Shakedown of elastic—plastic solids with frictionless unilateral contact boundary conditions

Abstract

Elastic perfectly plastic solids (or structures) in frictionless unilateral contact with a rigid obstacle and subjected to quasi-statically variable loads within a given domain are considered. In the hypothesis that the structure undergoes small displacements and complies with a d-stability requisite herein introduced, a Melantype shakedown theorem is presented. This theorem is conceptually similar to the classical one; namely, it requires that the unilateral-contact elastic stress response to the loads and to some initial plastic strains be plastically admissible everywhere in the body and for all load conditions. A method for evaluating the shakedown load boundary is also discussed. It is shown that, by virtue of the unilateral contact constraint, all the ratchetting collapse modes pertaining to the associated no-contact shakedown problem and characterized by ratchet normal displacements against the rigid obstacle are ruled out. A simple numerical example is presented.