Numerical solution for the degenerate scale in 2D Laplace equation for notch in half-plane using null field BIE

Abstract

This paper provides a numerical solution for the degenerate scale in the antiplane elasticity with the traction free condition along the half-plane boundary. The image method is used in the formulation of the fundamental solution. After using the Betti׳s reciprocal theorem between the fundamental field and the physical field, the null field boundary integral equation (BIE) is obtained. After performing the coordinate transform, the BIE can be alternatively formulated in the normal scale, and a linear algebraic equation is obtained after discretization. The influence matrix in the normal scale is invertible. The degenerate scale can be evaluated by the invertible property of the influence matrix.