Turchyn I. The Laguerre polynomials method in non-stationary thermoelasticity and elasticity problems for layered solids

In the work a highly efficient method for derivation and studying the solutions for initial boundary value problems in the mechanics of layered solids and media based on Laguerre's integral transformation was developed. At that, initial boundary value problem for the heat equation and the wave equation in each layer was reduced to triangular sequences of ordinary differential equations. General solutions of these sequences in the form of algebraic convolutions were obtained and the way to determine fundamental solutions in rectangular and cylindrical coordinates was presented. The method for solving algebraic equations which are modeling the force or temperature loads of boundary surfaces of inhomogeneous bodies and thermomechanical interaction of the components for their random number was developed. By using a method of Neumann series the analytic-numerical method for solving sequences of dual integral equations that arise when applying the method of integral transforms to unsteady problems with mixed boundary conditions was obtained. The conditions for input functions and parameters, in which sequences of infinite systems of linear algebraic equations, obtained in applying the above techniques, are quasi-regular, were found.