On Integral Equation Methods for the Crack Problems

Abstract

In this paper, integral equation methods for boundary value problems of elastic bodies with cracks are investigated. We use Somigliana's identities to represent displacements in elastic bodies, and deduce integral equations from the boundary conditions on the crack surfaces. In these integral equations, unknown functions are displacement differences between the upper and the lower crack surfaces. Divergent integrals are contained and they are evaluated in the sense of Hadamard's finite parts. The integral equations are solved analytically for the case of penny-shaped crack. Methods for numerical solutions of the equations are also studied.