Vovkodav O. Solution of problems of the stress - strain state of variable stiffness orthotropic spherical shells in refined formulation on the basis of spline-approximation

The thesis is devoted to the development of an effective numerical and analytic approach to the solution of the class of problems on stress-strain state of spherical orthotropic shells of variable thickness under different kinds of loads and with various conditions on the edges in the refined formulation. The problems are described by a system of partial differential equations with variable coefficients. To solve the problem an approach based on reduction of two-dimensional boundary problem to one-dimensional using the spline-collocation method along one of the coordinate directions is proposed. The obtained one-dimensional boundary problem is solved by the stable numerical discrete orthogonalization method. On the basis of the developed approach number of problems on stress-strain state of spherical shells under various conditions at the edges and different kinds of applied loads, depending on orthotropy of material, geometry of the shell and their thickness variation in one or two coordinate directions is solved.