Abstract
Here, we present a Navier close form solution method for some type of the higher-order theories for elastic shells of revolution developed using the CUF approach. The higher-order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. The higher-order cylindrical supported on the edges and axisymmetric shells, as well as the shallow spherical shells with rectangular planform, are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The numerical results can be used as benchmark examples for finite element analysis of the higher-order elastic shells.