Velichko E. The solution of periodically boundary problems of the elasticity theory for the multilayer plates with the help of the series

The work presents the method of the solution in trigonometric series of the basic boundary problems of the elasticity theory for the multilayer plates and the foundations, which are loaded by the periodic system of the forces. Such notion as the additional sequences of the layer and the compliance matrices of the plate (foundation). The cases of the plane deformation and the space deformation are considered. We have examined their properties and obtained the recursion relation for their calculation. The integral equations for some periodic contact problems for the multilayer plates and foundations have been obtained. The type of the particularities of the kerns of these equations is established. The approximate methods of the solution of the obtained integral equations with the help of the computers are proposed. The numerical results are given.