On Boundary Integral Equations for Cracked and for thin Bodies

Abstract

This paper addresses usual and hypersingular boundary integral equations for three-dimensional linear elasticity for two limiting cases-a body with a crack and a thin body. Degeneracy, or lack thereof, of the usual and hypersingular boundary integral equations, for these limiting cases, are critically examined in the context of a displacement discontinuity formulation and a regularization scheme based on "simple solutions" or "modes of deformation." Finally, the paper presents conversion of certain surface integrals on closure surfaces ("tents") into line integrals using Stokes' theorem.