A Galerkin boundary contour method for two-dimensional linear elasticity

Abstract

The Boundary Contour Method (BCM) is a recent variant of the Boundary Element Method (BEM) resting on the use of boundary approximations which a-priori satisfy the field equations. For two-dimensional problems, the evaluation of all the line-integrals involved in the collocation BCM reduces to function evaluations at the end-points of each element, thus completely avoiding numerical integrations.

With reference to 2-D linear elasticity, this paper develops a variational version of BCM by transferring to the BCM context the ingredients which characterize the Galerkin-Symmetric BEM (GSBEM). The method proposed herein requires no numerical integrations: all the needed double line-integrals over boundary elements pairs can be evaluated by generating appropriate “potential functions” (in closed form) and computing their values at the element end-points. This holds for straight as well as curved elements; however the coefficient matrix of the equation system in the boundary unknowns turns out to be fully symmetric only when all the elements are straight. The numerical results obtained for some benchmark problems, for which analytical solutions are available, validate the proposed formulation and the corresponding solution procedure.