Limit analysis in plasticity as a mathematical programming problem

Abstract

We study an infinite dimensional mathematical programming problem, which arises naturally in solid mechanics. It concerns the moment of collapse, and the collapse state itself, of a plastic structure subjected to increasing loads. The duality between the «static» and «kinematic» theorems of limit analysis is well-known in discrete plasticity; we prove the same duality for a continuum including existence of the collapse fields for stresses and velocities as the primal and dual solutions. We then discuss the approximation of the infinite problem by a family of finite convex programming problems. Numerical results for classical problems in limit analysis where this discretization is based on finite elements will be published separately.