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.