Element tests: Shells

1. Beam modelled with shell elements

A slender beam is modelled with shell elements comparing the computed stresses using 4-node and 9-node shell elements. In addition, the use of isotropic material and laminates for the computation of the stresses is tested. This test case is intended for computing stresses of non-layered and layered elements.

The model is meshed using Q4.S.MITC.E4 or Q9.S.MITC elements and uses either the normal isotropic material model or a laminate with three layers, the outer layers being very thin. The beam is modelled in the direction of the y-axis and the shell elements are placed in the xy-plane.

The beam is clamped at y=0 and loaded at y=200. For the in-plane bending case (case 1) and the traction case (case 2) the traction load along the edge is 0.2. For the out-of-plane case (case 3) the traction load along the edge is 0.02.

The tip of the beam is loaded on the corners in the x-, y- or z-direction, respectively, depending on the load case.

Table 17. Input options

eltype num Identifier to select the element type: num=1 selects Q4; num=2 selects Q9.
load num Select the direction of the load: 1: in-plane bending (in xy-plane); 2: tension in the length of the beam; 3: out-of-plane bending.
matid num Specifies the material of the elements: 1: isotropic, non-layered material; 2: same isotropic material as 1, but with 3 layers.
pcoeff val The value for the Poisson coefficient. Results calculated for p=0.0 and p=0.3.

Theoretical values (beam theory) for the tip displacement and for the stresses are readily available (see Python test program __init__.py). The figure below shows the deformation (amplified) in the three loading directions: Out-of-plane bending (blue), in-plane bending (green) and tension (yellow).

Cantilever beam deformation (green; case 1, yellow: case2, blue:case 3)

Figure 114. Cantilever beam deformation (green; case 1, yellow: case2, blue:case 3)