Procedure of Continuation of Boundary Conditions in the Problems of Elasticity Theory

To find solutions of two-dimensional problems of the theory of elasticity in domains bounded by two pairs of different coordinate lines, we propose to use solutions of simpler problems in domains bounded by one pair of coordinate lines with additionally imposed boundary conditions of the original problem outside the domain. The method is illustrated by finding the solutions of boundary-value problems of the theory of elasticity for a quarter plane, a half strip, and a rectangle.