The elastic torsion problem for a nonhomogeneous and transversely isotropic half-space

Abstract

The statical Reissner-Sagoci problem for nonhomogeneous transversely isotropic elastic half-space is investigated. The modulus of rigidity is assumed as \(C_{ii}(r,z)=\mu_{ii}r^{\beta}f(z)\), \(i=4,6\) and \(\beta\geq 0\), where \(\mu_{ii}\) are constants. The expressions for stresses, displacement and torque are given. The analysis is based on the assumption that the tangential displacement is prescribed within the area \(z=0\), \(r\leq 1\) and shearing stress is zero in the outside area \(r>1\), \(z=0\). The integral equation which is obtained is solved in the case when \(f(z)=\cosh^ 2kz\) and \(\beta\geq 0\), where k is a constant.