Sh. Zazashvili

Georgian Technical University Tbilisi, Georgia

THE BASIC AND MIXED BOUNDARY VALUE PROBLEMS OF ELASTIC MIXTURES THEORY FOR INFINITE PLANE

WITH CUTS

Suppose we have an infinite plane with curve cuts S_{1}, S_{2}, …, S_{n}. Let S_{J} = p_{j}q_{j}, j = 1, 2, …, n be simple nonintersecting sufficiently smooth curves with positive direction from p_{j} to q_{j}. The infinite plane with cuts is denoted by D.

The following boundary value problems (BVP) are investigated for the homogeneous system of equations of elastostatics of the theory of mixtures.

Find a regular solution of the system in the domain D satisfying the one of the following boundary conditions:

(i) the displacement vector is given on both sides of the cuts (the first basic BVP);

(ii) the stress vector is given on both sides of the cuts (the second basic

BVP); (iii) the displacement vector is given on one side of the cuts and the stress

vector is prescribed on the other side of cuts (the mixed BVP). Applying the general representation formula of solution by means of com-

plex valued potentials, the existence and uniqueness theorems are proved.