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.

_images/beam_bc.png — 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

_images/beam_shell_foam_2.png — Fig. 2 Beam with foam reinforcement - shell10x + hexahedral elements.

_images/beam_shell_2.png — Fig. 3 Beam without reinforcement - shell10x elements.

_images/beam_solid_2.png — Fig. 4 Beam without reinforcement - solid hexahedral elements.

_images/beam_solid_foam_2.png — 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/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.

_images/beam_shell_foam_displacement.png — 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 plot.py

_images/results.png — Fig. 7 Displacements along line $l_t$ .

Fig. 7 Displacements along line $l_t$ .