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Browsing Фахові видання by Subject "curvilinear bar"
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Item Analytical Determination of Reactive Forces for Curvilinear Bars with a Flat Axis of Arbitrary Shape / Аналітичне визначення реактивних зусиль для криволінійних брусів із плоскою віссю довільної форми(2019-12) Ковальчук, Станіслав Богданович; Горик, Олексій ВолодимировичItem Analytical Modeling of Concentrated and Localized Loads of Bars With a Curvilinear Flat Axis. Part 2. Modeling Localized Loads and Application Examples / Аналітичне моделювання зосереджених та локалізованих навантажень брусів із криволінійною плоскою віссю. Частина 2. Моделювання локалізованих навантажень та приклади застосування(2019-09) Ковальчук, Станіслав БогдановичItem Integral and differential relations for internal power factors in the bending of the bar with a curved flat axis of an arbitrary shape(Odessa State Academy of Civil Engineering and Architecture, 2018-03) Kovalchuk, S. B.; Goryk, O. V.; Ковальчук, Станіслав Богданович; Горик, Олексій ВолодимировичThe work is dedicated to the theoretical study of internal power factors in a curved bar with a flat axis of an arbitrary shape, that is in a plane bending condition by a surface load of an arbitrary type. The natural curvilinear cylindrical orthogonal coordinates associated with the structure of the bar and given by the characteristics of families of coordinate surfaces and Lame coefficients is used to describe the geometry of the bar and also the load distribution. The analysis of the equilibrium conditions of the elementary section of the bar made it possible to obtain integral relations between internal power factors and loads distributed on its longitudinal and end surfaces. The relations obtained were used to derive differential dependencies between internal power factors, that express the equilibrium conditions for the elementary section of a curved bar. Also, based on the equilibrium conditions of the bar cross-sections, integral relations between internal power factors and the stress state components were obtained. The presented integral and differential relations have a general form, invariant to the shape of the axis of the bar and allow to make a direct connection between loads and stresses. The results of the work can be used to solve theoretical and applied problems of a plane bending of curvilinear homogeneous and inhomogeneous bars with different types and combinations of external load.Item Аналітичне моделювання зосереджених та локалізованих навантажень брусів із криво-лінійною плоскою віссю. Частина 1. Моделювання зосереджених у точці навантажень(Одеська державна академія будівництва та архітектури, 2018-12) Ковальчук, Станіслав Богданович; Горик, Олексій ВолодимировичIn applied mechanics, the common types of load are concentrated force, moment, and also distributed load localized in a certain part of the beam. An effective approach to the analytical modeling of such loads is the use of generalized functions, with the help of which it is possible to avoid considering the many design sections of the beam, within which the load is a continuous function. However, in well-known scientific papers, this approach is developed only for rectilinear rods and partially for circular ones. This paper is devoted to the problem of modeling concentrated loads (force, moment) and loads localized on a surface for bars with a curvilinear plane axis of arbitrary shape in a natural coordinate system. In the first part, the mathematical substantiation of analytical modeling of forces and moments concentrated at a point of a longitudinal cylindrical or end surface of a curvilinear bar in a natural curvilinear coordinate system is illuminated. By limiting the transition from a statically equivalent local load to the boundary case of a load concentrated at a point on the surface of the beam, using the elements of the theory of generalized functions, we obtained general analytical relations for modeling the concentrated force. On the basis of the ratio obtained, by passing to the limit for a pair of concentrated forces as the pair’s arm tends to zero, a mathematical rationale for analytical modeling of the concentrated moment is constructed. The relations obtained are of a general nature and are invariant with respect to the coordinate system under consideration. Based on them, a number of relations have been obtained for modeling concentrated loads in individual cases of circular, elliptical and parabolic bars in natural coordinate systems. The results obtained can be used to solve a wide range of applied problems of deforming curvilinear bars.Item Природна система координат для криволінійних композитних брусів із незмінними лінійними розмірами поперечних перерізів(Луцький національний технічний університет, 2019-04) Ковальчук, Станіслав Богданович; Горик, Олексій ВолодимировичIt is known that there are some solutions of the elasticity theory for the tasks of composite bars deformation that are obtained only for multilayer bars with a rectilinear and circular axis, which impedes the efficient design of composite structures with curvilinear rod elements. The goal of this work is the mathematical justification and determination of parameters of the curvilinear cylindrical orthogonal coordinate system, which is natural for composite bars with stationary linear dimensions of cross sections over the length. The coordinate system is based on a one-parameter family of cylindrical surfaces evenly spaced from the base curve (the axis of a bar) and families of planes that are orthogonal to them. Two ways of parameterization of the proposed coordinate system are considered: by the coordinate of the cross section of a bar and by the angle between the cross section and the axis of the auxiliary Cartesian coordinate system, allowing one to take into account the features of axes of various shapes. General analytical relations for determining the parameters of the natural coordinate system by analytically given equation of the axis of a bar have been obtained for the types of parameterization mentioned above. Using these relations, we received the equations of the elasticity theory in the natural coordinate system for bars with a curvilinear plain axis of an arbitrary shape and stationary linear dimensions of cross sections. Some certain examples of implementation of the equations obtained for the bars with a parabolic, elliptic and cosinusoidal axis are given. The theoretical framework developed in this paper allows us to expand the possibility of applying the equations of the elasticity theory and relations for internal force factors for curvilinear composite bars in the natural coordinate system for solving a wide range of applied problems.Item Рівняння теорії пружності для композитних брусів із плоскою віссю довільної форми у природній криволінійній системі координат(Луцький національний технічний університет, 2018-07) Ковальчук, Станіслав Богданович; Горик, Олексій ВолодимировичThe work deals with the general dependences between the components of the stress-strain state for the composite discrete-inhomogeneous bar with a curvilinear plane axle of an arbitrary shape and the length-unchanged structural construction, that is subject to static, dynamic and temperature loads during the elastic behavior of orthotropic phase materials. To describe the geometry and the structural construction of the inhomogeneous bar it is proposed the use of natural curvilinear cylindrical coordinate system, which is tied to the shape of its axle, that allowed to reduce the number of variables in the functions of elastic characteristics and external load. The dependences between the components of the stress-strain state are constructed on the basis of the equations of the linear theory of elasticity in a rectangular spatial coordinate system by their coordinate transformation to the natural coordinate system. This made it possible to obtain relations invariant with respect to the shape of the bar, which can be used to solve a wide range of problems in mechanics of elastic deformation of structural elements of arbitrary curvature.