On the Asymmetric Problem of Elasticity Theory for an Infinite Elastic Solid Containing Some Spherical Cavities : 2nd Report.. An Infinite Solid Containing Three Spherical Cavities

Abstract

This paper contains a solution in series form for the stress distribution in an infinite elastic solid which posseses three spherical cavities. The loading consists of a uniform field of uniaxial tension at infinity in the direction perpendicular to the common axis of the cavities. The solution is based upon the Papcovich-Neuber stress function approach and deduced with use of the spherical harmonics. The method can be developed for a variety of cavity numbers and sizes. Numerical evaluations are given for the stress distributions in the infinite medium containing (i) three equidiameter spherical cavities or (ii) two outer cavities of the same size and the central cavity of any size. The results illustrate the interference of three sources of stress concentration in a three-dimensional problem.