On Solutions of the Lame System in a Flat Anisotropic Medium

Abstract

The Lamè system on the plane is considered for the displacement vector in a general anisotropic medium. Cases of explicit calculation of the roots of its characteristic equation are indicated. It is proved that this system cannot be written in the complex form of a single equation. An integral representation of general solution of the Lamè system is received in the class of continuous functions in a closed domain. The kernel and co-kernel of this representation are described. In orthotropic and isotropic an elastic medium, their explicit expression is given in terms of elastic modulus. Applications to the solution of two main boundary value problems of the theory of elasticity are also indicated.