Carrera Unified Formulation (CUF) for Shells of Revolution. I. Higher-order Theory

Here, 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. Following the Unified Carrera Formula (CUF), the stress and strain tensors, as well as the displacement vector, are expanded into series in terms of the coordinates of the shell thickness. As a result, all the equations of the theory of elasticity are transformed into the corresponding equations for the expansion coefficients in a series in terms of the coordinates of the shell thickness. All equations for shells of revolution of higher order are developed and presented here for cases whose middle surfaces can be represented analytically. 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.