A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures

Abstract

A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures has been developed. Strains of the composition materials are assumed to be small and decomposed into plastic and viscoelastic components. Instant plastic deformation of these materials is described by the flow theory with isotropic hardening. Viscoelastic deformation obeys the equations of a linear model of a five-constant body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The possible weak resistance of composite plates to lateral shear is modeled in the framework of a refined theory of bending. This allows one to determine the displacements of plate points and the stress-strain state in the components of the composition with varying degrees of accuracy. In a first approximation, from the obtained equations and boundary conditions, we obtain relations corresponding to the traditional nonclassical Reddy theory. A numerical solution to the formulated initial-boundary-value problem is sought according to an explicit “cross-type” scheme The viscoelastic-plastic dynamic deformation of rectangular, relatively thin fiberglass plates under the influence of an explosive type load is investigated. The plates have a traditional plane-cross (orthogonal) or spatial reinforcement structure. It is shown that even in the case of relatively thin composite plates the Reddy theory is unacceptable for adequate calculations of their dynamic viscoelastic-plastic deformation. It has been demonstrated that the magnitude and shape of the residual deflections depend not only on the reinforcement structure, but also on the magnitude of the viscoelastic characteristics of the materials of the composition components. It was found that, after dynamic inelastic deformation, the composite plate can have a corrugated residual shape with folds oriented in the longitudinal direction. It is shown that even in the case of a relatively thin plate, replacing the planar-cross reinforcement structure with a spatial structure can significantly reduce the amount of residual deflection and the intensity of residual deformation in the binder material and some fiber families. For relatively thick plates, the effect of such a replacement of the reinforcing structures manifests itself much more.