The refined model of the elastic-plastic dynamic behavior of reinforced curved panels sensitive to strain rate

The initial-boundary value problem of dynamic elastic-viscoplastic deformation of flexible curved panels (shallow shells) with plane -cross and spatial reinforcement structures is formulated. The inelastic behavior of the materials of the composition components is described by the constitutive equations of the theory of plastic flow with isotropic hardening, and their sensitivity to strain rate is taken into account. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The used kinematic and dynamic two-dimensional relations and the corresponding boundary conditions make it possible to describe, with varying degrees of accuracy, the mechanical bending behavior of shallow composite shells. This takes into account the possible weak resistance of such reinforced panels to transverse shears. In the first approximation, the used two-dimensional equations, the initial and boundary conditions degenerate into the relations of the traditional non-classical Ambartsumyan theory. For the numerical integration of the formulated nonlinear dynamic problem, an algorithm of time steps is applied, based on the use of an explicit scheme of the cross type. The elastoplastic and elastic-viscoplastic behavior of the reinforced cylindrical shallow shells under transverse dynamic loads generated by an air blast wave is investigated. Metal-composite and fiberglass thin-walled constructions are considered. It is shown that the refusal to take into account the dependence of the plastic properties of the components of the composition on the rate of their deformation does not allow adequately describing the inelastic dynamic behavior of both metal-composite and fiberglass shallow shells. It is shown that in the calculations of even relatively thin reinforced cylindrical panels (with a relative thickness of 1/50), the use of the Ambartsumyan theory leads to completely unacceptable results in comparison with the refined bending theory. It has been demonstrated that even for relatively thin curved fiberglass panels, replacing the traditional flat -cross reinforcement structure with a spatial structure with obliquely laid fiber families can significantly reduce not only the intensity of deformations in the binder, but also the maximum deflection values in modulus. For metal-composite shallow shells with a weakly expressed anisotropy of the composition, the positive effect of the indicated replacement of reinforcement structures is practically not manifested.