An analytical method of solution of mixed problems of the theory of elasticity

An analytical method of solution of integral, integrodifferential equations and their systems of special forms, is described here. The method consists of reducing the mentioned equations to Riemann's problem of the theory of analytic functions for a vector of the second or more order and its effecti ve solution by reducing them to infinite algebraic systems with exponential rate of convergence of the approximate solution to the coexact one. Soluti ons of some problems of the theory of cracks in composite bodies carried ou t with the help of this method are also given.