The existence and uniqueness of solutions by the covering domain method in linear elastostatics

The paper deals with problems of linear elastostatics with multiply connected solution domains. Generally, a multiply connected domain can be represented in a non-unique way by the intersection set of n > 1 domains, each of which covering completely the original solution domain. If exact analytical solutions can be found in the covering domains, then, making use of the superposition principle, the solution of the original problem can be constructed by summation of the n solutions of the covering domains. Following this idea, the ''Covering Domain Method'' is developed, by which the original problem is transformed into a system of Fredholm integral equations which finally offers the solution of the problem. In this paper we consider the existence and uniqueness of the solutions for different choice of covering domains. Two theorems are presented, which are useful for the application of the covering domain method in elasticity.