Behavior of rigid-plastic polygonal plates with a rigid insert under blast loads

Abstract

A method based on a perfect rigid-plastic body model is developed to analyze the dynamic behavior of hinged or clamped polygonal plates that have a perfectly rigid insert and rest on a viscoelastic foundation with supports. The plate is subject to an arbitrary blast load of high intensity uniformly distributed over the plate surface. Two cases of plate deformation are examined. In each of the cases, equations of motion are derived and realization conditions are analyzed. Analytic expressions for the deformation time and the maximum residual deflection are derived in the case of an arbitrary load of medium intensity and in the case of high-intensity load described by a rectangular function. Examples of numerical solutions are given Keywords: rigid-plastic plate, polygonal plate, rigid insertion, blast load, viscoelastic foundation, ultimate load, residual deflectionIntroduction. Study of the dynamic behavior of plastic structures under blast loads is of great importance for the evaluation of their damage. Under such loads, plastic strains are much greater than elastic ones, which makes the perfect rigid-plastic body model applicable [4]. This model was used in [5][6][7][8][9][10][11][12][13][14] to study the behavior of homogeneous plates with compound external boundary under arbitrary dynamic loads of high intensity.Structurally inhomogeneous plates are widely used in various fields of mechanical engineering. Thin plane parts often have reinforced inserts (washers). Therefore, it is necessary to study the dynamic behavior of plates with a rigid insert. Up to now, such a problem has only been solved for a circular plate with a rigid circle at the center under axisymmetric fixation and loading conditions [3]. The viscoelastic state of plates with elastic inclusions was analyzed in [4], and dynamic problems for plates with stress concentrators under a wave load were addressed in the experimental studies [17,18,20].The present paper gives a method based on the perfect rigid-plastic body model to calculate arbitrarily fixed polygonal plates with a perfectly rigid insert subjected to short-term intensive dynamic loads and resting on a resisting viscoelastic foundation. The method can widely be used for engineering calculations.1. Consider a perfect rigid-plastic plate with hinged or clamped n-corner boundary l described about a circle of radius R (Fig. 1a). The plate has, at its middle, a perfectly rigid insert Z a with a polygonal boundary similar to l with a similarity coefficient g <1, the sides of the insert boundary being parallel to the respective sides of the external boundary of the plate. Hence, a circle of radius R a can be inscribed into the boundary of the region Z a =R R a = g . The plate is subject to a blast load P t ( ) uniformly distributed over the surface. The load instantaneously attains its maximum P P t

Plastic quasistatic deformation of circular membranes and membrane shells considering thickness variation and hardening

“…It is quite difficult to perform a numerical analysis of the solutions to the problems of plastic quasistatic and dynamic deformation of circular plates, membranes and membrane shells based on the energy dissipation and external load power balance [13][14] or a direct integration of the initial system of nonlinear equations [15][16][17][18][19][20].…”