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

steel

210 GPa

0.3

foam

20 GPa

0.25

The applied boundary conditions are depicted in Fig. 1.

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

Running simulation

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

```sfepy-run example_shell_beam-1/beam_shell.py
sfepy-run example_shell_beam-1/beam_solid.py
sfepy-run example_shell_beam-1/beam_shell_foam.py
sfepy-run example_shell_beam-1/beam_solid_foam.py
```

The finite element meshes can be generated using the `gen_mesh.py` script.

Results

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.

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