Dynamic Deformation of a Curved Plate with a Rigid Insert

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

doi:10.1007/s10808-006-0051-y

Cited by 4 publications

(5 citation statements)

References 9 publications

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“…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].…”

Section: Discussionmentioning

confidence: 99%

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

Starov¹,

Kalashnikov²,

Chauskin³

2017

AIP Conference Proceedings

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Section: Discussionmentioning

confidence: 99%

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

Starov¹,

Kalashnikov²,

Chauskin³

2017

AIP Conference Proceedings

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“…The dynamic behavior of a curvilinear plate of varying thickness with a rigid insert will be studied separately. The motion of curvilinear and annular plates of constant thickness with a rigid insert was studied in detail in [4,7,13].…”

Section: Dynamic Behavior Of the Plate Under High Loadsmentioning

confidence: 99%

Dynamics of a rigid-plastic curvilinear plate of varying thickness with an arbitrary hole

Nemirovskii

Romanova

2010

Int Appl Mech

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A perfect rigid-plastic body is used as a model to develop a general procedure for analyzing the dynamic behavior of an arbitrary curvilinear plate of variable thickness with an arbitrary internal hole. The plate is subjected to an arbitrary, uniform, short-term dynamic surface load. Two plate deformation patterns are considered. Analytic formulas for plastic zones, ultimate loads, and residual deflections are presented. Numerical examples are given Keywords: perfect rigid-plastic plate, curvilinear boundary, explosive load, free hole, ultimate load, residual deflectionIntroduction. The dynamic behavior of various curvilinear thin-walled structural elements under explosive loading is of interest because they are used as components of many engineering structures. The solutions to the bending problem for plastic plates with a free hole known from the literature are related to the dynamic behavior of the following plates of constant thickness: annular plates [12,14,15], curvilinear plates [5, 6], circular plates with an arbitrary hole [9], and to the limiting analysis of annular [1] and square [10,16] plates.We will analyze the dynamic behavior of hinged and clamped arbitrary curvilinear plates with varying thickness and an arbitrary free hole. An elliptic plate with a free rhombic hole and with piecewise-linear thickness function will be considered as an example.1. Model, Assumptions, and Equations of Motion. Let us consider a hinged or clamped perfect rigid-plastic plate with varying thickness and arbitrary smooth convex boundary L 1 (Fig. 1).There is a free hole with an arbitrary boundary L 2 in the middle of the plate. The plate is subject to a high explosive load P t ( ) uniformly distributed over the surface of the plate, instantaneously peaking (P P t

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“…2 and is described by Eqs. (4)-(7) with the initial conditions (8) and (16). In this phase, the size of the region Z p decreases by the law described by Eq.…”

mentioning

confidence: 99%

“…As the model of motion proposed was derived under the assumption that h(ν 1 ) = const = h c in the region Z p , it follows from Eqs. (16) and (17) that there are restrictions on the value of P max :…”

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Dynamic deformation of rigid-plastic curvilinear plates of variable thickness

Nemirovsky

Romanova

2007

J Appl Mech Tech Phys

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A general solution is obtained for the problem of dynamic bending of an ideal rigid-plastic plate of variable thickness with a simply supported or clamped curvilinear contour under the action of a shorttime high-intensity explosive-type load uniformly distributed over the surface. Several mechanisms of plate deformation are demonstrated to exist. For each mechanism, equations of dynamic deformation are derived and conditions of mechanism implementation are analyzed. Examples of numerical solutions are given. Introduction.Studying the dynamic behavior of structural elements under explosive loading is extremely important for estimating the degree of structural damage, analyzing the risks, and predicting emergency situations. The model of an ideal rigid-plastic body is widely used to solve problems of this type [1]. Based on this model, the dynamic behavior of curvilinear plates of constant thickness under dynamic loading was examined in [2-9].The most important task in creating shields protecting from explosive loads is the choice of the material and its distribution in the structure providing the minimum degree of damaging. This problem is directly related to optimal design, which has been fairly well studied, as applied to static and dynamic harmonic actions on various structures [10,11]. The necessity of solving problems of structural optimization under dynamic loading has been intensely discussed in the literature [12]. Nevertheless, we are unaware of any research in this field, except for beams [13] and shells of revolution [14]. The present paper continues the research in this field, as applied to flat plates with a complicated convex support contour.A method based on the model of an ideal rigid-plastic body is proposed in the paper. This method allows one to calculate curvilinear plates of variable thickness of a certain type under the action of short-time high-intensity dynamic loads. The method can be used for various engineering calculations.1. Let us consider a thin ideal rigid-plastic plate of variable thickness with a curvilinear contour, which is simply supported or clamped. The plate is subjected to an explosive load uniformly distributed over the surface. The load has an intensity P (t), which instantaneously reaches the maximum value P max = P (0) at the initial time t = 0 and then rapidly decreases. The plate has an arbitrary piecewise-smooth convex contour l defined in a parametric form as x = x 1 (ϕ), y = y 1 (ϕ), 0 ϕ 2π. The radius of curvature of the contour l (except for singular points) is

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Dynamic Deformation of a Curved Plate with a Rigid Insert

Cited by 4 publications

References 9 publications

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

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

Dynamics of a rigid-plastic curvilinear plate of varying thickness with an arbitrary hole

Dynamic deformation of rigid-plastic curvilinear plates of variable thickness

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