The Dual Reciprocity Boundary Element Method for the Transient Dynamic Analysis of Elastoplastic Problems

Abstract

The Dual Reciprocity Boundary Element Method 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 utilizes the static fundamental solution of the associated elastic state. 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 Dual Reciprocity Boundary Element Method (DR-BEM) which gives accurate results and is computationally efficient because the number of unknowns is reduced only to the boundary. Interior cells, in addition to boundary elements, are required to take care of the inelastic integrals. However, these cells 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 discretization, resulting in a considerable reduction in the size of the problem. A solution procedure for the proposed boundary element method is provided. Numerical examples are presented to illustrate the advantages of the proposed method.