Modeling the Viscoelastoplastic Deformation of Flexible Reinforced Plates with Weak Resistance to Transverse Shear

摘要

Based on the time step algorithm, we have developed a mathematical model of the viscoelastoplastic deformation of flexible plates cross-reinforced in planes parallel to the middle plane. The strains of the plate composite components are assumed to be small and are decomposed into elastic and plastic components. The viscoelastic behavior of the composite materials is described by the Maxwell-Boltzmann body relations. The inelastic deformation is represented by the equations of the theory of a plastic flow with isotropic hardening. The normal stresses in the transverse direction are approximated linearly over the plate thickness. For this reason, the linear strains in the transverse direction and their rates are excluded from the governing equations for the composite components. The weakened resistance of fibrous plates to transverse shear is taken into account within the nonclassical Reddy bending theory. The geometric nonlinearity of the problem is considered in the Karman approximation. The formulated initial-boundary value problems are solved numerically with the application of an explicit cross-type scheme. A workaround is used to obtain a stable numerical scheme: the stresses in the Maxwell-Boltzmann viscoelastic relations at the current discrete time are expressed via the stress rate by the trapezoid formula with a backward step. We have investigated the elastoplastic and viscoelastoplastic bending dynamic behavior of relatively thick, orthogonally reinforced fiberglass rectangular plates subjected to blast loads. A change in the reinforcement structure is shown to lead to a change in the residual deflection of the structure. We demonstrate that the amplitude of reinforced-plate oscillations in the vicinity of the initial time exceeds significantly the residual deflection.