Linear Bricks vs. Quadratic Tetrahedrals
Linear Bricks vs. Quadratic Tetrahedrals
(OP)
Hello,
I think analysts in industry tend to shy away from using quadratic tetrahedrals and advocate meshing the whole model with bricks even if it takes 2+ weeks. As far as accuracy goes Comparing the shape functions, quadratic tetrahedral elements are just as (or more) accurate as a linear brick element. I understand that computation time is a concern, but I believe the extra time spent brick meshing the whole model would be better served doing the analysis and debugging. Some people also advocate doing a hybrid (brick and tetrahedral model, but I'm not so sure that doing this is a good idea because it could cause discontinuities in the nodal solutions (due to discontinuities in the shape functions).
What are the feelings of other people on this board concerning this subject?
Regards
MMATguy
I think analysts in industry tend to shy away from using quadratic tetrahedrals and advocate meshing the whole model with bricks even if it takes 2+ weeks. As far as accuracy goes Comparing the shape functions, quadratic tetrahedral elements are just as (or more) accurate as a linear brick element. I understand that computation time is a concern, but I believe the extra time spent brick meshing the whole model would be better served doing the analysis and debugging. Some people also advocate doing a hybrid (brick and tetrahedral model, but I'm not so sure that doing this is a good idea because it could cause discontinuities in the nodal solutions (due to discontinuities in the shape functions).
What are the feelings of other people on this board concerning this subject?
Regards
MMATguy





RE: Linear Bricks vs. Quadratic Tetrahedrals
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RE: Linear Bricks vs. Quadratic Tetrahedrals
RE: Linear Bricks vs. Quadratic Tetrahedrals
tet4's have given a bad name to the tet family, but it is also the application of those tets. Too many analysts let their automesher put tet4 elements a single layer through the thickness of their solid model and fail to understand the impact of the results. Of course, the same analysts stick one brick through the thickness and present their "pretty picture" to management...nevermind. I feel myself climbing on my "soapbox"!
RE: Linear Bricks vs. Quadratic Tetrahedrals
RE: Linear Bricks vs. Quadratic Tetrahedrals
Not all 'bricks' are first order.
> Too many analysts let their automesher put tet4 elements a single layer through the thickness of their solid model and fail to understand the impact of the results. Of course, the same analysts stick one brick through the thickness and present their "pretty picture" to management...nevermind.
A single tet4 is not always inappropriate - modelling simple thermal loads, for example, using these elements can be perfectly reasonable. For stress modelling the use of these in regions where stress results are important these elements have limited use, as they are way too stiff. As for the single brick through the thickness, this is also perfectly acceptable in some instances, given that the element isn't subject to large stress gradients. But even when stress gradients are present, a higher order brick will often capture the response adequately.
Every element has its appropriate place in FE. It all depends on the loading and the geometry. Amen.
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RE: Linear Bricks vs. Quadratic Tetrahedrals
I'll concede the thermal element single brick application and agree that not all bricks are linear, but a single, linear brick through the thickness even in areas not expected to have a high stress gradient isn't advisable. I suppose it could be justified it extremely large models where you are really struggling to keep the run time reasonable, but there would always be the "what if". You also have the questions of when and how to transition.
RE: Linear Bricks vs. Quadratic Tetrahedrals
Don't agree. So a single linear brick in a regular plate under say simple tension (no gradient per se) wouldn't give a reasonable approximation of the stress? You need to consider the type of loading the element is under and not generalise. I've carried out studies with single bricks through thickness under bending load and found the results to be reasonable (not exact, but reasonable); of course, these are higher order bricks. As I say, though, under gradients I wouldn't advise single bricks through thickness. Two through thickness under bending gives a good correlation.
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RE: Linear Bricks vs. Quadratic Tetrahedrals
(emphasis added)
My soapbox is now, and has always been, that many "analysts" fail to do the work that it appears that you have done with regards to testing their element types. I don't like generalizations, but that includes the implication that single bricks through a thickness is OK.
Other than this, we'll have to agree to disagree, I suppose. I'll leave it to you to close the thread as you see fit.
RE: Linear Bricks vs. Quadratic Tetrahedrals
Brick elements yield better stress results in contact analyses
RE: Linear Bricks vs. Quadratic Tetrahedrals
Why is that? I would think that two coincident and lined up (node for node) tet10 meshes would model contact well.
RE: Linear Bricks vs. Quadratic Tetrahedrals
This falls into the category of sweeping generalisations methinks. Would be interested to know why you think this is so.
> I would think that two coincident and lined up (node for node) tet10 meshes would model contact well.
Contact in spatial 3D elements (such as bricks, tets and planar elements) is actually modelled using the gauss points of the element(s) - not the nodes. But yes, a well 'matched' mesh (of any element type) usually provides good modelling contact conditions in general, although there are many, many other factors that come into play here, most of which are off topic for this thread.
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RE: Linear Bricks vs. Quadratic Tetrahedrals
As far as I know there are 3 kinds of contact algorithm:
1- node to node contact
2- node to surface contact
3- surface to surface contact
In the first case the boundaries of both contacting surfaces are defined by their respective nodes. This is not completely accurate as some relative penetration is likely to occur.
The second case is often referred to as the “master-slave” approach, as the assumption is that the “slave” surface, defined by nodes, cannot penetrate the “master” surface, defined by element faces (or segments in 2D case). However, edges of the master surface may still penetrate gaps between nodes of the slave side.
The third algorithm is the most accurate. Here master and slave surfaces are iteratively swapped and effectively prevent any relative penetration. It is also the most computational intensive.
The formulation of second order tetrahedrons (the only tetrahedrons relevant for stress analyses) as well as second order wedges and membrane shells suffer from a problem that makes them not entirely suitable for contact analyses:
The direction of nodal forces developing as a reaction to a uniform face pressure is not consistent for all nodes: mid-side nodes will develop a force whose direction is opposite to that of corner nodes.
Not only this will make convergence more difficult, but assuming that it is reached, the resulting prediction of contact pressure will be wrong.
ABAQUS have developed a special modified tetrahedron to overcome this problem, but in my experience it still does not yield results as good as in the case of hexahedral elements.
RE: Linear Bricks vs. Quadratic Tetrahedrals
RE: Linear Bricks vs. Quadratic Tetrahedrals
ANSYS. Perhaps you've heard of it?
For surface to surface contact -- by far the most commmon type of contact used -- we populate the contact surface with gauss points, which are then used to transmit pressures. Hence: (1) the gauss points are used to model contact and (2) the reason for my statement on the types of element that are used for this contact (see above). All of the other types transmit forces at the nodes.
> The formulation of second order tetrahedrons (the only tetrahedrons relevant for stress analyses) as well as second order wedges and membrane shells suffer from a problem that makes them not entirely suitable for contact analyses
This appears to be a problem unique to ABAQUS (in fact, I've heard ABAQUS users talk of this problem before), as ANSYS does not suffer from such problems, so be careful not to generalise (see above). Tets or bricks in ANSYS are both excellent and can be used as and when necessary in contact analyses -- if anything, the tets are better.
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RE: Linear Bricks vs. Quadratic Tetrahedrals
I have done some research.
1- You are right in saying that Ansys (which I have heard of, but never used) provides a surface to surface contact algorithm based on gauss points. This overcomes the problem I mentioned regarding high order tetrahedrons
2- I have used several FE softwares and none had this feature. All of these softwares (and not just Abaqus) suffer from the limitation I mentioned regarding high order tets. In Ansys'own words (from one of their brochures) this feature is unique to their software, therefore it is you who are generalising, not me, as Ansys is the exception in this case.
3- I think the bottom line is "For contact analyses always use bricks if you can, unless you have Ansys". This thread was being general and not referring to any particular software, hence my statement on tet elements.
Regards