Fasoliak A. Cylindrical shell dynamics in an elastic three-dimensional inertial medium

The dissertation is devoted to the study of the dynamic stress-strain state of the thin cylindrical shells in the elastic inertial medium. The research is carried out by numerical-analytical approaches using the method of integral transforms and bipolar coordinates, as well as numerical methods, in particular, the finite element method. Using the method of integral transforms, the non-stationary cylindrical shell dynamics in the unbounded elastic inertial medium is analyzed. On the basis of an axisymmetric problem, different approaches to describing the shell motions have been compared. An effective approach to the analysis of non-stationary dynamics of discretely reinforced by ribs of rigidity of the cylindrical shells in the elastic medium is also proposed. For modeling of shell dynamics in the medium with a surface, the bipolar coordinate system (BCS) was used. In this case the basic equations of the elastic theory were obtained BCS, as well as the classical equations of the shell motions. An approach, which is based on a finite-difference scheme by space variables and an iterative process by time variable, was proposed to solve the problem. On the basis of the finite element method, the shell dynamics in the medium with the surface (cases, when the shell axis is parallel to the surface and perpendicular to it), and two coaxial shells in an unbounded medium and in the medium with the surface (both for the same depth of location, and for different ones) are analyzed. A comparison of analogous results is performed.