Singular integral equation method in optimization of stress-relieving hole: a new approach based on the body force method

Abstract

This paper is concerned with a method of decreasing stress concentration due to a notch and a hole by providing additional holes in the region of the principal notch or hole. A singular integral equation method that is useful for this optimization problem is discussed. To formulate the problem the idea of the body force method is applied using the Green's function for a point force as a fundamental solution. Then, the interaction problem between the principal notch and the additional holes is expressed as a system of singular integral equations with a Cauchy-type singular kernel, where densities of the body force distribution in the x- and y-directions are to be unknown functions. In solving the integral equations, eight kinds of fundamental density functions are applied; then, the continuously varying unknown functions of body force densities are approximated by a linear combination of products of the fundamental density functions and polynomials. In the searching process of the optimum conditions, the direction search of Hooke and Jeeves is employed. The calculation shows that the present method gives the stress distribution along the boundary of a hole very accurately with a short CPU time. The optimum position and the optimum size of the auxiliary hole are also determined efficiently with high accuracy.