tet vs hex element in FE analysis

Hope the link below helps a bit.

Hexes and Quads are generally preferred for linear and nonlinear.

you lost me here! Hexahedral and tetrahedral refers to the number of hedres ('sides') of the element. Quadratic refers to the number of nodes ..as far as i can remember we can have a hex linear and a hex quadratic element. Correct me if i am wrong cos i am a bit rusty with fea.

As already indicated in one of the earlier answers it has all to do with accuracy. Especially in plate bending type problems linear elements suffer greatly from a phenomenon called shear locking: linear elements are not able to represent the shear stress free stress field as assumed in thin plate theory. Hex8 elements suffer less from this effect due the presence of some higher order term in the displacement functions. Further in many codes the hex8 performance is improved by a trick called reduced integration.

The most convincing test you can do you yourself: model a rectangular plate under pressure and check the results using Roark or Timoshenko. Using tet4 elements you will easily get errors in displacement of 100% or more. So you have a choice of two solutions: switch to quadratic elements tet10 of use hex elements,

For fairly solid structures the errors from using tet4 elements will be less, but then the problem is to define what fairly solid means.

When using tet meshing the default is therefore often tet10 .

Timo

Quads are 2D shell elements. Hexes are 3d solid elements. The order of the element shape function is another matter.

Jeff I am quite sure that we can get a quad 3D solid element solid95 for example in ANSYS. I agree that the degree of interpolation is another matter. You just mention quad and hex as being two different kinds of the same 'order'. however i think they describe two completely different attributes of the element. Anyhow, Timo gave a very nice answer to the initial query. ;)

Jeff was correct. ANSYS Solid95 is 3D element so it is called a hex, not a quad which refers to a 2D element. In ANSYS, the Shell63, and the

2D surface effect, 2D "not solved" elements are considered quads.

So far, no one has explained why hex is superior in an era of cheap memory and fast CPUs. Yes, in some problems the tet cannot capture linear stress - but, IN THEORY, use more elements, or more mid-side nodes. So far, I cannot figure out a CPU-indepdendent justification for the hex, that is founded in the very nature of the hex and the specificity of the problem's nonlinearity.

link will give you an idea. However you have to stop confusing hexahedral or tetrahedral with quadratic or linear or whatever else. By definition of these words tetrahedral and so one define sides (hedra in greek mean side the rest is the number of the sides). Now solid95 is a quadratic 3D element with quadratic meaning the interpolation of the nodes (i.e adding one node at the middle of the defining edge nodes...as a rough description). My argument was not serving an answer to the original post just to set straight that quad does not refer to neither a hex or a tet it refers to the interpolation...

Quad is short for quadrilateral as in the 4 sided shape. You seem to be one of the few people that uses quad to refer to quadratic. Whatever..

lost in terminology... it is a typical example of different backgrounds. apparently we never use quadrilateral... cos in short hand can confuse you with quadratic.... i agree whatever...

Then you have never used Nastran.

thats true only ansys and abacus... but it has to do also with the mathematical background. We use the names from first principles, and ussualy they are not the latin. however, thanks for teaching me that one ;)

This is an interesting discussion. But may I also ask if either of you know what it is about hex elements that make them preferable to tet (other than simply more nodes, less chance for distortion)

The distortion (shear locking) is not something to simply discount.

In non-linear analysis you always try to keep it as small as possible. On the other hand to create a hex model may be to expensive. A typical engine model is more than 3,000,000 dofs, mostly because at least the head is modeled with TETs. Takes some time to solve.

If you want to closely investigate a problematic region, element quality might be important. It is easier to control the quality of a hex mesh than of a tet mesh. From this point of view a hex mesh will provide better results than a tet mesh.

Rainer