First and second fundamental axisymmetric problems of elasticity theory for doubly-connected domains bounded by the surfaces of a sphere and a spheroid

Abstract

The method of constructing solutions of the fundamental boundary-value problems for a homogeneous Lamé equation of multiconnected domains bounded by canonical surfaces of cylindrical and spheroidal coordinate systems described in /1/ is extended to domains with other geometry. The problems under consideration reduce to infinite systems of linear algebraic equations of the second kind with completely continuous opertors. A solution in the form of expansions in a small parameter for the problem of the hydrostatic pressure of a sphere with a centrally located spheroidal cavity is presented as an example.