BEM Treatment of Body Forces in Plane Orthotropic Elastostatics

Abstract

A new boundary-element formulation is given in this paper to treat gravitational and centrifugal body forces in plane orthotropic media. In this method, two functions have been defined to satisfy the orthotropic potential equations. After recasting the elasticity equations of equilibrium for orthotropic media including body forces in the form of scalar orthotropic potential equations, for which a relatively simple fundamental solution exists, the inhomogeneous terms, i.e. the effects of the body forces in the partial differential equations can be incorporated into the boundary values. Thus only boundary integrals are needed. Several examples of solutions obtained by the present method are presented. Each solution has been compared with an analytical solution or a solution obtained by the finite-element method (FEM). By means of these examples, the method is shown to be effective for evaluating displacements and stresses resulting from body forces due to gravity or constant rotation.