A general algorithm for plastic flow simulation by finite element limit analysis

Abstract

Limit analysis has been rendered versatile in many structural and metal forming problems. In metal forming analysis, the slip-line method and the upper bound method have filled the role of limit analysis. As a breakthrough of the previous work, a computational approach to limit solutions is considered as the most challenging area. In the present work, a general algorithm for limit solutions of plastic flow is developed with the use of finite element limit analysis. The algorithm deals with a generalized Holder inequality, a duality theorem, and combined smoothing and successive approximation in addition to a general procedure for finite element analysis. The algorithm is robust such that from any initial trial solution, the first iteration falls into a convex set which contains the exact solution(s) of the problem. The idea of the algorithm for limit solutions is extended from rigid/perfectly plastic materials to work-hardening materials by the nature of the limit formulation, which is also robust with numerically stable convergence and highly efficient computing time. (C) 1998 Elsevier Science Ltd. All rights reserved.