FEM – Sandwich Panel Buckling

About the development of the FEM module/workbench.

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HarryvL
Posts: 783
Joined: Sat Jan 06, 2018 7:38 pm

FEM – Sandwich Panel Buckling

Postby HarryvL » Mon Apr 02, 2018 7:17 pm

With reference to the discussion on mixed meshes (https://forum.freecadweb.org/viewtopic. ... 9&start=70), I thought I would do an example where such an option would add much value. Against expectation, I managed to achieve excellent results with existing FreeCAD options and would like to show that here.

I analysed the buckling load of a 1x2 m sandwich panel composed of two 1mm thick aluminium sheets glued to a 5cm thick Polyurethane core. The FreeCAD model for this assembly is shown below. In addition, I add two 5x5x100cm steel blocks at either end of the panel to ensure uniform introduction of loads.

Sandwich Panel Model.png
Sandwich Panel Model.png (210.61 KiB) Viewed 331 times

At first I tried to mesh this model with maximum element size of 5 mm, to ensure reasonable aspect ratios for the C3D10 elements in the aluminium cladding, but had to abort the mesh generation after a 30 minutes wait. With a maximum element size of 50mm, the mesh generation only took 5 seconds, but I was convinced that the aspect ratio of 1:100 (see below) would yield rubbish results.

Sandwich_Panel_Mesh_Detail.png
Sandwich_Panel_Mesh_Detail.png (246.28 KiB) Viewed 331 times

In the INP file I then manually replaced the *STATIC card with a *BUCKLE card and put the Poisson ratio for all materials to zero to prevent lateral contraction and thus avoid sensitivity to lateral constraints in the boundary conditions.

The first buckling mode appears to agree well with that of the classical Euler solution.

Sandwich_Panel_Buckle_2.png
Sandwich_Panel_Buckle_2.png (142.81 KiB) Viewed 331 times

However, the buckling load is 4% in error compared to the Euler buckling load, which is rather much for such a fine mesh.

I therefore looked further into the effect of shear deformation; an effect that is normally ignored for slender structures, but that is important in sandwich panels with a soft core. Two simple corrections exist for shear deformation, one by Engesser (1889) that shows agreement within 0.3% of the CalculiX result and one by Haringx (1942) that is even closer, with less than 0.1% error.

So we can conclude that for this particular example, the C3D10 elements with extreme aspect ratios perform well. However, similar results could have been achieved with much simpler meshes based on mixed solid (core) and shell (cladding) elements. I am therefore very much looking forward to this ongoing development.
thschrader
Posts: 1331
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: FEM – Sandwich Panel Buckling

Postby thschrader » Mon Apr 02, 2018 8:56 pm

Harry,
thanks for your work you are doing and giving it to the forum.
You are the first who is doing such a systematically work here.
When the replies to your posts come late or none:
the reason is: hard stuff, and much work to understand.
Keep up the spirit!
regards Thomas
jake77
Posts: 19
Joined: Thu Jan 17, 2019 6:23 am

Re: FEM – Sandwich Panel Buckling

Postby jake77 » Thu Jan 17, 2019 6:30 am

@HarryvL, thank you for the contribution. Could you perhaps submit the .inp file for the buckling calculation?
I'm just starting to use freeCAD and Calculix hoping to solve mainly linear strength and buckling problems. I have extensive experience with ANSYS Classical and I'm not afraid of getting my hand dirty with input macros but I have a hard time finding resources (simple examples e.g. buckling of a beam or a plate) on how the analyses should be defined in CalculiX. :?
Thank you in advance!
jake77
Posts: 19
Joined: Thu Jan 17, 2019 6:23 am

Re: FEM – Sandwich Panel Buckling

Postby jake77 » Thu Jan 17, 2019 8:41 am

jake77 wrote:
Thu Jan 17, 2019 6:30 am
@HarryvL, thank you for the contribution. Could you perhaps submit the .inp file for the buckling calculation?
I'm just starting to use freeCAD and Calculix hoping to solve mainly linear strength and buckling problems. I have extensive experience with ANSYS Classical and I'm not afraid of getting my hand dirty with input macros but I have a hard time finding resources (simple examples e.g. buckling of a beam or a plate) on how the analyses should be defined in CalculiX. :?
Thank you in advance!
OK I found the way:
replace the line
*STATIC
with the following two lines:
*BUCKLE
X
with X being the number of buckling modes requested.
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HarryvL
Posts: 783
Joined: Sat Jan 06, 2018 7:38 pm

Re: FEM – Sandwich Panel Buckling

Postby HarryvL » Thu Jan 17, 2019 10:30 am

Yup. Please let me know if I can be of further help.
jake77
Posts: 19
Joined: Thu Jan 17, 2019 6:23 am

Re: FEM – Sandwich Panel Buckling

Postby jake77 » Thu Jan 17, 2019 10:57 am

HarryvL wrote:
Thu Jan 17, 2019 10:30 am
Yup. Please let me know if I can be of further help.
Thanks. I'm fighting my way up the learning curve.