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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...

Институт теоретической и прикладной механики СО РАН, НовосибирскПолучены условие пластичности в моментах и закон пластического течения пластины изо льда − материала, имеющего разные значения предела текучести на растяжение и сжатие. На их основе в рамках модели жесткопластического тела построено точное решение задачи определения предельной нагрузки круглой, свободно опертой или защемленной по контуру, усиленной жесткой вставкой ледяной пластины, находящейся на несжимаемом основании, под действием нагрузки, равномерно распределенной по вставке.Ключевые слова: жесткопластическая модель, ледяная пластина, предельная нагрузка, разносопротивляющийся материал, жесткая вставка, несжимаемое основание. ВведениеАктивное освоение районов Севера и Северо-Востока нашей страны, поиск запасов углеводородного сырья в прибрежных зонах Северного Ледовитого океана и приполярных районах требуют создания временных и стационарных дорог и площадок для переброски, хранения и длительного функционирования оборудования и товарных складов. Буровые установки, комплектующие перекачивающего оборудования и магистральных труб, складские и жилые помещения на таких ледяных платформах создают достаточно высокие нагрузки на ледяной покров, и обеспечение требуемой безопасной несущей способности ледяных баз и платформ приводит к необходимости усиления их несущей способности искусственным путем [1]. В результате проблема оценки пригодности таких ледяных платформ сводится к задаче определения несущей способности ледяной пластины с жесткой вставкой на жидком основании. Лед обладает рядом своеобразных свойств, резко отличающих его от других материалов [2−4]. Описывать деформирование льда с помощью одного универсального закона, учитывающего все его исследованные свойства, по-видимому, невозможно [5]. В зависимости от характера нагружения, температуры и цели исследования целесообразно использовать какую-либо из известных моделей: упругую, вязкоупругую, жесткопластическую, упругопластическую и т.д. Решение упругой задачи, справедливое при малых уровнях нагрузки, получено в [6]. При анализе несущей способности целесообразнее использовать модель жесткопласти-ПРОБЛЕМЫ ПРОЧНОСТИ И ПЛАСТИЧНОСТИ, вып. 73, 2011 г. *) Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проект 10-01-90402-Укр_а).

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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