The equations of bending of multilayer axisymmetrical shells, taking into account continuous heterogeneity in thickness of each layer

The axisymmetrical shells from multilayer anisotropic materials are considered. All layers are nonuniform in thickness (i.e. the mechanical performances of each layer are arbitrary continuous functions from transversal coordinates). For the specified constructions at arbitrary type of loading on the basis of the offered hypotheses from a variation principle of possible displacements, the equilibrium equations and natural boundary conditions are derived. The given equations allow to satisfy to all necessary conditions of continuity on boundary of layers and take into account transversal shear stresses satisfying the boundary conditions on extreme shell surfaces. Thus the order of equations set does not depend on number of layers.