Stresses in a Circular Cylinder Having an Eccentric Spherical Cavity under Tension

Abstract

This paper contains an analysis of the distribution of stresses in a circular cylinder having an eccentrically located spherical cavity under axial uniform tension. The method of approach is based upon the harmonic stress functions which are the general solutions of the equations of equilibrium in terms of displacements proposed by Dougall and Neuber. Owing to the linearity of elasticity, a solution can be obtained by superposing two solutions; one is expressed in terms of the cylindrical harmonics whose origin lies on the center axis of the cylinder, and the other is in terms of the spherical harmonics whose origin is at the center of the cavity. In order to superpose these solutions, we get the transformation formulae between these harmonics by altering Graf's formula. Then, making use of these relations, we can satisfy the boundary conditions on both surfaces of the cylinder and the cavity. Numerical results are given for eccentric distance c=0.25 with the ratio of the cavity radius to the cylinder radius varying 0.1∼0.5, and the stress distributions around the cavity are shown graphically.