Stress analysis of toroidal hole in an infinite body

This paper deals with stress analysis of toroidal hole in an infinite body under uniform tension. The problem is formulated as a system of singular integral equation with Cauchy-type singularity, 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 hole boundary, eight kinds of fundamental density functions are introduced in the similar way of previous papers treating plane stress problems. Then the body force densities are approximated by a linear combination of those fundamental density functions and polynomials. In the analysis, shape of toroidal hole is varied systematically; then, the magnitude and position of the maximum stress are shown in tables. The stress distributions along the boundary are shown in figures. The accuracy of the present analysis is verified by comparing the present results with the results obtained by the conventional method. It is found that this method gives rapid convergence numerical results for the stress distribution along the boundary and stress concentration factors of toroidal hole are close to stress concentration factors of notched round bar and deep notch when a/d-->1.