Fundamental Solutions for a Piecewise-Homogeneous Transversely Isotropic Elastic Space

Abstract

The problem of construction of the fundamental solutions for a piecewise-homogeneous transversely isotropic space is reduced to a matrix Riemann problem in the space of slowly increasing distributions. We propose a method for the solution of this problem. As a result, in the explicit form, we obtain expressions for the components of the vector of fundamental solution and simple representations for the components of the stress tensor and the vector of displacements in the plane of joint of transversely isotropic elastic half spaces subjected to the action of concentrated normal and tangential forces. We study the fields of stresses and displacements in the plane of joint of the half spaces. In particular, for some combinations of materials, we present the numerical values of the coefficients of influence of concentrated forces on the stresses and displacements. We also establish conditions under which the normal displacements are absent in the plane of joint of transversely isotropic elastic half spaces.