Optimum shakedown design under residual displacement constraints

Abstract

We consider the minimum weight design of suitably discretized elastoplastic structures subjected to variable repeated loads and constraints on the amount of residual (or permanent) deflections. The optimization problem is formulated on the basis of the classical lower bound theorem of shakedown, supplemented by appropriate constraints on deflections obtained from existing bounding results. The primary purpose of the paper is to show that, even for large size structures, this important and challenging problem can be modeled and solved directly as a mathematical programming problem within the industry standard modeling framework GAMS. Examples concerning truss-like structures are presented for illustrative purposes.