Uniformly loaded, elastic-plastic plate

Figure 1 shows the geometry for this case. Two types of meshes are provided: a single-element mesh using higher-order plane stress and shell elements (CPS8R, S8R5, S9R5, and STRI65) and a mesh using linear shell and continuum shell elements (S4R and SC8R). Two edges have simple support. The load history is shown in Figure 2 and is prescribed with an amplitude curve (Amplitude Curves). The load distribution is a uniform, direct stress on the element edge. Since the strain should be uniform, the edge nodes are constrained using an equation constraint (Linear Constraint Equations) to move together in the direction normal to the edge. Then the total load on the edge is simply given on one of the edge nodes.

The case is set up with the same geometric model (Figure 1). However, the loading is more complex (see Figure 2).

First, the plate is loaded into the plastic range in uniaxial tension in the x-direction, unloaded slightly, and reloaded. Biaxial loading then follows, with ${\sigma }_x$ and ${\sigma }_y$ prescribed, as shown in Figure 2, so that the quantity $\sqrt{{\sigma }_x^2+{\sigma }_y^2-{\sigma }_x{\sigma }_y}$ remains constant at 276 MPa (40000 lb/in²). This loading is defined by an amplitude curve by reading in a file of values previously calculated in the small program AMP (see elasticplasticplate_amplitude.f).