Tet Mesh and Hex Mesh 3

[Badri07]

Hi All,
I am having a problem with mesh i have generated on my model,the model is a curved plate and i am applying a force normal to the curved surface,and i have meshed it with Tet mesh,i came to know that i need to use hex mesh because my problem invovles more of bending.

i wish could somebody explain me on this.

Regards
Badri07

 

[corus]

Why not hex mesh it then?

corus

 

[Badri07]

Hi,
Thanks for your post,what i am asking is that when do you use hex over tet elemnts.

Regards
Badri07

 

[rb1957]

i'm surprised that tet10s were unsuitable ... tet4s are to be avioded (IMHO).

 

[SWComposites]

Curved plate, hmmm, why not use shell elements?

What FE code are you using?

 

[ThomasH]

How thick is the plate compared to it's other dimensions?

 

[Badri07]

Hi,
The plate thickness 5mm compared to its height of 1.8m.
and i am using Ansyswb

Thanks
Regards
Badri07

 

[TGS4]

SWComposites is pointing you in the right direction. Unless you are expecting to see severe through-thickness variation of stress, you are much much better off with the shell element.

 

[crisb]

The original question was ...hex or tet for a thin plate in bending? There are those who claim that hex's are more accurate. If you can manage to mesh it, a hex model will have less nodes but will probably have taken many times longer to mesh it. In the real world I find that I end up having to use tets to mesh models with any degree of complexity.

I have compared results form similar models using shells, tets, and hex's and find they all give good results, as does the following obtained from googling: -

http://ansys.belcan.com/d/thin_plate_solid_mesh.pdf

 

[ThomasH]

Since the original question war hex vs tet I would say hex. There are mixed terms in the element formulation that better describe bending. But it should also work with TET10's. TET4's should be avoidid for several reasons, one is that they are numerically to stiff.

But for the particular problem I would say plates. 5mm thick and 1.8 m side, that's a thin plate.

Just consider that to model it properly you need 3 - 4 elements trough the thickness. That means that the element side will be approximatly 1.5mm. And if you want the have an aspect ratio of 1.0 that means 1.8/0.0015 = 1200 elements in the other direction. Assuming it's a square plate the model will have 1200*1200*4 = 5.8 million elements.

So it's plate elements and if its square you probably don't need FEM at all, just a handbook.

Good Luck

Thomas

 

[crisb]

ThomasH

<<Just consider that to model it properly you need 3 - 4 elements through the thickness.>>

I have come across statements like this many times. However on several occasions I have done comparisons with different numbers of elements through the thickness and found that a single layer of 10 node tets gives accurate results, comparable to multiple layers or shell elements. However the above comment might depend on the element formulation in the code being used.

 

[ThomasH]

crisb

I have also seen the statement many times, that's partially why I used it.

To use a single layer might be possible but I wouldn't do it without verification. As for choice of elementtype I would say, if you model a beam use beamelements, for a plate use plate elements.

I have never really liked the idea to use solids for everything. But that might be just me beeing stubborn ;-).´

Would you have used solids or plates? Not really the question from the original post but I'm just curious.

Regards

/Thomas

 

[crisb]

ThomasH

As you asked... I usually prefer to use 3D elements to plates, although accept its not the conventional wisdom. I can model (and modify) 3D entities much quicker than setting up shell midsurfaces, and dont have worries about errors with viewing the wrong side of elements or setting the wrong thickness. I dislike the approximations or complicated midside offsets one so often has to make when using shells. I also believe that 3D elements more accurately represent effects at transverse intersections where shells can easily give rise to singularities or unrealistically high stresses. Its often of interest for me to take sections through the thickness to assess direct and shear stresses in welds which again I find easier with 3D elements. Of course if the geometry is simple and the thickness is tiny compared to the other dimensions, use shells.

 

[GBor]

10-node tets have a mid-plane series of nodes that make them more accurate than a single element through the thickness that you would get from 4-node tets...it's like having 2 elements through the thickness.

Just an observation.

I tend to use plates in one software packages, 3-D elements in another, and the third package I use has an interesting formulation method where every element is the same...long story that is analytically beyond me

 

[johnhors]

Surely the bottom line on the validity of using solid elements instead of shells in a model is the acceptability of the stress gradient within any single element in the model.

Using single solid elements through a thickness is acceptable if the stress gradient through the thickness is relatively small.

Consider a tube in bending, elements on one side are all in tension whilst on the opposite side they are all in compression. A smooth transition of tension to compression takes place over the diametric width. In this situation it is probably okay to have a single element through the thickness.

However a plate type structure under bending will have say tension on the top surface and compression on the bottom surface, it is clearly evident that the full range of stresses within the model takes place through the thickness and it is most probably unacceptable to have a single element through the thickness.

Thus to use shell elements, or single or multiple solid elements through the thickness is determined by the geometry of the structure and the type of loading to be applied.

 

[crisb]

John

I am still curious about this....as my experience is that a single layer of 10 or 11 node tets works well with high bending (through the thickness) with either elastic or perfectly plastic materials. However I imagine this could not be true for more complex material models. Increasing the number of elements through the thickness (x3) potentially increases the size of the model by 3^3=27 which can be a serious deterrant.

Another check on simple elastic bending:

http://www.padtinc.com/epubs/focus/common/focus.asp?I=11&P=article2.htm

Could the 3 elements through the thickness be a throwback to earlier days when quadrilateral elements were less common and element formulation less advanced?

 

[johnhors]

Chris,

On the face it what you have shown is that for a simple flat structure with simple loading a single tet through the thickness works well, as the stress varies linearly and the element formulation can handle this. But why would you ever bother to model a problem so simple that a hand calc can solve ?

For a complex structure and/or complex loading then this would not be the case. Which category does the OP's curved plate fall in to ? Depends on the degree of curvature I suppose.

Here is an article of interest:-

http://66.195.41.10/Articles/Feature/Elements-of-Finite-Element-Analysis-20050101278.html

 

[prost]

Since you are looking for the exact solution to some set of equations, it would seem counterintuitive that you should consider the nature of the exact solution BEFORE you start doing the problem. Hence, use shells when the exact solution is a stress field can be closely approximated by in plane stress only (for instance, in a classical beam bending problem or a pressure loaded thin cylinder or sphere), because that's just the kind of stress field shell elements capture well.

If your exact solution has high stress gradients and is three dimensional in general, hex20 works better than hex8. Why do they work better? Hex8 (8 nodes, only at the corners of a cube) are linear elements, which mean they can capture quite well linear displacement fields. Now think about what kind of stresses you can get from linear displacement fields? The first spatial derivative of the displacement is the strain, which is related to the stresses through some material constants, therefore linear displacement fields can give you AT BEST constant strain fields (hence the name "constant strain triangle" referring to a 3 noded, 2 dimensional triangular shaped element).

Think about what kind of strain/stress field you get from same pure bending--you want a linear stress field. Integrating to displacements, you know you need a quadratic displacement field to capture a linear stress field. That means your tet4 (I am guessing this is a 4 noded tetrahedron which is linear) does a very poor job of calculating a quadratic displacement field; the best you could hope for with the tet4 is a piecewise linear displacement field--you can imagine you'd need quite a few piece wise linear displacements fields to approximate well a quadratic displacement field.

My personal preference is never use linear elements--they were needed when computers were still reading card decks and had limited memory, in my opinion, but they appear to work rather poorly for most interesting deformations and stress fields. You save some space on your computer by using them, but you don't need to save space in most cases any way.

 

[051174]

It depends from the solver used. Nastran for example seems to give wrong results using any solid element except hexa.
Pressure load for example.