МОДЕЛИРОВАНИЕ УПРУГОВЯЗКОПЛАСТИЧЕСКОГО ПОВЕДЕНИЯ АРМИРОВАННЫХ ПЛАСТИН В РАМКАХ УТОЧНЕННОЙ ТЕОРИИ ИЗГИБА

Abstract

The dynamic problem of elastic-viscoplastic deformation of flexible plates with spatial reinforcement structures is formulated. The plastic behavior of the components of the composition is described by equations of flow theory with isotropic hardening, taking into account the sensitivity of these materials to the rate of their deformation. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The relations used, with varying degrees of accuracy, describe the mechanical state of the bent plates and allow for the possible weakened resistance of the reinforced constructions to transverse shears. In a first approximation, the equations used, the boundary and initial conditions are reduced to the equalities of the widely used non-classical Reddy theory. To solve the stated nonlinear initial-boundary-value problem, a step-by-step algorithm is used, based on the use of an explicit numerical of the “cross” type scheme. The elastic-viscoplastic dynamic behavior of rectangular composite plates of different relative thicknesses under the action of a load corresponding to excess pressure in an air blast wave is investigated. Fiberglass-plastic and metal composite structures are considered. It is shown that for composite plates with a relative thickness of the order of 0.1, the calculation by the Reddy theory underestimates the maximum values of the strain intensity of the components of the composition by more than 12% compared with the calculation by the refined theory. A fairly simple Reddy theory is quite acceptable for calculating relatively thin plates. It is shown that for fiberglass-plastic plates with a relative thickness of the order of 0.1, replacing the traditional plane-cross reinforcement structure with the spatial structure of the reinforcement reduces the maximum deflection by more than 20%, and the greatest value of the strain intensity of the components of the composition is reduced by 10-20% or more. For metal-composite plates of any thickness and for fiberglass-plastic plates having a small relative thickness, the positive effect of from such a replacement of the reinforcement structures is practically not observed.