Elastic half-space with several domains subjected to tangential displacements

Abstract

The mixed boundary value problem for a transversely isotropic elastic half-space is considered for the case when uniform tangential displacements are prescribed over several domains of arbitrary shape, and the rest of the half-space boundary is stress free. The problem can be interpreted either as that of two elastic half-spaces interconnected by several regions of general shape and subjected to remote shear loading, or as a contact problem of several flexible punches, connected to the half-space, with different tangential displacements prescribed. A general theorem is established which relates the resulting tangential forces, acting on each domain, with their generalized displacements through a system of linear algebraic equations. The theorem is applied to the case of arbitrarily located elliptical domains subjected to uniform tangential displacements. Several specific examples are considered.