Stolyarchuk I. The periodical problems of the elasticity theory for the multilayer foundations

The object of the study - elastic deformation of the multilayer foundation. The aim is to generalize the compliance functions technique for solving of boundary problems for multilayer foundations to the class of planar and space periodical boundary problems of the elasticity theory; the development of the methods for the approximate solving of the planar periodical contact problems for multilayer foundations; the development approach to solving of the space contact problem, connected with the pressing of the die-stripe on the multilayer foundation. Methods: Fourier integral method, and methods of the theory of functions of complex variables, compliance functions technique, methods of approximate solving of singular integral equations, method of dual integral equations. Exact solutions of the new periodical planar and space problems for the foundations have been obtained by means of the generalized compliance functions technique. The space contact problem for the die-stripe is reduced to solving of the Fredholm integral equation of the second type. A new method for the approximate solution of planar periodical contact problems has been proposed. The conditions of the detachment of the surface of the foundation from the planar bottoms of the periodic system of identical dies, which presses on the foundation, have been determined. The scope of use - in research and design institutes in the highway design and the calculations of the strength and stiffness of the roadway surfacing.