Stress Concentrations of a Hollow Circular Cylinder with a Semicircular Notch under Internal Pressure

Abstract

This paper deals with the stress concentration problem of a hollow circular thick walled elastic cylinder with a semicircular groove under internal pressure. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of a thick plate. The Green's functions are defined as solutions for a thick plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. A principle of the method of solution is to imagine a hollow cylinder with a notch and to distribute axisymmetric body forces in the thick plate so as to satisfy the boundary conditions of the hollow cylinder. The problem is formulated by an intergral equation with unknown functions of body forces. Stress concentrations at the notch are investigated by numerical calculations and stress distributions near the notch and form factors are shown. The maximum stress appears at the bottom of notch or the inner boundary of smallest cross section depending on the inner radius of cylinder and the notch radius.