Deformation of a foam-reinforced shell beam

FE Model

We consider a thin-walled beam made of steel fully fixed at its one end and loaded by a uniform load at the top edge of the second end. The beam is reinforced by a foam material placed inside it. The outer dimensions of the beam are 30x40 mm, the wall thickness is 2 mm, and its length is 400 mm. The thin-walled beam is modeled using shell10x elements and the foam part by the classical linear solid elements. The material properties of the constituents are summarized in the following table:

Table 1 Material properties

Young modulus

Poisson ration


210 GPa



20 GPa


The applied boundary conditions are depicted in Fig. 1.


Fig. 1 Boundary conditions applied to the beam.

In order to show the credibility of the above model (see Fig. 2), we compare its results with the results of the following models:

  • beam without reinforcement using shell10x elements, see Fig. 3

  • beam without reinforcement using solid hexahedral elements, see Fig. 4

  • beam with reinforcement using solid hexahedral elements for both the constituents, see Fig. 5


Fig. 2 Beam with foam reinforcement - shell10x + hexahedral elements.


Fig. 3 Beam without reinforcement - shell10x elements.


Fig. 4 Beam without reinforcement - solid hexahedral elements.


Fig. 5 Beam with foam reinforcement - solid hexahedral elements.

Running simulation

To run the numerical simulation, download the archive, unpack it and run by:

sfepy-run example_shell_beam-1/
sfepy-run example_shell_beam-1/
sfepy-run example_shell_beam-1/
sfepy-run example_shell_beam-1/

The finite element meshes can be generated using the script.


To plot the deformed foam-reinforced structure run the following command:

sfepy-view results/beam_shell_foam.vtk -f uf:wuf:f10:m2:p0 0:vw:m2:p0 us_disp:wus_disp:f10:m1:p1 --camera-position="-0.4,0.16,0.57,0.02,0,0.23,0.22,0.97,-0.11" --grid-vector1="0, 1.6, 0"

The resulting image is depicted in Fig. 6.


Fig. 6 Resulting displacements.

The displacements in the y-direction along line l_t (see Fig. 1) obtained by the different models are compared in Fig. 7. The figure is plotted by


Fig. 7 Displacements along line l_t.