Transient dynamic elastoplastic analysis by the dual reciprocity BEM

Abstract

The dual reciprocity boundary element method (DR-BEM) for the transient dynamic analysis of elastoplastic structures is presented. The formulation of the method takes place within the framework of small deformation theory of inelasticity and utilises the elastostatic fundamental solution. The integral equation of the problem includes not only boundary integrals but domain integrals as well, due to inelastic and inertial terms. However, the inertial domain integral can be further transformed into boundary integrals by approximating the accelerations within the domain. The resulting integral equation forms the basis for a DR-BEM which gives accurate results and is computationally efficient because the number of unknowns is reduced only to the boundary. Interior cells, which are required to take care of the inelastic domain integrals, can be restricted only to those portions of the domain expected to become inelastic. Moreover, the number of unknowns in the resultant algebraic systems depends only on the boundary discretisation, resulting in a considerable reduction in the size of the problem. A complete solution procedure for the proposed DR-BEM is constructed, in which the Houbolt time integration method is used and inelastic effects are accounted for by special algorithms at each time step. The proposed DR-BEM has distinct advantages over the finite element method. Several numerical applications are presented to illustrate the use and demonstrate the advantages of the DR-BEM.