Numerical solution of singular integral equations in stress concentration problems

In this paper, the numerical solution of singular integral equations in stress concentration problems is considered. The idea of the body force method stress field induced by a point force in an infinite body is used as a fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of r(-1). In solving the integral equations, the boundary conditions satisfied by two types of numerical procedure are examined. Then, it is found that the unknown functions of body force densities should be approximated by the product of a polynomial and several types of fundamental density functions. The calculation shows that this latter method gives a smooth variation of stresses along the elliptical boundary for various geometrical and loading conditions. In addition, this method gives rapidly converging numerical results and highly satisfied boundary conditions along the entire boundary. (C) 1997 Elsevier Science Ltd.