Spytsia O. Analytical and numerical approaches to solving the problems of the theory of elasticity for multilayer environments

The dissertation is devoted to the analytical investigation of the stress-strain state of a multilayer plate. The method compliance of functions and the finite element method have been employed. The manuscript suggests new approach for the solution of the first spatial boundary value problem for multilayered plates with isotropic and transversally isotropic layers. The approach uses compliance functions and Fourier integrals. The analytical solution of axisymmetric contact problems reduces the problem to integral equations. Kernels of these equations have been represented by compliance functions. The solution for contact between one or two stamps and an elastic multilayer plate has been reduced to Fredholm integral equations of the second kind. These equations have been solved using the finite sums method. The finite element models for contact problems have been implemented. The results of these models have been compared with corresponding analytical models and approaches. Analytical results have better accuracy compared to the finite element method models. New scientific results have been described in the manuscript. Analytical models and approaches can be employed in computer-aided engineering problems. The exact solutions of the boundary value problems of the theory of elasticity for multilayer plates can be used as a reference in the development of numerical methods.