explain, you can assume a displacement field on a QUAD (linear in two directions) and solve for the normal stresses, this is less easy for a triangle (i think because they interact on the hypotenuse). now in the olde days there were elements that were based on a stress distribution assumption (rather than displacement based) (ie assume a linear stress distribution, and calc the nodal displacements) ... these may work better (but i don`t know if any are around these days)

TET4s suffer a similar limitation.

TRIA6 and TET10 don't.

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