Shakedown Load Bounds by Elastic Finite Element Analysis

Abstract

Abstract A simple method for calculating lower and upper bound shakedown loads based on iterative elastic finite element analysis and the bounding theorems of classical plasticity is presented. Elastic and residual stress and strain fields, suitable for substitution into Melan’s lower bound theorem and Koiter’s upper bound theorem, are obtained by applying the elastic compensation method, in which the elastic modulus of each element in an iterative elastic finite element analysis is systematically modified according to calculated stress values from the previous iteration to form suitable residual stress fields. As a demonstration a sample plane stress problem — a biaxially loaded square plate with a central hole — is presented and the shakedown load bounds derived here for specific load cycles are compared with results available in the literature.