Modeling the dynamic behavior of spatially reinforced plates of nonlinear elastic materials within the refined bending theory

Refined mathematical models are constructed for the flexible deformation of spatially reinforced flexible plates of nonlinear elastic materials of the composition components. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The obtained equations allow determining the deformed state of such structures with different degrees of accuracy taking into account their possible weak resistance to transverse shear. As a special case, based on these equations the relations of the traditional non-classical Reddy theory are obtained. The solution of the initial boundary value problem is obtained using an explicit numerical scheme of the “cross” type. It is shown that in a general case of plates an explicit numerical scheme cannot be developed for all spatial structures of reinforcement. The dynamic behavior is investigated for the flat and spatially reinforced plates of different shapes and relative thickness under the action of an air blast wave. It is shown that in the case of a strongly denominated anisotropy for relatively thick rectangular plates, the replacement of a flat structure with a spatial reinforcement structure reduces deflections modulo several tens of percent, and reduces the intensity of deformation of the components of the composition by several times. The reduction of the anisotropy degree of the composition and the relative thickness of the plates leads to a weakening of the effect of replacing the flat reinforcement structure on the spatial structure. This effect does not occur in annular plates with a rigid inner insert. On the contrary, the replacement of the flat reinforcement structure with the spatial structure leads to the deterioration of dynamic characteristics of such structures even of their relatively large thickness. It is shown that the dynamic behavior of plates calculated according to the Reddy theory significantly differ from the calculations according to the refined theory, especially when comparing the strain states of the components of the composition.