Numerical solution of singular integral equations of the body force method in stress concentration problems; for longitudinal shear loading

摘要

This paper deals with numerical solutions of singular integral equations in stress concentration problems for longitudinal shear loading. The body force method is used to formulate the problems as a system of singular integral equations withCauchy-type singularities, where unknowns are the densities of body forces distributed in the longitudinal direction of an infinite body. In order to satisfy the boundary conditions along elliptical boundaries, four kinds of fundamental density functionsare newly introduced. Then the body force densities are approximated by a linear combination of those fundamental density functions and polynomials. The calculations are carried out for several arrangements of elliptical holes, and it is found that thepresent method yields rapidly converging numerical results. The body force densities and stress distributions along the boundaries are shown in figures to demonstrate the accuracy of the present solutions.