Mathematical Modeling of Three-dimensional Stress-strain State of Homogeneous and Composite Cylindrical Axisymmetric Shells

The study is devoted to the application of the asymptotic splitting method for solving static problems of deformation of homogeneous isotropic and composite cylindrical shells. The problem of deformation of a composite cylindrical shell subjected to an internal axisymmetric load is considered. The solution is constructed by expanding the components of the stress tensor and the displacement vector in powers of differential operators acting along the cylinder axis. A small parameter is the ratio of the shell thickness to its length. A governing differential system of equations describing the deformation of a cylindrical shell is obtained. It is shown that the developed mathematical model allows to compute all components of the stress tensor for both thick-walled and thin-walled cylindrical shells. The obtained analytic and numerical solutions are compared with the finite element solution of the 2D axisymmetric problem.