Viscoplastic deformation of reinforced plates with varying thickness under explosive loads

Abstract

The problem of viscoplastic bending of reinforced plates with varying thickness is formulated. An original method for the integration of this initial-boundary-value problem is developed. The numerical solution is compared with an analytical solution obtained with a rigid-plastic model of an isotropic circular plate. The efficiency of the method is demonstrated by analyzing the inelastic dynamics of reinforced plates with constant and varying thickness. It is shown that the maximum residual deflections of plates can be reduced severalfold by means of rational profiling and reinforcement Keywords: reinforced plate, explosive loading, inelastic dynamics, viscoplastic bending, rational shaping and reinforcementIntroduction. Plates and slabs are the basis of many safety barriers and responsible members in marine, mechanical, and aircraft engineering and building structures. Their damageability under high dynamic loads determines, in many respects, whether they can be in operation afterwards. Therefore, dynamic design of such structural members is one of the major challenges in solid mechanics. The majority of solutions is based on a perfect rigid-plastic model [4, 10, etc.]. As a rule, such solutions are approximate, based on extreme principles of the dynamics of a rigid-plastic body [6], and describe the behavior of homogeneous isotropic plates of constant thickness, with the dependence of the yield stress on the strain rate being neglected [22][23][24][25].For the last decades, slabs reinforced with high-strength bars (fibers) have been used in engineering as effective protective elements. The study into the inelastic dynamic deformation of such structures is in its initial stage [12]. The rationally chosen thickness of a plate is known to influence considerably its resistance (including dynamic) to external loads, and the dependence of the yield stresses of the phases (e.g., steels [3]) of the composition may be considerable, thus affecting the deformability of thin-walled structures under dynamic loading. For example, neglecting this dependence is one of the reasons why the calculated values of residual deflections are 30-80% greater [10] than their experimental values.The objective of the present study is to develop a method to solve an initial-boundary-value problem of dynamic viscoplastic bending of reinforced plates with constant and varying thickness taking into account the viscoplastic hardening of the phases and to analyze the effect of the structure of reinforcement and the profile of plates on their residual deflections under explosive loads.1. Viscoplastic Dynamics of Reinforced Plates. Problem Formulation. Consider a plate with varying thickness H consisting of an isotropic matrix and fine-fibered homogeneous reinforcement of constant cross-section and subjected to transverse dynamic bending. Assume that the reinforcement is regular and quasihomogeneous across the thickness of the plate.To describe the plate, we choose an orthogonal (possibly, curvilinear) coordinate system x 1 , x 2 , z such that the p...

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