Limit analysis in the presence of plasticity and contact

This paper presents a mathematical programming based approach for the limit analysis of structures involving elastoplasticity and contact conditions. The contact model is one of unilateral (nonassociative) Coulomb friction. The main feature of the proposed scheme is a single-step computation of the maximum load such that plasticity and contact conditions are simultaneously satisfied. The formulation is cast as a challenging nonconvex and nonsmooth optimization problem, known as a mathematical program with equilibrium constraints (MPEC). The equilibrium constraints are in fact complementarity conditions used to describe both plasticity and contact laws. A penalty based nonlinear programming (NLP) algorithm is proposed to solve the MPEC. Application is illustrated by an example discretized with locking-free mixed finite elements.