A Multi-Surface Plasticity Method for Lower Bound Shakedown Load

Abstract

A new direct method for calculation of lower bound shakedown limits based on Melan’s theorem and a novel, non-smooth multi-surface plasticity model is proposed and implemented in a Finite Element environment. The load history is defined by a finite number of extreme points defining the load-envelope of a periodic load set. The shakedown problem is stated as a plasticity problem in terms of a finite number of independent yield conditions, solved for a residual stress field that satisfies a piecewise, non-smooth yield surface defined by the intersection of multiple yield surfaces. The implemented Finite Element procedure is applied to two shakedown problems and the results compared with lower and upper bound elastic shakedown solutions given by the Linear Matching Method, LMM. The example analyses show that the proposed Elastic-Shakedown Multi Surface Plasticity (EMSP) method defines robust lower bound shakedown limits between the LMM lower and upper bound limits, close to the LMM upper bound.