The Hypersingular Boundary Contour Method for Three-Dimensional Linear Elasticity

Abstract

A variant of the usual boundary element method, called the boundary contour method, has been presented in the literature in recent years. In the boundary contour method in three-dimensions, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. The boundary contour method employs global shape functions with the weights, in the linear combinations of these shape functions, being defined piecewise on boundary elements. A very useful consequence of this approach is that stresses at points on the boundary of a body, where they are continuous, can be easily obtained from the boundary contour method. The hypersingular boundary element method has many important applications in diverse areas such as wave scattering, fracture mechanics, symmetric Galerkin formulations, and adaptive analysis. This paper first presents the derivation of a regularized hypersingular boundary contour method for three-dimensional linear elasticity. This is followed by a discussion of special cases of the general formulation, as well as some numerical results.