On the existence of optimal shapes in contact problems — Perfectly plastic bodies

Abstract

The optimal shape design of a two-dimensional elastic perfectly plastic body (a punch) on a rigid frictionless foundation is analysed. The problem is to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that certain energy integral of the system in the equilibrium will be minimized. It is assumed that the material of the body is elastic perfectly plastic, obeying the Henckys law. The variational formulation in terms of stresses is utilized. The existence of optimal shapes is proved.