Dynamic elastic-plastic analysis by a symmetric Galerkin boundary element method with time-independent kernels

Abstract

Boundary integral equations formulated by the combined use of single-layer and double-layer sources in such a way that the integral operator is symmetric (with respect to a suitable bilinear form), and their discretization by a Galerkin weighted-residual procedure are the basic features of the ‘symmetric Galerkin boundary element method’ (SGBEM). This approach, which has been applied to various mechanical problems in the last few years, is proposed and developed herein for elastic-plastic dynamic analysis using elastostatic kernels (i.e. time independent Green functions for unbounded spaces) for displacements and tractions on the boundary and for stresses and displacements on the domain. Thus only double integrations are required (instead of quadruple required by elastodynamic kernels) at the price of domain integrals. Regularization procedures for singular integrals are developed. Assuming material behaviours as elastic-plastic stable (in Drucker sense) and suitable multifield modelling in space, basic results for a computational theory are established (extremum property and uniqueness of time-step solution, convergence of an iterative solution algorithm, algorithmic stability along the step sequence). Finally, the SGBEM developed is corroborated by two numerical comparative tests.