Analytical Solution for a Transversely Isotropic Half-Space due to Torsion on the Wall of a Finite Length Cylindrical Cavity

In this article، a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. To this end، the equation of equilibrium has been written in a cylindrical coordinate system، by dividing the involved domain to two regions and considering the equation of equilibrium in each region and by means of Fourier cosine integral transforms، the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform، the displacements are determined in the real domain. By writing boundary and continuity conditions، a governing generalized Cauchy singular integral equation is obtained. By solving the governing integral equation، the shear stress and the torsional displacement are obtained for any point. The degenerated results for isotropic media are compared with existing results reported in the literature، where there exists an excellent agreement. The results of the paper may be used as the benchmark for the related research in the transversely isotropic media.