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**Cinzia_L****Member**- Registered: 2018-02-08
- Posts: 8

Hello everyone,

I tried to perform a beam nonlinear buckling analysis, created with tria quadratic shell elements with COQUE3D modelization, fixed on one and.

Material is linear elastic.

I’ve done modal analysis first, to find the first buckling mode and respective critical load, that is 16652 N such as for theory.

Then I pre-formed my model about 1.0 mm and I perform non linear analysis imposing a displacement, for node on other and, about 5 mm in 500 steps.

I’ve search the sum of nodal reactions for node in the joint, that are non linear, as I expect, but critical load is 65 kN, not 16 kN. Why?

I tryed also a 3 mm pre-deformation but critical load is 64 kN.

How can I solve this problem?

I attach .comm and .rmed (1.0 deformed) file about non linear analysis.

Thanks a lot for any suggestion.

Cinzia

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**jeanpierreaubry****Guru**- From: nantes (france)
- Registered: 2009-03-12
- Posts: 3,191

hello

a file with the input mesh would help in understanding

EDIT

using the mesh 'traveI_shell_bucklingnl.med' from your previous post

and altering the present 'Stage3.comm' file as required

i find a very non linear behavior with a maximum reaction of 2.17054E+05

jean pierre aubry

*Last edited by jeanpierreaubry (2018-04-16 14:21:59)*

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**Cinzia_L****Member**- Registered: 2018-02-08
- Posts: 8

Hello,

thank you for your reply,

now I attach all my file.

In folder number 1 there is my input mesh and stage 1-2. After perfoming analysis with these files, I get deformed mesh (defo1.rmed), that becomes the input mesh of Stage 3, that is in folder 2.

I obtain non linear relation, but from stage 3 results (reazioni) , I see that structure have critical load approximately at 64 kN, while for Euler's critical load should be 16,65 kN (Fcr = π2 E I / L2 where L=2l, so Fcr = π2 E I / (2l)2

E = modulus of elasticity = 70000 Pa (N/mm2)

L = length of column (mm) -->l=1500

I = minimum area moment of inertia of the cross section of the column = 216979 (mm4)

I don’t understand why reaction on encastre results wrong.

PS: From stage 1 I find a critical load value that is equal to -1.28093E+03, that multiplied to 13 (that are node where I applied force nodale) is 16652 N, the right value by Euler’s formula.

Thanks a lot for any suggestion.

Cinzia

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**jeanpierreaubry****Guru**- From: nantes (france)
- Registered: 2009-03-12
- Posts: 3,191

why should the non linear analysis gives the same results as the critical Euler analysis ?

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**Cinzia_L****Member**- Registered: 2018-02-08
- Posts: 8

jeanpierreaubry wrote:

why should the non linear analysis gives the same results as the critical Euler analysis ?

Because I want to study the structure's behavior in pre and post buckling phase, by imposing a shift to one end, and encastre reactions sum between linear and non linear behaviour should be equal to Euler's critical load. I want to study a beam's non linear geometry, modeled with shell elements.

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**Cinzia_L****Member**- Registered: 2018-02-08
- Posts: 8

Hello,

thank you for your reply,

I tried to do same exercise with ADINA and results are those that I expected.

The chart that I've attach show the relation between imposed displacement (x-axis) and reaction's sum on fixed end (y-axis).

On blue line there are results obtained using salome-meca and on orange line there are results using ADINA.

I'm very interested to solve this problem. Can someone help me to understand the error on my model or code?

Best regards

Cinzia

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**Volker****Member**- From: Chemnitz
- Registered: 2016-05-23
- Posts: 61

Hi,

I don’t want to obtrusive the discussion but I think perhaps there is an old programming error:

With code_aster version 11.6.0 I got also very strange results. Formerly I thought the problem is sitting in front of the computer. "Guilty" was there COEF_R in

```
ChamDepl = CREA_CHAMP(INFO=2,
TYPE_CHAM='NOEU_DEPL_R',
OPERATION='ASSE',
MODELE=MODELE,
ASSE=_F(CHAM_GD=ChampPoj,
COEF_R=-20.0,
TOUT='OUI',
CUMUL='NON',),
)
```

The solution was I had to shift the whole model by a certain vector away from the origin of coordinate system, so that all nodes have no any zero values in the node-coordinates left.

In the picture right is the mesh with zero coordinate values and in the left without. The left mesh is that I was expected. But 3 years ago I forgot it nearly.

I hope it helps a little.

Kind regards Volker

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**Cinzia_L****Member**- Registered: 2018-02-08
- Posts: 8

Hi Volker,

thank you for your reply, every suggestion is helpful for me, because I’m learning to use the program.

I tried to shift my model to have node with any zero coordinate values, but result are the same (wrong). I don’t understand if it's a programming error (and how to solve it) or my procedure is wrong.

Best regards

Cinzia

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**Volker****Member**- From: Chemnitz
- Registered: 2016-05-23
- Posts: 61

Hi Cinzia,

your model consist of trias with 7 nodes each. The 7. node is the center node which is there to achieve an higher calculation precision. And for this node you get only displacement results in DRX, DRY and DRZ, not for DX, DY and DZ. If you deform your mesh to achieve a preset (also kown as imperfection) all center nodes remain flat. I checked my comm file and saw that I project at first the buckle results on a mesh without center nodes. Then I deformed a mesh without center nodes and then I computed new center nodes with MODI_MAILLE=_F(OPTION='TRIA6_7' ... ) . With this mesh I have done the non linear calculation with great displacements.

I hope this helps a little to understand what happens there.

Kind regards Volker

*Last edited by Volker (2018-04-21 21:18:36)*

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**Volker****Member**- From: Chemnitz
- Registered: 2016-05-23
- Posts: 61

Hi Cinzia,

I updated my old .comm file to version code_aster version 13 (the code looks a little bit ugly) and created a small test case.

So I think the results are quite good. Between an analytical solution and the buckle simulation with CALC_MODES is a difference of approx. 1 %. Between the simulation acc. theory 2nd order with STAT_NON_LINE and CALC_MODES there are nearly no differences.

Maybe you know already this: I saw you want to calculate with aluminium or something else (not steel). Then you need a specific preset (also known as imperfection). I have chosen the preset acc. EC3. You can also calculate the specific preset by an iteration process.

Kind regards

Volker

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**Cinzia_L****Member**- Registered: 2018-02-08
- Posts: 8

HI Volker,

thank you for your help, I corrected my .comm file about central node and it’s all ok, but nodal reaction are always wrong, so I will try to perform an analysis more similar to yours to understand where I’m wrong. In my testcase I imposed an imperfection about 1 mm, then 3 mm, but I don't know if error is this.

Best regards

Cinzia

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