Generalization of Vlasov’s equations for a cylindrical shell to the case of a transversely isotropic material

Differential equations of the general theory of transversely isotropic cylindrical shells are obtained; in a certain sense, these equations are generalizations of Vlasov’s and Ambartsumyan’s equations. This allowed us on the basis of Novozhilov’s criterion (comparison of variability of the stress state in the principal orthogonal directions) to divide the initial equations according to Goldenweiser into approximate equations of the type of the semi-momentless theory, theory of the edge effect and flexural state, which are also generalizations of equations that describe the elementary stress states of an isotropic shell. Numerical values are found for criteria of matching of approximate equations that describe the elementary stress states in the asymptotic synthesis of the full stress state. Examples of calculations and experimental data for a shell with and without allowance for transverse shear strain are given.