A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors

Abstract

A numerical scheme is presented aimed at computing shakedown load safety factors in elastic-plastic structures discretized by finite elements. Its main features are the use of a local, a posteriori linearization of the yield surface, which allows the prescription of a maximum violation of the constitutive law, and the use of a physically oriented solution algorithm to the linear complementarity problem to which the shakedown analysis is reduced. There is no need to construct the envelope vector of the elastic stresses, at the basis of many mathematical programming approaches to this problem. The accuracy and computational effectiveness of the proposed technique are illustrated by means of benchmark examples studied in the literature.