Boundary integral equation for notch problems in an elastic half-plane based on Green’s function method

Abstract

This paper studies a boundary integral equation (BIE) for notch problems in an elastic half-plane based on Green's function method. The boundary along the half-plane is traction-free. A fundamental solution is suggested, which is composed of a principal part and a complementary part. The process for evaluating the complementary part from the principal part is similar to the Green's function method for Laplace's equation. After using the Somigliana identity or Betti's reciprocal theorem between the field of the fundamental solution and the physical field, the displacements at the domain point are obtained. Letting the domain point approach the boundary point and using the generalized Sokhotski-Plemelj formula, a BIE of the notch problem for a traction-free half-plane boundary is obtained. The accuracy of the suggested technique is examined. Computed results for elliptic notches and a square notch with rounded corner are presented in the paper.