Mechanics of Solids

Modeling of elastoplastic behavior of flexible spatially reinforced plates under refined theory of bending

A. P. Yankovskii

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation

Abstract: On the basis of the time-steps algorithm the structural model is constructed for elastic-plastic deformation of bended plates with spatial reinforcement structures. The inelastic behavior of the composition phase materials is described by equations of the theory of plastic flow with isotropic hardening. The possible weakened resistance of the reinforced plates to the transverse shear is taken into account on the basis of the refined theory, from which the relations of the Reddy theory are obtained in the first approximation. The geometric nonlinearity of the problem is considered in the Karman approximation. The solution of the formulated initial boundary value problems is based on an explicit numerical “cross” scheme. The dynamic inelastic deformation of spatially- and flat-cross-reinforced metal-composite and fiberglass flexible plates of different relative thickness is investigated in the case of the load caused by an air blast wave. It is demonstrated that for relatively thick fiberglass plates, the replacement of the flat-cross reinforcement structure by the spatial structure with the preservation of the total fiber consumption leads to a decrease in the structural flexibility in the transverse direction by almost 1.5 times, as well as to a decrease of the maximum of intensity of deformation in the binder by half. For relatively thin both fiberglass and metal-composite plates, the replacement of flat-cross 2D reinforcement structure with 3D and 4D spatial structures does not lead to a noticeable decrease in their deflections, but allows to reduce the intensity of deformations in the binder by 10 % or more. It is shown that the widely used non-classical Reddy theory does not allow obtaining reliable results of calculations of the elastic-plastic dynamic behavior of the bended plates, both with plane and spatial reinforcement structures, even with a small relative thickness of the structures and weak anisotropy of the composition.

Keywords: composite plate, spatial-cross reinforcement, flat-cross reinforcement, Reddy theory, refined theory of bending, elastic-plastic deformation, geometric nonlinearity, explosive load, “cross” scheme.

UDC: 539.4

MSC: 74K20

Received: September 18, 2018
Revised: February 11, 2019
Accepted: March 4, 2019
First online: March 20, 2019

DOI: 10.14498/vsgtu1644

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