Numerical Solution of Singular Integral Equations of the Body Force Method in Notch Problems : 3rd Report, Application to 3D Problems

Abstract

This paper deals with numerical solutions of singular integral equations of the body force method in 3D stress concentration problems. As examples, the problems of ellipsoidal cavities and a toroidal hole under uniform tension are considered. The problems are formulated as a system of singular integral equations with Cauchy-type singularities, where the densities of body forces distributing in the r and z directions are unknown functions. In order to satisfy the boundary conditions along the notches, several types of fundamental density functions are proposed ; then, the body force densities are approximated by a linear combination of the fundamental density functions and polynomials. The accuracy of the present analysis is verified by comparing the present results with the results obtained by the conventional method. The present method is found to give rapidly converging numerical results for the stress distribution along the boundaries.