Optimization of the Position and Size of Auxiliary Hole to Minimize Stress Concentration.

Abstract

In this paper the optimum position and size of an auxiliary hole are considered in order to minimize the stress concentration due to notches and holes in plates under tension. To solve these problems, the body force method is applied. Then, the problems are formulated as a system of singular integral equations with Cauchy-type singularities, where the densities of body forces distributed in the x- and y-directions are unknown functions. In order to satisfy the boundary conditions along the auxiliary hole and the notch, eight kinds of fundamental density functions proposed in our previous paper are used ; then the body force densities are approximated by a linear combination of the fundamental density functions and polynomials. To obtain the optimum conditions, the direct search method proposed by Hooke-Jeeves is employed. The results show that the position and size of the auxiliary hole are determined efficiently with high accuracy.