An Iterative Method for Elastic-Plastic Stress Analysis

Abstract

Most numerical methods to solve incremental problems in elastic-plastic stress analysis are based on the use of so called the “elastic-plastic matrix”, which is derived from a backward or a forward finite difference approximation of constitutive equations. This kind of approximation, however, has a difficulty in satisfying some conditions which characterize the original problem, and this causes some question on the accuracy of those methods. As well known, the normality of plastic strain increments is a remarkable condition imposed on the solution of plasticity problem. Also, the conditions that stress point must move on yield surface during plastic deformation and that plastic strain increments relate to hardening parameters in a definite rule are essential in the usual formulation of plasticity problem. However, the second or the third condition is, unfortunately, not satisfied in many approximate methods. It is because those conditions are not simultaneously satisfied by a simple finite difference approximation of constitutive equations.