A Boundary Element Formulation of Problems in Linear Isotropic Elasticity with Body Forces

Abstract

Traditional formulations of the Boundary Element Method (BEM) applied to elastostatics [1] [2] are extremely convenient when the loading on the body under analysis is limited to surface loading, since it is necessary to discretize only the boundary of the body and not the whole domain as must be done when using a technique such as the Finite Element Method (FEM). When body forces are present these have usually been handled by evaluating a domain integral [3]. Unfortunately this requires the domain of the problem to be divided into integration cells since for any practical problem the domain integral must be evaluated numerically. This greatly increases the amount of data preparation required and causes the BEM to lose much of its advantage over domain type methods. However, Cruse [4] and Cruse, Snow and Wilson [5] have shown that for certain types of commonly encountered body forces the domain integral may be transformed to a boundary integral or boundary integrals which may be evaluated at the same time as the boundary integrals involving the surface displacements and tractions. Ref. [5] is concerned exclusively with axisymmetric geometry; however, the authors’ use of the Galerkin vector to achieve the required transformation from domain to boundary integrals provides the key to the present paper which relates to two and three dimensional geometry. The three dimensional case was derived in Ref. [4] without resort to the Galerkin vector. However, the Galerkin vector approach is used below both to demonstrate the power of the technique and to present the results of [4] in a slightly more general form. The two dimensional formulation is also presented.