Analysis of the Fields of Displacements and Stresses in an Orthotropic Toroidal Shell Depending on the Changes in its Thickness and in the Curvature of its Axis

Abstract

A numerical-analytic approach is used to study the stress-strain state of orthotropic toroidal shells of variable thickness. The problem is solved with the use of a nonclassical Timoshenko-type shell theory based on the model of a rectilinear element. The system of partial differential equations is reduced to a one-dimensional problem by applying the method of spline approximation in one coordinate direction. The boundary-value problem for the system of ordinary differential equations is solved by the stable numerical method of discrete orthogonalization. We also present the data on the distribution of the fields of displacements and stresses depending on the curvature of the axis of the shell and the parameter of variability of its thickness.