Учёные записки Казанского университета. Серия Физико-математические науки (Dec 2017)
The axisymmetric problems of geometrically nonlinear deformation and stability of a sandwich cylindrical shell with contour reinforcing beams
Abstract
A numerical investigation of the problem of geometrically nonlinear axisymmetric deformation of a sandwich cylindrical shell with a transversally soft core reinforced in the end sections by elastic rods has been carried out. To describe the process of deformation, we have used the previously derived equations of the refined geometrically nonlinear theory that allow to both study the subcritical behavior of the shell and to reveal all possible buckling forms of the carrier layers. These equations are based on the introduction, as unknown variables, of the contact force of the interaction of the outer layers with the core, as well as of the outer layers and the filler with the reinforcing bodies at all points on the surfaces of their conjugation. Numerical methods for solving the formulated problems have been developed. They are based on the preliminary reduction of the original problems to a system of integro-algebraic equations, for the solving of which the finite sum method is used. A method has been proposed for investigating the subcritical and supercritical geometrically nonlinear behavior of a shell with its end compression through contour reinforcing rods, according to which unstable equilibrium positions are determined by the method of continuation of the solution with respect to the parameter when the external forces are selected as a parameter. A method has been proposed for finding the critical load (the bifurcation point) at which the shell buckling occurs. This method is based on the linearization of the initial geometrically nonlinear problem in the neighborhood of its nonlinear solution, followed by the formulation of the eigenvalue problem with a nonlinear presence of the parameter. The results of the numerical experiments have been discussed. The results of the experiments have been analyzed.
