Stress Concentration Around an Ellipsoidal Cavity in an Infinite Body Under Arbitrary Plane Stress Perpendicular to the Axis of Revolution of Cavity

Abstract

This paper contains an exact closed solution for the stress distribution around a cavity in the shape of an ellipsoid of revolution in an infinite elastic body which is otherwise in an arbitrary uniform plane state of stress perpendicular to the axis of revolution of the cavity. The solution is based upon an extension to orthogonal curvilinear co-ordinates of the classical three-function approach to three-dimensional problems of the theory of elasticity. The technically important features of the ensuing stress concentration are discussed in detail.