Refined model of viscoelastic-plastic deformation of flexible shallow shells with spatial reinforcement structures | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 26 > №1 / 2020 / Pages: 24-42

Refined model of viscoelastic-plastic deformation of flexible shallow shells with spatial reinforcement structures

Abstract:

A model of viscoelastic-plastic deformation of spatially reinforced flexible shallow shells is developed. The instant elastoplastic behavior of the components of the composition is determined by the theory of plastic flow with isotropic hardening. The viscoelastic deformation of these materials is described by the equations of the Maxwell – Boltzmann model. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The obtained relations make it possible to determine with varying degrees of accuracy the displacements of shell points and the stress-strain state in the components of the composition (including residual ones). In this case, the weakened resistance of the composite structure to transverse shear is modeled. In a first approximation, the obtained equations and boundary conditions correspond to the traditional non-classical Reddy theory. The solution of the formulated problem is constructed numerically using an explicit «cross» type scheme. The viscoelastic-plastic dynamic behavior of composite cylindrical rectangular panels under the action of a load generated by an air blast wave is investigated. Designs have a «flat»-cross or spatial reinforcement structure. It has been demonstrated that in some cases, even for relatively thin composite curved panels, the Reddy theory is unacceptable for adequate calculations of their dynamic viscoelastic-plastic deformation. It is shown that the size and shape of the residual deflections of the reinforced gently shallow shells substantially depend on which of their front surfaces (concave or convex) is subjected to an external load. It was found that in both cases of loading residual longitudinal folds are formed in a thin cylindrical shallow composite shell. It has been demonstrated that even for a relatively thin panel, replacing a «flat»-cross reinforcement structure with a spatial reinforcement structure can significantly reduce the amount of residual deflection and the intensity of residual strain in the binder. In the case of relatively thick shallow shells, the effect of such a replacement of the reinforcement structures is manifested even more.

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