Stress-based finite element analysis of plane plasticity problems

Abstract

A stress-based model of the finite element method is evolved for two-dimensional quasi-static plasticity problems. The self-equilibrating fields of stresses are constructed by means of the Airy stress function, which is approximated by three types of elements: the Bogner-Fox-Schmit rectangle, the Hsieh-Clough-Tocher triangle and its reduced variant. Traction boundary conditions are imposed by the use of the Lagrange multiplier method which gives the possibility of calculation of displacements for boundary points. The concept of multi-point-constraints elements is applied in order to facilitate the application of this technique. The iterative algorithm, analogous to the closest-point-projection method commonly used in the displacement-based finite element model, is proposed for solving non-linear equations for each load increment. Two numerical examples with stress- and displacement-controlled load are considered. The results are compared with those obtained by the displacement model of FEM. Bounds for limit loads are obtained. Copyright (C) 1999 John Wiley & Sons, Ltd.