Hypersingular formulation for boundary strain evaluation in the context ofa CTO-based implicit BEM scheme for small strain elasto-plasticity

Boundary element method (BEM) formulations for usual and sensitivity proble ms in small strain elastoplasticity, using the concept of the consistent ta ngent operator (CTO), have been recently proposed by Bonnet, Mukherjee and Poon. "Usual" problems here refer to analysis of nonlinear problems in stru ctural and solid continua, for which Simo and Taylor first proposed use of the CTO within the context of the finite element method (FEM). The BEM appr oach is shown to work well in the illustrative numerical examples in the pa pers by Bonnet, Mukherjee and Poon. Stresses on the boundary of a body must be computed accurately in order for the CTO-based algorithm to work. There are at least two approaches for calculating boundary stresses in the BEM. The first involves local tangential differentiation of the shape functions of boundary displacements, together with the local use of constitutive equa tions. The second is the use of a hypersingular BEM formulation. The first approach has been used in the previous work mentioned above, while the seco nd is employed in the present work. Here, a new algorithm is proposed for r egularization of hypersingular BEM equations for elastoplastic problems. Nu merical results are presented for the elastoplastic equivalents of the Lame and Kirsch problems in two-dimensional linear elasticity. The results are compared with FEM and are seen to be acceptably accurate. (C) 1998 Elsevier Science Ltd. All rights reserved.