On the Computational Aspects of a Symmetric Multidomain Boundary Element Method Approach for Elastoplastic Analysis

Abstract

The symmetric boundary element method (SBEM) is applied to the elasto-plastic analysis of bodies subdivided into substructures. This methodology is based on the use of: a multidomain SBEM approach, for the evaluation of the elastic predictor; a return mapping algorithm based on the extremal paths theory, for the evaluation of inelastic quantities characterizing the plastic behaviour of each substructure; and a transformation of the domain inelastic integrals of each substructure into corresponding boundary integrals. The elastic analysis is performed by using the SBEM displacement approach, which has the advantage of creating system equations that only consist of nodal kinematical unknowns at the interface boundary among substructures. The elasto-plastic solution utilizes a strain-driven strategy that is characterized by the evaluation of the elastic predictor that is a function of the initial conditions and the load increment. The predictor phase is followed by the use of a return mapping algorithm defined by introducing the extremal paths theory to remove the time integration. Then the computed plastic strains are considered to be constant inelastic actions imposed inside the substructure in a step-by-step procedure. Their presence involves domain integrals with singular kernels. These integrals are considered as Cauchy principal values with which the related free term is associated. In order to compute these domain integrals, the radial integral method is applied to remove the strong singularity.