PLASTICITY IN PLATE WITH HOLE
Opposed to the continuous forming of metal plates where an Eulerian description is appropriate, the stretching of a plate with hole is analyzed with a Lagrangian calculation. One of the features of Tochnog Professional is to allow the specification of boundary conditions, external forces, post-processing, etc. by means of geometrical entities. In this way the user does not need to find which specific element or node numbers are located on edges or otherwise. The user can focus on the description of the physical problem at hand; Tochnog Professional automatically applies the specified options on geometrical entities on the correct nodes and elements.
This option is especially convenient in combination with the build-in mesh refinement algorithms in Tochnog Professional. Changing element and node numbers due to mesh refinement due not influence user specified conditions on geometrical entities, these remain valid such that the user needs minimal effort to apply mesh refinements.
In the stretching of the plate, geometrical lines are defined of the lower edge, left edge and the top edge. Boundary conditions are defined for the lower and left edge (rolling support), and a prescribed displacement is defined for the top edge. The first picture shows the calculated displacement field, whereas the second picture shows the vertical stress distribution in the plate.