Axisymmetric stress-transfers from an embedded elastic cylindrical shell to a half-space

Abstract

Within the framework of three-dimensional classical elastostatics and thin shell theories, a rigorous mathematical formulation is presented for the torsionless axisymmetric stress-transfer problem of a cylindrical shell of finite length embedded in a semi-infinite solid. By virtue of a set of ring-load Green’s functions for the shell and a group of fundamental solutions for the half-space, the mechanical interaction problem is shown to be reducible to a pair of Fredholm integral equations. Through the analysis of an auxiliary set of Cauchy integral equations, the singularities of the resultant contact stress distributions are rendered explicit, the results of which are incorporated in a numerical procedure. Typical solutions for the axial and radial load-transfers, contact stress distributions, as well as other related responses are included as illustrations. In addition to furnishing results of direct relevance to a number of engineering applications, the present treatment is apt to be useful as a basis of assessment for various approximate methods for this class of contact problems.