Miroshnikov V. The solution of the basic and some mixed problems of the theory of elasticity for a multilayer medium with longitudinal circular cylindrical cavities and inhomogeneities

The object of the research is the stress-strain state of space, half-space, and layer, which have several longitudinal cylindrical cavities; layer and multilayer medium, which have one cylindrical cavity or inclusions.The subject of research is the influence of boundary conditions, conditions of joining bodies, and geometric parameters on the stress-strain state of the medium.The aim of the study is to solve the scientific problem of high-precision resolution of a new class of spatial problems of the theory of elasticity, which have not been studied before. Research method—the work has been carried out on the basis of the generalized Fourier’s method.The scientific novelty of the research lies in solving a class of problems in the theory of elasticity, in particular, for multilayer bodies with longitudinal cylindrical cavities or inclusions.For the first time, problems have been solved for cylindrical cavities in elastic space and half-space with contact-type conditions on the boundary surfaces.An approach has been proposed and new problems have been solved for an elastic layer with one or several cylindrical cavities.For the first time, within the framework of the generalized Fourier’s method, a solution to the problem for a layer with a cylindrical cavity and a given periodic load has been proposed.For once, the conditions for conjugation of elastic fields for adhered and smoothly contacting layers and a layer, as well as an elastic cylinder or pipe have been considered and implemented in an analytical form.New problems have been solved for a layer connected to a half-space, one of which has a cylindrical cavity or a solid cylindrical inclusion or a pipe.For the first time, problems have been solved for two layers rigidly connected to each other, one of which has a cylindrical cavity.The practical significance of the results obtained lies in the created algorithms and the development of a complex of programs that carry out the numerical implementation of the dissertation provisions on a PC and allow an analysis of the stress-strain state of spatial models:composite materials containing a longitudinal cylindrical cavity, or reinforced ones; protective screens of structures; in the construction industry—floor slabs, underground utilities, reinforcement of structural elements; components and assemblies in mechanical engineering.The analysis of the stress state in the solved problems of the presented work can be applied in the selection of geometric parameters at the design stage.The results of the thesishave been introduced into the practice of design engineering of the Construction Group International,Construction Company.