Orlenko S. Dynamics of three-layer shells of rotation with a discrete inhomogeneous placeholder

The dissertation is devoted to the development of computational models of asymmetric three-layer shells of rotation with discrete-symmetric lightweight, rib-reinforced filler, improvement of numerical finite-difference methods and development of finite-element methods for solving corresponding initial-boundary value problems of mathematical physics, stress-strain state assessment of three-layer shell structures depending on their geometric and physico-mechanical parameters under different types of non-stationary loading. The introduction substantiates the relevance of the chosen topic of the dissertation, gives a general description of the work, proves the need for scientific research, formulates the purpose and objectives of the study, indicates the relationship of work with research programs, topics, plans. The first chapter covers general issues of the development of methods for solving problems of the stress–strain state of layered shell structures, given in the works and monographs of well-known scientists. These works remain a solid mathematical basis for selecting suitable hypotheses for constructing computational models of three-layer shell elements and determining the application of analytical and numerical methods for calculating real structures. Based on a thorough analysis of the current state of the problem of determining the nature of nonstationary oscillations and stress-strain state of three-layer shells with filler of complex geometry and significantly different physical and mechanical properties, the place of this work among previous developments is determined and the choice of research directions is substantiated. In the second section the problem statement is presented, the calculation model is created and the solving systems of equations of oscillations of asymmetric three-layer shells of rotation with discrete-symmetric lightweight, rib-reinforced filler at forced dynamic loads are derived. Reinforcing elements are fixed at distances that significantly exceed their transverse dimensions, and are located along the main lines of curvature of the shell. In the third section, the regularities of the flow of wave processes in asymmetric three-layer cylindrical shell structures with a discrete-symmetric lightweight, rib-reinforced filer under nonstationary loads are investigated. The fourth section investigates a discrete-symmetric inhomogeneous in thickness elastic structure of conical type, which is a system consisting of inner and outer smooth conical shells (inner and outer bearing layer) with corresponding thicknesses and radiuses. It is assumed that the midlines of these shells are parallel, ie the angle of taper α is common. The shells are rigidly connected by discrete ribs and a lightweight filler. It is believed that the three-layer conical structure is loaded by an internal axisymmetric distributed non-stationary normal load. In the fifth section, the problems of axisymmetric oscillations of three-layer spherical shells with a discrete-symmetric filer of different structure and at different types of boundary conditions and nonstationary loads are investigated.