Stresses in an Elastic Circular Cylinder with a Prolate Spheroidal Cavity Under Tension

Abstract

This paper contains an exact solution for the stresses arising in an elastic circular cylinder with a prolate spheroidal cavity under tension. The solution can be reduced to a combination of the solutions, one being regular in the outside of a cavity and the other regular in an infinite circular cylinder, and is deduced with the aid of Dougall's stress functions. Two sets of simple harmonic stress functions are given by expressions referred both to the cylindrical and the prolate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied with the aid of the relations between the cylindrical and prolate spheroidal harmonics. Numerical results are given for some different equatorial semiaxes and shape ratios, and the stress distributions in the neighbourhood of the cavity are shown graphically.