Static clamped beam: Elmer and Analytical solutions differ

Numerical methods and mathematical models of Elmer
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Kankreu
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Static clamped beam: Elmer and Analytical solutions differ

Post by Kankreu »

Dear all,

I'm having a problem with Elmer solver:
In my real case, I have a clamp beam with a static load at the other side. The beam is an I-type with triangular holes.
I'm having results from Catia with the GPS module and I wanted to reproduce this case with Elmer.
Unfortunately, the results are completely different from my reference for the Von Misses as well as for the displacement.

As I couldn't find what was wrong, I decided to simplify my case to a simple geometry for which analytical results exists.
So I have a circular beam, not hollowed, clamp at one side and loaded perpendicularly at the other side.

It's possible to compute analytically the stresses and displacement for that case.
I could reproduce similar value from Catia+GPS, but once again, Elmer is giving completely different results.
I tried also an other solver (z88Aurora) which is also "wrong" (and with different results from Elmer).

So I'm really wondering what is wrong in my case. I was thinking of a unit issue but I did my analyses in m and mm and
results are coherent between the 2 cases.

Please find attached the files (mesh + sif) in meter and millimeter.

The Beam is 1m long (L) and 25cm Radius (R), load (F) is 1000N. Steel: Young modulus (E): 210e9Pa
I=pi*D^4/64
Stress=F*L*R/I
Displ=F*L^3/(3*E*I)

Stress Displ
Analytical 81.46e6[N/m^2] 5.2e-3[m]
Catia 74.13e6[N/m^2] 4.9e-3[m] (acceptable)
Elmer [m] 1.49e5[N/m^2] -8.3e-6[m]
Elmer [mm] 1.54e-1[N/mm^2] -8.09e-3[mm] (similar to Elmer [m])

I'm not completely sure about this last if it's necessary to convert the load from N=(kg*m/s^2) to kg*mm/s^2 but if I don't do,
I have different results. I'm also not sure the output is in N/mm^2 maybe it's kg*mm/(s^2*mm^2) Then the results are different.


Could somebody have a look to my sif (and meshes) and tell me what's wrong?

Thanks a lot

PS:I did also a Dynamic study (clamped) and modes are similar in Elmer and Catia
Attachments
beam_mm.zip
Mesh and sif in [mm]
(75.04 KiB) Downloaded 302 times
beam_m.zip
Mesh and sif in [m]
(75.17 KiB) Downloaded 298 times
nguyent
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Re: Static clamped beam: Elmer and Analytical solutions differ

Post by nguyent »

Didn't check your sif, but a quick look at your mesh.elements file reveals you are using linear tetrahedral elements (504). You'll want to up them to quadratic elements to avoid the so-called "locking."

I think the command to increase the element order is something like:

Code: Select all

ElmerGrid 2 2 [mesh folder name] -increase
Kankreu
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Re: Static clamped beam: Elmer and Analytical solutions differ

Post by Kankreu »

Hinguyent,

thanks for the info, I'll try that but do you really think it can affect that much the solution (10^3)?
And what is the locking?

Thanks
raback
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Re: Static clamped beam: Elmer and Analytical solutions differ

Post by raback »

Hi

Or you can equally well set in the Solver section

Code: Select all

Element = p:2
to envoke the quadratic elements using the hierarchical p-basis.

Google for "shear locking".

-Peter
Kankreu
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Re: Static clamped beam: Elmer and Analytical solutions differ

Post by Kankreu »

Dear Peter,

thanks for the explanation. I read about it and understand. Indeed I did a run with quad elements but it didn't improve my results. As expected, it will not cover the "e3" gap between the analytical results and Elmer results. I think I get something like 1.56e5 instead of 1.49e5 with linear elements. Still far away from 8.14e7 of analytical results.
I tried with quad element mesh or with "Element = p:2": same results.

Any other ideas?

Thanks,
Max
raback
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Re: Static clamped beam: Elmer and Analytical solutions differ

Post by raback »

Hi

Had a look on the .sif file. My suspect would be the interpretation of "Force 3". To clarify, it is a distributed force hence the SI unit for it is [F]/[A]=N/m^2.

-Peter
Kankreu
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Re: Static clamped beam: Elmer and Analytical solutions differ

Post by Kankreu »

Hello Peter,

thanks for the post.
I'm not sure to clearly understand the definition you wrote (I know what a distributed force is).
When you say "...it is [F]/[A]...", I understand that the value I put in the BC editor is 1000 (N) distributed on the A defined (this is the behaviour in Catia (distributed force, defined in N)).
If I put a value of 1000 is it?
- 1000N/m^2 -> 1.9635e-3N (surface is 19.36cm^2)
which means that I have to put 500000N/m^2 to be equivalent.
Apparently it is.
I redid completely my computation and I realized I made a mistake (2 in fact):
- Analytically and in Catia I did R=0.25m while it is R=0.025 in Elmer...
So here are the correct table:
_ Stress Displ
Analytical 8.149e7[N/m^2] 5.2e-3[m]=5.2[mm]
Catia 7.428e7[N/m^2] 4.9e-3[m]=4.9[mm] (acceptable)

- The Force definition 1000N vs 1000N/m^2
Elmer [m] 1.84e5[N/m^2] 7.9e-6[m]=7.9e-3[mm] With F=1000 [N/m^2]
Elmer [m] 9.38e7[N/m^2] 4.0e-3[m]=4.0[mm] With F=509000[N/m^2]

So, it's now coherent.
I should have payed more attention to the dimension and read the manual to know it was in N/m^2.
Maybe it's good to put in the BC editor that the distributed force is per unit of surface.

Thanks a lot for your help, I'm very happy with the tool and the support.
Greetings
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