M. Basheleishvili

Contact and Boundary-Contact Problems of Statics of Anisotropic Inhomogeneous Elastic Body

abstract:
The paper presents the proofs of the existence and uniqueness of solutions of the contact and boundary-contact problems of inhomogeneous anisotropic elastic body in the two-dimensional case. The potential method and the theory of Fredholm integral equations is used. These problems for isotropic elastic body have been solved earlier by D.I. Sherman [1], who used for their solution the method of general solutions due to Kolosov-Muskhelishvili, complex potentials and also the methods of the theory of a complex variable. The boundary conditions of the above-mentioned problems will be written in natural way. In his work D.I. Sherman instead of a stress vector takes its integral. First we consider the contact problem after which the boundary-contact problems are treated comparatively elementarily.

Mathematics Subject Classification: 70C20, 74B05

Key words and phrases: Inhomogeneous anisotropic contact problem, Fredholm elastic body, integral equation