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#1 2019-05-13 06:31:18

manonB
Member
From: Allemagne
Registered: 2019-04-02
Posts: 38

[SOLVED] Integration points of finite elements

Hi everyone,

I had a look at the R3.01.01 about shape functions and integration points and I was wondering how do we know which integration formula is applied to the elements ? Is it assigned according to the type of modelization we choose ?
And so for example for a tetraedron, when is the 5 points or 15 Points integration formula used ?

And if for instance I'm doing "MECANIQUE" and 3D and my mesh is composed of HEXA8 elements, how can I find out which integration formula is used ?

Manon

Last edited by manonB (2019-05-15 17:52:15)

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#2 2019-05-13 09:29:30

mecour
Member
From: Ostrava (Czech)
Registered: 2011-04-04
Posts: 93

Re: [SOLVED] Integration points of finite elements

Hello,

the number of integration point depends on the mesh you prepare. If you create simple linear mesh (HEX8 for example) the aster use simple eight gauss point integration scheme, if you create quadratic or biquadratic finite element mesh the aster use higher integration scheme.

mecour

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#3 2019-05-13 09:52:50

manonB
Member
From: Allemagne
Registered: 2019-04-02
Posts: 38

Re: [SOLVED] Integration points of finite elements

Hello thanks for the quick reply.

I get it now for hex elements.
But sometimes like for tetra elements there are several integration formulas: There is with 1, 4, 5 and 15 points. I'm assuming ( might be wrong) that 1 Point is for TETRA4 and 4 Points for TETRA10 (if we compare with Abaqus for instance). So do you know when are the 5 points and 15 points formaulas used ?

Manon

Last edited by manonB (2019-05-13 12:08:56)

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#4 2019-05-13 10:21:25

mecour
Member
From: Ostrava (Czech)
Registered: 2011-04-04
Posts: 93

Re: [SOLVED] Integration points of finite elements

The same problem as hex elements.

When you prepare linear tetra mesh which is TETRA 4 (IT IS REALLY NOT POSSIBLE TO CREATE "TETRA"HEDRON ONLY WITH ONE NODE) the aster use four gauss points if you prepare quadratic tetrahedron mesh TETRA 10 then aster use ten gauss point.

According to documentation aster provides only tetra4 and tetra10 elements. From documentation of Abaqus I can read that there are also C3D4 (four node tetrahedron) and C3D10 (ten node tetrahedron), so it is not clear to me where did you get  1, 4, 5 and 15 points?

Every integration scheme in every mesh is dependent strictly on the mesh type you create. The solver works with your data.

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#5 2019-05-13 11:48:58

manonB
Member
From: Allemagne
Registered: 2019-04-02
Posts: 38

Re: [SOLVED] Integration points of finite elements

I'm not talking about the number of nodes sorry my Messages were not clear.
It's clear to me that there is tetra with four nodes or 10 nodes. I'm talking about the integration Points (also called "Not" in R3.01.01).
In Abaqus you have the same C3D4 and C3D10 elements that have respectively 4nodes/1 Integration Point and 10 nodes/4 Integration Points.
So I'm guessing it is the same for Code_Aster, and so I'm womdering when the formulas with 5 and 15 Integration Points are used (R3.01.01 pages 14 and 15).

Last edited by manonB (2019-05-13 12:09:30)

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#6 2019-05-13 12:38:34

mecour
Member
From: Ostrava (Czech)
Registered: 2011-04-04
Posts: 93

Re: [SOLVED] Integration points of finite elements

For example u3.14.01 document page 2

LInear mesh TETRA4 with 3D modelisation 4 gauss point, with modelisation 3D_SI 1 gauss point (underintegrated)
Quadratic mesh TETRA10 with 3D modelisation 15 gauss point, with modelisation 3D_SI 5 gauss point (underintegrated)

That is how I understand it.

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#7 2019-05-13 12:58:38

manonB
Member
From: Allemagne
Registered: 2019-04-02
Posts: 38

Re: [SOLVED] Integration points of finite elements

Then I don't understand what you mean....
Maybe I understand wrong how the theory works. I joined a Picture from Abaqus where we can see for example a C3D4 (so TETRA4) it has 4 nodes and one Integration Point in the Center. Same for C3D10 (TETRA10) we have 10 nodes but 4 Integration Points represented with the crosses.
What I get from U3.14.01 is that TETRA4 has a linear shape function (Interpolation = linear) and TETRA10 has quadratic shape function (Interpolation = quadratic). But the document doesn't say anything about the number of integration points (just that for TETRA10 with 3D_SI it is reduced Integration, but without giving the number of Points)

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#8 2019-05-15 07:47:42

mecour
Member
From: Ostrava (Czech)
Registered: 2011-04-04
Posts: 93

Re: [SOLVED] Integration points of finite elements

Hello

You little bit confused me, so I did some study with tetra elements and gauss points in aster.
You were right with linear tetra it use only 1 gauss point and 3D_SI is not possible with linear tetra. With quadratic tetra and 3D aster use 5 gauss points and 4 gauss points with 3D_SI modelisation.
Unfortunately now I am not able to create tetra elem with more gauss points, so I really don't know how to create tetra elem with 15 gauss points.

mecour

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#9 2019-05-15 08:27:23

manonB
Member
From: Allemagne
Registered: 2019-04-02
Posts: 38

Re: [SOLVED] Integration points of finite elements

Hello,

Sorry I was also confused myself. It is not really easy to find this type of info in the documentation.

So where did you find that quadratic tetra have 5 Integration Point in 3D and 4 in 3D_SI ? Because I thought that quadratic tetra had 4 integrations Points in 3D...

Later I also found that in Abaqus in coupled thermic problems, a 15 points integration scheme is used. So it might be the same in Code_Aster.

Manon

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#10 2019-05-15 11:54:01

mecour
Member
From: Ostrava (Czech)
Registered: 2011-04-04
Posts: 93

Re: [SOLVED] Integration points of finite elements

I just prepared one tetrahedron mesh, run simple mechanic analysis and visualize ELGA field in paravis.

I could not find any aster documentation with information how to prepare or defined the element with specific integration scheme.

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#11 2019-05-15 17:51:54

manonB
Member
From: Allemagne
Registered: 2019-04-02
Posts: 38

Re: [SOLVED] Integration points of finite elements

Thanks a lot mecour!

I applied your method for the other solid elements so now I should know which integration formula is used for which element.

Manon

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