The Refined Model of Viscoelastic-Plastic Deformation of Reinforced Cylindrical Shells

The paper formulates the initial-boundary-value problem of the viscoelastic-plastic bending behavior of cylindrical circular shells cross-reinforced along equidistant surfaces. The instant elastoplastic deformation of the shell composition components is described by the governing equations of the theory of plastic flow with isotropic hardening. The viscoelastic deformation of these materials is described by the defining relations of the Maxwell - Boltzmann model of body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The used system of two-dimensional resolving equations and the corresponding initial and boundary conditions make it possible to determine displacements and stress-strain state (including residual one) in materials of the composition of flexible cylindrical shells with varying degrees of accuracy. In this case, the weak resistance of the considered composite structures to transverse shears is taken into account. In the first approximation, the equations are used, the initial and boundary conditions correspond to the relations of the widely used non-classical Reddy theory. A numerical solution of the initial-boundary-value problem posed is constructed using an explicit step-by-step "cross" scheme. The elastoplastic and viscoelastic-plastic dynamic deformation of a relatively thin long circular cylindrical shell is investigated. The structure is rationally reinforced in the circumferential direction and is loaded with an internal pressure of an explosive type. It has been demonstrated that under intense short-term loading even of a relatively thin cylindrical reinforced shell by internal pressure, the traditional Reddy theory does not guarantee that the maximum residual deflection and the intensity of residual deformations of the components of the composition are accurate to within 10% compared to calculations performed by the refined theory. The difference in the results of the corresponding calculations increases with an increase in the relative thickness of the composite shell. It was found that after plastic deformation of a long reinforced cylindrical shell in its residual state, not only appear zones of edge effects, but also a local zone of an intense deformation located in the vicinity of the central section of the shell. The length of the local central zone is comparable with the length of the zones of edge effects. It is shown that the amplitude of the transverse vibrations of the reinforced shell in the vicinity of the initial moment of time significantly (by an order of magnitude) exceeds the value of the maximum modulus of the residual deflection. Therefore, the calculations performed in the framework of the theory of elastoplastic deformation of composition materials do not allow a very approximate determination of the magnitude of the residual displacements and the magnitude of the residual deformed state of the components of the composition of the cylindrical shell.

MODELING OF THE ELASTIC-VISCOPLASTIC BEHAVIOR OF REINFORCED PLATES WITHIN THE REFINED BENDING THEORY

The dynamic problem of elastic-viscoplastic deformation of flexible plates with spatial reinforcement structures is formulated. The plastic behavior of the components of the composition is described by equations of flow theory with isotropic hardening, taking into account the sensitivity of these materials to the rate of their deformation. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The relations used, with varying degrees of accuracy, describe the mechanical state of the bent plates and allow for the possible weakened resistance of the reinforced constructions to transverse shears. In a first approximation, the equations used, the boundary and initial conditions are reduced to the equalities of the widely used non-classical Reddy theory. To solve the stated nonlinear initial-boundary-value problem, a step-by-step algorithm is used, based on the use of an explicit numerical of the “cross” type scheme. The elastic-viscoplastic dynamic behavior of rectangular composite plates of different relative thicknesses under the action of a load corresponding to excess pressure in an air blast wave is investigated. Fiberglass-plastic and metal composite structures are considered. It is shown that for composite plates with a relative thickness of the order of 0.1, the calculation by the Reddy theory underestimates the maximum values of the strain intensity of the components of the composition by more than 12% compared with the calculation by the refined theory. A fairly simple Reddy theory is quite acceptable for calculating relatively thin plates. It is shown that for fiberglass-plastic plates with a relative thickness of the order of 0.1, replacing the traditional plane-cross reinforcement structure with the spatial structure of the reinforcement reduces the maximum deflection by more than 20%, and the greatest value of the strain intensity of the components of the composition is reduced by 10-20% or more. For metal-composite plates of any thickness and for fiberglass-plastic plates having a small relative thickness, the positive effect of from such a replacement of the reinforcement structures is practically not observed.

MODELING OF BENDED BEHAVIOR OF SPACE-REINFORCED PLATES OF NONLINEAR-ELASTIC MATERIALS

Based on the procedure of time steps, a mathematical model of bending behavior is constructed for spatially-reinforced plates with nonlinear elastic deformation of the materials of the composition components. The solution of the formulated initial-boundary value problem is based on an explicit numerical “cross” scheme. The possible weakened resistance of reinforced plates to transverse shear is taken into account on the basis of kinematic hypotheses of the Reddy theory. The geometric nonlinearity of the problem is considered in the Karman approximation. It is shown that in the framework of Reddy theory, an explicit numerical scheme cannot be constructed for all arbitrary structures of spatial reinforcement of plates. The dynamic nonlinear elastic behavior of plane-cross and spatially reinforced rectangular plates under the action of an air blast wave is investigated. It is shown that with a strong anisotropy of the composition for relatively thick plates, the replacement of the plane-cross structure of the reinforcement with the spatial structure allows to reduce the flexibility of the structure in the transverse direction by tens of percent (up to 30% or more), and the intensity of deformations in the binder - at times. The reducing the relative thickness of the plate and the degree of anisotropy of its composition reduces the effect of replacing the plane-cross structure of the reinforcement on the spatial structure. In some cases, this effect may not appear even in relatively thick composite structures of more complex geometric shape, for example, in annular plates with a rigid inner insert.

The Influence of First Order Shear Deformation on Dynamic Buckling of Composite Bar

Taking stress wave propagation into account, the governing equations of composite bar with the clamped-fixed boundary conditions considering FSDT (first order shear deformation theory) are derived on the basis of Reddy’ theory and solved by the variable-separated method. The analytic expression of the critical buckling load is obtained basing on the characteristics of homogeneous linear equations having nonzero-solution. The results of the theoretical study and the numerical calculation indicate that FSDT has influence on dynamic buckling of composite bar, and the critical buckling load is small when FSDT is considered. They also show that the magnitude of effect taken by FSDT is small when the layer angle is big.