Green Tensor and Solution of the Boussinesq Problem in the Generalized Theory of Elasticity

Abstract

The fundamental spatial problems of the theory of elasticity such as the problem of constructing Green tensor and the Boussinesq problem of the action of a concentrated force on a half-space are considered. According to the classical theory of elasticity, these problems are singular. It is shown that ananalytical solution of such problems can be constructed by the Papkovich—Neuber representation without invoking symmetry conditions. This makes it possible to present the solution of the problems under consideration in a single form and allows us to write an explicit solution of half-space loaded by a concentrated vector-force having non-zero projections onto the normal to the plane bounding the half-space and onto the plane itself.

This paper deals with the generalized regular solutions of the considered fundamental problems of the elasticity. The solutions are limited at a singular point and damp at infinity.