NUMERICAL IMPLEMENTATION OF A CTO-BASED IMPLICIT APPROACH FOR THE BEMSOLUTION OF USUAL AND SENSITIVITY PROBLEMS IN ELASTOPLASTICITY

Boundary element method (BEM) formulations for usual and sensitivity p roblems in small strain elastoplasticity, using the concept of the con sistent tangent operator (CTO), have been recently proposed by Bonnet and Mukherjee. 'Usual' problems here refer to analysis of nonlinear pr oblems in structural and solid continua, for which Simo and Taylor fir st proposed the use of the CTO within the context of the finite elemen t method (FEM). It was shown by Bonnet and Mukherjee that the sensitiv ity of the strain increment, associated with an infinitesimal variatio n of some design parameter, solves a linear problem which is governed by the (converged value of the) same global CTO as the one that appear s in the usual problem. This paper presents a general numerical implem entation of the above formulations. Numerical results for the usual an d sensitivity problems are presented for a two-dimensional (plane stra in) example. Sensitivities are calculated with respect to a material p arameter that characterizes isotropic strain hardening. The crucial ro le of the CTO, in providing accurate numerical results for the mechani cal variables as well as their sensitivities, is examined in this pape r. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.