M. Basheleishvili
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