Yaremchenko S. Numerical analysis of unhomogeneus sturcture cylinders and spheres stationary deformation on the basis various models

Thesis of candidate for a degree of doctor of sciences in physics and mathematics, speciality 01.02.04 ``Mechanics of deformable solid''. -- S.P. Timoshenko Institute of mechanics, NAS of Ukraine, Kyiv, 2021. The thesis is devoted to the development and improvement of an approach to the study of stationary deformation of a wide class of thick-walled cylindrical and spherical shells with different types of inhomogeneity. This approach includes mechanical-mathematical models of stress-strain state and vibrations based on the refined theory of shells and three-dimensional spatial theory of elasticity; development of an appropriate computational scheme and application of a numerical discrete-continuous approach based on spline collocation, discrete orthogonalization, step-by-step search and a discrete approach based on the finite element method. Algorithms implemented in problem-oriented computing programs realized on modern personal computers have been made. The proposed approach was used to solve the following classes of problems. The problems on the stress-strain state of noncircular thick-walled cylindrical shells with different cross sections and with oblique cuts are solved within the framework of the refined theory of shells. The study of stress-strain state of inhomogeneous cylindrical bodies of finite dimensions is carried out under various types of loading and boundary conditions. resonant frequencies of piezoceramic cylinder was defined on the base of electoelasticity equations. The analysis of the influence of the type of inhomogeneity (shells with oblique cuts, variable thickness, continuously inhomogeneous structure of the material) on the distribution of displacement fields and stresses of the studied mechanical objects is a feature of these studies. The results comparison in solving some of the problems presented on the basis of the discrete-continual and discrete approaches makes it possible to assess the reliability of these calculations. The obtained standards and the revealed effects of stationary deformation of cylindrical and spherical inhomogeneous bodies on the basis of different models can serve as the basis for further research in this field of solid mechanics and can be used to assess the strength and reliability of structural elements, and machine parts of cylindrical and spherical shapes.