2. Large displacements of cantilever beam

This test set checks the geometrically nonlinear response of a simple beam, clamped on one side and free at the other side. The beam is modelled with shell elements (element type Q4.S.MITC.E4). The geometry is shown in below:

Beam geometry: Length L=50, height b=3, and width t=1

Figure 115. Beam geometry: Length L=50, height b=3, and width t=1


The model is clamped at x=0 and an end load of 1.666 per unit length at x=L is applied in the global z-direction (out of plane load) along the edge y. The material is a simple linear isotropic material with modulus of elasticity E = 1.e4, Poisson ratio P=0.

The nonlinear analysis runs to a load factor of 10 (i.e. 10 times the nominal load) to test the performance of the non-linear elements.

In-plane bending behaviour

Figure 116. In-plane bending behaviour


The test allows the evaluation of the nonlinear performance of the elements. The nonlinear response is similar for all elements for a load factor of 1. Divergence may occur in the highly nonlinear region. The figure shows the load-displacement curve for the in-plane bending case for the beam and shell element as well as the final deformed state of the shell model.