Brick v Tetrahedra mesh in Benchmark test

[allanmcguire]

I am getting a substantially different result using tetrahedra mesh compared to a brick mesh as I try do do some standard benchmark tests between Algor and other tools. My model is very basic:

• 6m x 0.1m x 0.2 m bar (x,y,z respectively)
• one of the small ends (y-z) are fixed
• the other small end has a 1 N load in the y direction
• Young's Modulus = 10e6 N/m^2
• Poisson's = 0.3
• Mass Density = 2.53881e-4 kg/m^3

This should result in so decent tip displacement tip displacement.

Using the brick with 6 segments (produces 26 elements), Algor compares very favourably with other FEA analysis at a tip displacement of near 0.420.  However, I switch Algor to tetrahedra and it produces 52 mesh elements and a displacement of 0.004 m!

Algor brick meshes of 82 and 4042 elements produce displacements of 0.429 and 0.431 m respectively. However, when using the same mesh parameters. But with tetrahedra, 164 and 8084 elements produce displacements of  0.038 and 0.352 m respectively (yes, there are order of magnitude differences here!).

The other FEA program used to do all the above with tetrahedra mesh, ranges from 0.426 m at a very coarse mesh (~50 elements) to 0.431 with over 27,000 elements (I know, this is way overkill but just testing).

Any thoughts on this?

Thanks

[S.LI · Accepted solution]

1.) For tet elements, please try it with mid-side nodes.

2.) Currently, Algor use de-generated brick to simulate tet for hybrid mesh model. It might cause some accuracy issue.

[xli]

Hi,

The test you conducted seems having the issue of locking of brick element, i.e. when the incompatible mode is off it turns to be "very strong" for bending no matter how fine your mesh will be. When it uses 8-node bricks the incompatible mode is by default turning on so that you obtained reasonable results. But it has to be off for tet and other degenerated elements. As S.Li sugested, using midside in tet elements would likely resove such locking problem in genertal.

thanks.

-xli

[S.LI]

Not sure if you get a chance to test Beta of Autodesk Simulation 2012.

Please give a try if not yet.

[allanmcguire]

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@S.LI wrote:

1.) For tet elements, please try it with mid-side nodes.

2.) Currently, Algor use de-generated brick to simulate tet for hybrid mesh model. It might cause some accuracy issue.

---

Thank you for the insight here.  I think "some accuracy issue" is a little understated in this model 🙂

I know now prefer brick over tet elements in Algor.

[allanmcguire]

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@S.LI wrote:

Not sure if you get a chance to test Beta of Autodesk Simulation 2012.

Please give a try if not yet.

---

I saw it available on the website.  I am a bit apprehensive to use it since Algor 2011 gives me enough trouble with crashing but I will start the process of downloading it to see.  Thanks.

[S.LI]

1.) using de-generated brick to simulate tet is a normal way. lots of FEA packages have this feature. Even some package provides a tool to convert them. 2.) As I said, please have a try on Beta release. After the formal release of autodesk simulation 2012, I'll share some my result for your model with tet here.

[allanmcguire]

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@S.LI wrote:

1.) For tet elements, please try it with mid-side nodes.

---

I was sitting down to see how this would work and have two questions:

1)  Are not mid-side nodes used when the model is thin compared to the mesh size?

2)  Also, how is this set.  I have been looking for how to set this in the mesh settings and I must be totally missing it.

Thanks.

[S.LI · Accepted solution]

I guess you can find more info by searching mid-side nodes in Help. where to set mid-side nodes: This is not in mesh setting. It's in element definition dialog, after the material model selection part. There is a dropdown list for mid-side nodes, please select "included" to enable mid-side nodes. Why we need mid-side nodes: This topic is too big, and let me focus on tet element with mid-side nodes. Tet element is a kind of stress-constant element, which means stress is a constant in each tet element. (Brick element is not.) This property of tet element makes itself simple, but might lose accuacy in some cases, for example your model. Also x.li explained this in his previous message. By googling "locking", you can find more information why the first-order tet is not good enough. To overcome this problem, tet element needs mid-side nodes. With mid-side nodes, tet element becomes to the second-order element, which allows smooth deformation, such bending. So "locking" problem is resolved here. In structural analysis, more and more people use the second order tet instead of the simple one. But in some other analysis, such as thermal, people still prefer first order tet.

[allanmcguire]

s.li

Thank you much.  There is not much info in the help on this so your notes were very helpful to get me where I needed to be.  Tet element tests give the same order of mag. in displacement though still not very accurate.

Your further explanation on the use of tet v brick elements is also useful and will be a great further learning experience for me.

BTW, just finished downloading Simulation 2012 so will work on installing it.

Thanks again,

Allan

[SaMurgie]

Hi

Are midside nodes turned on?  1st order tets (we default to 1st order) are stiffer than bricks and 2nd order (midside nodes) tets.

You should see much closer results with midside nodes turned on.

Sam

[allanmcguire]

Sorry for taking so long to get back.  Been very busy actually doing the models and installing and trying out a bunch of new Autodesk software.  Changing to midside nodes did help in producing similar results to Inventor Simulation though still not as accurate as brick in my situation.

Again, thank you for your help here.

[SaMurgie]

np

BTW, how close are the results with 2nd order tets?

[allanmcguire]

If I recall, there was about a 10% difference with same size mesh but was much lower using a finer mesh with the tets.  Unfortunately, I do not have time to go study in more detail unless it is needed in an upcoming project.

[SaMurgie]

Thanx for the info that you have given us. 

Cheers.

[S.LI]

My testing results on Autodesk Simulation 2012 Beta are : number of elements end deflection 8586 0.4309 174 0.4280 89 0.4248 I guess your results should be similar.

[S.LI]

try to make it clear

number of tet elements      end deflection

• 8586                          0.4309
• 174                            0.4280
• 89                              0.4248

I have to say this result looks not bad, even compared with other FEA packages.