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

Abstract

Abstract Boundary element method (BEM) formulations for usual and sensitivity problems in small strain elastoplasticity, using the concept of the consistent tangent operator (CTO), have been recently proposed by Bonnet, Mukherjee and Poon. “Usual” problems here refer to analysis of nonlinear problems in structural 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 approach is shown to work well in the illustrative numerical examples in the papers 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 equations. The second is the use of a hypersingular BEM formulation. The first approach has been used in the previous work mentioned above, while the second is employed in the present work. Here, a new algorithm is proposed for regularization of hypersingular BEM equations for elastoplastic problems. Numerical 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.