Modelling the viscoelastic-plastic deformation of flexible reinforced plates with account of weak resistance to transverse shear

A mathematical model of viscoelastic-plastic deformation of flexible plates cross-reinforced in planes parallel to the middle plane is developed on the basis of the algorithm of time steps. The deformations of the components of the composition of the plates are assumed to be small and they are decomposed into elastic and plastic components. The viscoelastic behavior of the composition materials is subject to the relations of the Maxwell-Boltzmann body. Inelastic deformation is defined by the equations of the theory of plastic flow with isotropic hardening. The normal stresses in the transverse direction are linearly approximated over the thickness of the plates. Therefore, linear deformations in the transverse direction and their velocities are excluded from the governing equations for the composition components. The weakened resistance of fibrous plates to transverse shear is taken into account in the framework of the non-classical Reddy bending theory. The geometric nonlinearity of the problem is considered in the Karman approximation...