Na. Noda et T. Matsuo, SINGULAR INTEGRAL-EQUATION METHOD IN OPTIMIZATION OF STRESS-RELIEVINGHOLE - A NEW APPROACH BASED ON THE BODY FORCE METHOD, International journal of fracture, 70(2), 1995, pp. 147-165
This paper is concerned with a method of decreasing stress concentrati
on due to a notch and a hole by providing additional holes in the regi
on of the principal notch or hole. A singular integral equation method
that is useful for this optimization problem is discussed. To formula
te 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, th
e interaction problem between the principal notch and the additional h
oles is expressed as a system of singular integral equations with a Ca
uchy-type singular kernel, where densities of the body force distribut
ion 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 o
f the fundamental density functions and polynomials. In the searching
process of the optimum conditions, the direction search of Hooke and J
eeves 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 th
e auxiliary hole are also determined efficiently with high accuracy.