PLANE INHOMOGENEOUS PROBLEM IN ELASTICITY THEORY.

The elasticity problem for inhomogeneous media arises when we consider problems associated with the stress-strain state of solids that are subjected to various nonmechanical effects, e. g. , radiation or temperature effects, such that the elastic properties of the bodies change. This problem becomes particularly pressing in polymer mechanics and in the mechanics of various viscoelastic media whose properties depend markedly on temperature. For an inhomogeneous isotropic elastic body of this type, the plane static problem in elasticity theory are used. This solution is determined in two stages: 1) in the first stage, two arbitrary holomorphic functions are used to find a family of solutions satisfying the differential equilibrium conditions; 2) in the second stage, the boundary conditions are used to isolate the required solution from this family.