FreeCAD
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 (210.61 KiB) Viewed 330 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 (246.28 KiB) Viewed 330 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 (142.81 KiB) Viewed 330 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.
