Integral equations of plane static boundary value problems of the elasticity theory for an inhomogeneous anisotropic medium

Abstract

The static boundary value problems of plane elasticity for an inhomogeneous anisotropic medium in a simply connected domain are reduced to the Riemann–Hilbert problem for a quasianalytic vector. Singular integral equations over the domain are obtained, and their solvability is proved for a sufficiently wide anisotropy class. In the case of a homogeneous anisotropic body, the solutions of the first and second boundary value problems are obtained in closed form.

For compound elastic media with anisotropy varying over a domain (of a sufficiently wide class), uniquely solvable integral equations of boundary value problems of static elasticity for an inhomogeneous anisotropic medium are obtained, which readily permits finding generalized solutions that satisfy the matching conditions on the interfaces between the subdomains.