Refined nonlinear deformation models of cylindrical shape for fibre-reinforced composite plates. 2. Third-order model of accuracy

Based on the known approaches and in development of the previously obtained results, a refined mathematical model is proposed for describing the process of nonlinear deformation along the cylindrical shape of fibrous composite plates, based on the approximation of tangential displacements by a third-degree polynomial along the transverse coordinate, in which the correspon­ding expansion coefficients are considered independent, and the deflections are considered to be a linear law. Kinematic relations for determining the deformation components are constructed based on the previously proposed consistent geometrically nonlinear relations of the elasticity theory with conservation of terms, which make it possible to identify classical bending and non-classical (in particular, transverse-shear under transverse bending conditions) forms of loss of stability of the plate. Physically nonlinear behavior of the material is taken into account in the relations for transverse tangential stresses. The issues of correctness of the constructed equations in formulating certain conditions of fastening and loading of the end sections of the plate are considered. It is shown that in the solutions determined on the basis of the constructed equations, when satisfying the boundary conditions of clamping the cross-section in its vicinity, a transition to a solution according to the S.P. Timoshenko model with a constant transverse tangential stress across the thickness is realized. This conclusion is formulated based on the analysis of the exact analytical solution of the linear problem of transverse bending along the cylindrical shape of a cantilever-fixed plate.