Dynamic behavior of doubly connected polygonal plastic slabs

Nemirovskii, Yu. V.; Romanova, T. P.

doi:10.1007/bf00888058

Cited by 4 publications

(6 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the polygonal plate obtained, the contour of the internal region which moves translationally becomes a polygonal contourl 2 . Nemirovsky and Romanova [1987;1988] showed that segments of the internal contourl 2 are parallel to the corresponding segments of an external contourl and line normal to any segments ofl 2 is also normal to corresponding side ofl. Hence, as the number of segments of the polygonal contourl tends to be infinity, the contourl 2 comes closer and closer to l 2 , and the normal to the curve l 2 at any point of l 2 is also a normal to the contour l.…”

Section: Appendix Amentioning

confidence: 99%

“…Under the loads lower than the limit load (low loads, 0 < P max ≤ P 0 ), the plate remains at rest. For the loads slightly higher than the limit load (moderate loads, P 0 < P max ≤ P 1 ) as in the cases of a bending of beams [Mazalov and Nemirovsky 1975;Komarov and Nemirovsky 1984], circular and annular plates [Hopkins and Prager 1953;1954;Perzyna 1958;Florence 1965;1966;Youngdahl 1971], rectangular and polygonal plates [Jones et al 1970;Virma 1972;Mazalov and Nemirovsky 1975;Nemirovsky and Romanova 1987;1988], the plastic hinge line l 1 is formed in the internal area of the plate (see Assumption 1). Let us call this mechanism of deformation mechanism 1 (Figure 1).…”

Section: Model Assumptions and Equations Of Motionmentioning

confidence: 99%

See 1 more Smart Citation

Untitled

2008

JOMMS

View full text Add to dashboard Cite

See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year.Subscriptions, requests for back issues, and changes of address should be sent to Mathematical Sciences Publishers, 798 Evans Hall, Department of Mathematics, University of California, Berkeley, CA 94720-3840. ELASTIC CONSTANTS AND THERMAL EXPANSION AVERAGES OF A NONTEXTURED POLYCRYSTAL ROLAND DEWITThis paper gives expressions for the overall average elastic constants and thermal expansion coefficients of a polycrystal in terms of its single crystal components. The polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. Upper and lower bounds for the averages are easily found by assuming a uniform strain or stress. The upper bound follows from Voigt's assumption that the total strain is uniform within the polycrystal while the lower bound follows from Reuss' original assumption that the stress is uniform. A self-consistent estimate for the averages can be found if it is assumed that the overall response of the polycrystal is the same as the average response of each crystallite. The derivation method is based on Eshelby's theory of inclusions and inhomogeneities. We define an equivalent inclusion, which gives an expression for the strain disturbance of the inhomogeneity when external fields are applied. The equivalent inclusion is then used to represent the crystallites. For the self-consistent model the average response of the grains has to be the same as the overall response of the material, or the average strain disturbance must vanish. The result is an implicit equation for the average polycrystal elastic constants and an explicit equation for the average thermal expansion coefficients. For the particular case of cubic symmetry the results can be reduced to a cubic equation for the selfconsistent shear modulus. For lower symmetry crystals it is best to calculate the self-consistent bulk and shear modulus numerically. IntroductionA polycrystal, whose properties vary in a complicated fashion from point to point over a small microscopic length scale, may appear on average to be uniform or perhaps, more generally, its properties appear to vary smoothly. The determination of such overall properties from the properties and geometrical arrangement of the constituent monocrystal grains is our aim. In the simplest case the polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. General expressions for averages can then be derived. Many different properties can be averaged, such as dielectric constants, diffusivity, elastic constants, electrical conductivity, magnetic permeability, magnetostriction, piezoelectric constants, thermal conductivity, or thermal expansion. In this paper we treat the elastic constants, which have already received more attention than most other physical properties, and the thermal expansion. Elastic constants are fundamental physical data needed for the characterization of materials. In addition to their fundam...

show abstract

Section: Appendix Amentioning

confidence: 99%

Section: Model Assumptions and Equations Of Motionmentioning

confidence: 99%

Untitled

2008

JOMMS

View full text Add to dashboard Cite

show abstract

“…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).…”

mentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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

Nemirovskii

Romanova

2008

Int Appl Mech

Self Cite

View full text Add to dashboard 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

show abstract

“…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.…”

mentioning

confidence: 99%

Dynamic Deformation of a Curved Plate with a Rigid Insert

Nemirovsky

Romanova

2006

J Appl Mech Tech Phys

Self Cite

View full text Add to dashboard 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...

show abstract

Dynamic behavior of doubly connected polygonal plastic slabs

Cited by 4 publications

References 3 publications

Untitled

Untitled

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

Dynamic Deformation of a Curved Plate with a Rigid Insert

Contact Info

Product

Resources

About