Torsional loading of an elastic transversely isotropic nonhomogeneous semi-infinite solid

Abstract

The problem of torsion of a transversely isotropic nonhomogeneous and elastic semi-infinite solid due to certain distributions of shearing forces prescribed on the plane boundary has been considered. The elastic properties of the material are continuous function of position. The shear moduli of the material are chosen as \(C_{ii}(z')=\mu_{ii}\cosh^ 2(k'z'),\quad i=4,6\), where \(\mu_{ii}\) and k' are constants. The aim of this paper is to determine the torsional deformation and shear stresses in the semi-infinite solid.