Solution of contact problems for a transversely isotropic elastic layer bonded to an elastic half-space

Abstract

The idea, first used by the author for the case of crack problems, is applied here to solve a contact problem for a transversely isotropic elastic layer bonded to an elastic halfspace, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the layer's free surface. The governing integral equation is derived; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charged discs in the shape of the domain of contact. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half-space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.