Singular Integral Equation Method in the Analysis of Interaction Between Cracks and Defects

Abstract

Singular integral equation method has been applied to a lot of crack problems. However, the method has not been widely applied to stress concentration problems such as notch, hole, cavity, or inclusion. In this paper, general solution for elliptical boundaries is formulated in terms of singular integral equations and interaction problems among elliptical holes, ellipsoidal cavities, and cracks are discussed. To formulate the problem, the body force method is applied. Using the Green's function for a point force and a force doublet as fundamental solutions, notch and crack problems are formulated as a system of singular integral equations with a Cauchy-type and a hypersingular kernel, respectively. In solving the integral equations of the body force method, the continuously varying unknown functions of body force densities are approximated by a linear combination of fundamental density functions and polynomials. The accuracy of the present analysis is verified by comparing with the results obtained by the other researchers. The calculation shows that the present method gives rapidly conversing numerical results with high accuracy. Furthermore, it is found that the present method gives the stress distribution along the boundary of hole or cavity very accurately with short CPU time. The present method can be applied to the interaction problems among holes, inclusions, and cracks that are regularly or randomly distributed.