Dynamic bending of polygonal plastic slabs

Nemirovsky

2008

JOMMS

A rigid, perfectly-plastic model of solids is applied to study the dynamic behavior of simply supported or clamped, arbitrarily shaped plates on visco-elastic foundation. The role of membrane forces and transverse shear forces in the yield condition and the influence of geometry changes are neglected. The plate is subjected to explosive loads uniformly distributed over the surface. Several mechanisms of dynamic deformation of the plate are considered. For each mechanism, equations of the dynamic behavior are obtained. Operating conditions of these mechanisms are analyzed. Analytical expressions for the limit and high loads and for the maximum final deflections are obtained. Detailed analyses are given for an astroid-shaped plate, for a plate with a contour consisting of two arcs and for a plate with an internal free hole or a rigid insert.

Section: Model Assumptions and Equations Of Motionmentioning

confidence: 99%

Section: Appendix Amentioning

confidence: 99%

Dynamic rigid-plastic deformation of arbitrarily shaped plates

Nemirovsky

2008

JOMMS

“…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).…”

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confidence: 99%

“…1a). As in bending of beams [4], circular and ring plates [1,15,16], rectangular and polygonal plates [4][5][6], and plates with compound boundary [8][9][10][11][12][13][14], when P max is rather high, a translating region of intensive plastic deformation Z p may be observed near the insert Z a (case 2, Fig. 2b; high-intensity load).…”

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confidence: 99%

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

Nemirovskii

2008

Int Appl Mech

Self Cite

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

“…1. As in the case of flexure of beams [1], circular and annular plates [12][13][14], rectangular and polygonal plates [1][2][3]11], and plates with a sophisticated contour [4][5][6][7][8][9], the plate dynamics in the case of rather high values of P max can be accompanied by the emergence of a zone of intense plastic deformation Z p moving translationally. There are also possible situations where some part of the pivot l 1 is retained or the zone Z p does not cover the entire insert Z a (high loads; scheme in Fig.…”

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confidence: 99%

Dynamic Deformation of a Curved Plate with a Rigid Insert

Nemirovsky

2006

J Appl Mech Tech Phys

Self Cite

A general solution is obtained for dynamic bending of ideal rigid-plastic plates with a clamped or simply supported curved contour containing an absolutely rigid insert of an arbitrary shape. The plate is affected by a short-time high-intensity explosive dynamic load uniformly distributed over the surface. It is shown that there are several mechanisms of plate deformation. Equations for dynamic deformation are derived for each mechanism, and conditions of occurrence are analyzed. Examples of numerical solutions are given.Introduction. The issues of calculating structures under the action of intense short-time loads are very important in modern mechanics of deformable solids. To solve such problems, the model of a rigid-plastic body is widely used [1]. The model is based on the assumption that the body starts deforming when the stress reaches the ultimate value and plastic deformation becomes possible. Elastic deformations are neglected. For thin-sheet structural elements, this simplification allowed solving numerous issues of practical importance. The model of a rigid-plastic body was used in [2-9] to study the behavior of homogeneous plates with a complicated external contour under the action of arbitrary dynamic loads of high intensity.Structurally inhomogeneous plates are constitutive elements of many structures used in various areas of engineering. Flat shields are often equipped by reinforced closed technological hatches. Therefore, damage of plates with rigid inserts has to be examined. Up to now, this problem has been considered only for a circular plate with a rigid circle at the center under conditions of axisymmetric loading and attachment [10]. The method proposed in the present work allows, on the basis of the theory of an ideal rigid-plastic body, calculating plates with an arbitrary curved contour, which are attached in an arbitrary manner, have an absolutely rigid insert of an arbitrary shape, and are subjected to intense short-time dynamic loads. The method can be used for a wide class of approximate engineering calculations.1. We consider a plate made of an ideal rigid-plastic material with an arbitrary smooth convex contour l, which is clamped or simply supported (Fig. 1). In the central part, the plate has an absolutely rigid insert Z a with an arbitrary contour l 2 . The plate is subjected to a high-intensity dynamic load P (t) uniformly distributed over the surface. We consider explosive loads characterized by instantaneous reaching the maximum value P max = P (t 0 ) at the initial time t 0 with their subsequent rapid decrease. As the insert Z a remains rigid during its deformation, we assume that the ultimate flexural moment in the insert is greater than M 0 (the ultimate flexural moment in the remaining part of the plate) and ρ a /ρ 1, where ρ and ρ a are the surface densities of the plate and insert materials, respectively.The dynamics of the plate made of a rigid-plastic material can follow one of the three schemes of deformation, depending on the value of P max . Under loads lower than t...