A Torsional Contact Problem for an Indented Half-Space

This paper is concerned with the torsion of a rigid disk bonded to the bottom of a cylindrical indentation on an elastic half-space. By virtue of Fourier sine and cosine transforms, the mixed boundary value problem in classical elastostatics is shown to be reducible to a pair of integral equations, of which one possesses a generalized Cauchy singular kernel. With the aid of the theory of analytic functions, the inherent fractional-order singularity in the contact problem is rendered explicit. Illustrative results on the torsional stiffness of the base of the indentation and the corresponding contact stress distribution are presented for engineering applications.