The Elastostatic Axisymmetric Problem of a Cracked Sphere

Abstract

The problem of a cracked sphere is solved with the use of Boussinesq stress functions. Two coordinate systems—oblate spheroidal for representing the crack surface and spherical polars for the spherical surface—are used to satisfy boundary conditions. Integral representations and transformations of harmonic functions are used to relate stress functions in the two coordinate systems. This procedure leads to a system of algebraic equations which is solved, for axisymmetric tractions on both the surfaces. Graphical results are presented for one specific loading case.