Vlasiy O. Mathematical modeling of mechanical and heat processes in building constraction elements of discrete-continuous structure.

The thesis is devoted to the development of new mathematical models of oscillation processes and heat transfer processes in building constraction elements of discrete-continuous structures including concentrated factors.The methods for exact analytic boundary problems solving for the generalized quasi-differential equations are proved. The special classes of quasi-differential equations, for which formulas for constructing exact analytical solutions of boundary value problems are obtained, are improved. The new patterns of heat transfer and oscillation processes in bodies with discrete-continuous structure are obtained. The conditions of convergence of solutions of approximating problems sequence for first order differential equations systems with measures to solution of the original problem are established. Appropriate software is designed. This software is used for computer modeling problems of free and forced oscillations of cantilever beams of varying stiffness with continuously distributed mass and concentrated masses and moments in the case of various conditions fixing of the beams ends, as well as modeling of heat transfer in multilayer bodies with regard to point sources of heat.