Труды сотрудников ИВМ СО РАН

[Текст] : статья / V. K. Andreev // Journal of Siberian Federal University. Mathematics & Physics = Журнал Сибирского федерального университета. Математика и физика. - 2008. - Т. 1, № 4. - С. 349-370
Аннотация: The invariant solution of the equations of thermodiffusional motion is investigated. This solution describes the motion of two immiscible incompressible binary mixtures with a common flat interface under the action of pressure gradient and thermocapillary forces. The stationary flow of such system is found. If the pressure gradient in one of the mixtures tends to zero sufficiently fast, then the motion of mixtures is slowed down by the viscous friction. On the other hand, if there exists a finite limit of pressure gradient when time tends to infinity, then the solution tends to the stationary state.

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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Андреев, Виктор Константинович

[Text] / V. V. Denisenko, S. S. Zamai, A. V. Kitaev // Geomagn. Aeron. - 2003. - Vol. 43, Is. 6. - P680-686. - Cited References: 15 . - ISSN 0016-7932РУБ Geochemistry & Geophysics

Аннотация: The effect of viscous friction at the boundary between the plasma sheet and the solar wind on electric field generation in the plasma sheet is estimated. The boundary layer is modeled by a viscous layer with two mixing plasma flows. The distribution of the flow velocity in the inner parts of the plasma sheet outside the boundary layer is specified on the basis of experimental data. The calculated distribution of the electric potential in the plasma sheet and at the magnetopause is projected along magnetic lines onto the ionosphere. It has been indicated that, within the scope of the adopted model, viscous friction on the magnetotail flanks for an effective Reynolds number of Re = 3 x 10(3) results in an increase in the potential across the polar cap from 11 to 18 kV. In this case the maximum and minimum of the electric potential at the polar cap boundary are shifted from the nightside to the dayside. It is emphasized that the total distribution of the electric potential in the polar cap under quiet conditions results from the operation of several mechanisms of electric field generation.


Доп.точки доступа:
Zamai, S.S.; Kitaev, A.V.; Денисенко, Валерий Васильевич

[Text] / A. A. Chesnokov, I. V. Stepanova // Appl. Math. Comput. - 2015. - Vol. 265. - P320-328, DOI 10.1016/j.amc.2015.05.019. - Cited References:19. - The work is supported by Russian Foundation of Basic Research (project 14-31-50572), the Program of Leading Scientific Schools Supporting (project 2133.2014.1) and Integrating project of SB RAS (44). . - ISSN 0096-3003. - ISSN 1873-5649РУБ Mathematics, Applied

Аннотация: A mathematical model describing motion of an inhomogeneous incompressible fluid in a Hele-Shaw cell is considered. Linear stability analysis of shear flow class is provided. The role of inertia, linear friction and impermeable boundaries in Kelvin Helmholtz instability is studied. Hierarchy of simplified one-dimensional models of viscosity- and density stratified flows is obtained in long wave approximation. Interpretation of Saffman-Taylor instability is given in the framework of these models. (C) 2015 Elsevier Inc. All rights reserved.

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Держатели документа:
Novosibirsk State Univ, Novosibirsk 630090, Russia.
RAS, SB, Lavrentyev Inst Hydrodynam, Novosibirsk, Russia.
RAS, SB, Inst Computat Modeling, Krasnoyarsk, Russia.

Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Russian Foundation of Basic Research [14-31-50572]; Program of Leading Scientific Schools Supporting [2133.2014.1]Integrating project of SB RAS

[Text] / I. V. Krasnov, L. P. Kamenshchikov // Laser Phys. - 2015. - Vol. 25, Is. 11. - Ст. 115501, DOI 10.1088/1054-660X/25/11/115501. - Cited References:26 . - ISSN 1054-660X. - ISSN 1555-6611РУБ Optics + Physics, Applied

Аннотация: On the basis of numerical simulations and analytical calculations it is proved that the dissipative optical superlattice induced by the rectified gradient force is able to create and trap cold ion Coulomb clusters. In contrast to our previous work (2014 Opt. Commun. 312 192), in the present paper, we do not use the approximation of slow ions (SI), but take into account the non-conservative nature of the trapping force in the optical superlattice as well as the velocity dependence of the friction coefficient of ions and multiplicative nature of the quantum fluctuations of optical forces. It is shown that these factors significantly affect both the formations conditions of the ion Coulomb clusters and their characteristics. It is also demonstrated that their consequences can be well-described by the renormalized SI model. In this model, the electric ion charge is replaced by the effective charge which depends on the light field parameters.

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Держатели документа:
Russian Acad Sci, Inst Computat Modelling, Siberian Div, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Kamenshchikov, L.P.; Каменщиков, Леонид Петрович; Краснов, Игорь Васильевич

/ B. D. Annin, V. A. Kovtunenko, V. M. Sadovskii // Springer Proceedings in Mathematics and Statistics. - 2015. - Vol. 121: 2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013 (24 November 2013 through 29 November 2013, ) Conference code: 136889. - P49-56, DOI 10.1007/978-3-319-12583-1_3 . -
Аннотация: This contribution is devoted to the mathematical theory of elastoplastic and granular solids as well as the quasibrittle fracture of nonlinear cracks. Basic variational and hemivariational inequalities describing nonlinear phenomena due to plasticity, internal friction, interfacial interaction, and alike dissipative physics are outlined from the point of view of nonsmooth and nonconvex optimization. Primary results of the nonlinear theory and its application to solid mechanics are surveyed. © Springer International Publishing Switzerland 2015.

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Держатели документа:
Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstr. 36, Graz, Austria
Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russian Federation
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Annin, B. D.; Kovtunenko, V. A.; Sadovskii, V. M.

[Текст] : статья / Г. Г. Крушенко, И. В. Кукушкин // Вестник Сибирского государственного аэрокосмического университета им. академика М.Ф. Решетнева. - 2016. - Т. 17, № 4. - С. 1053-1061 . - ISSN 1816-9724
   Перевод заглавия: SOME TOOLS AND WAYS OF CONNECTING THE MATING PARTS OF AEROSPACE PRODUCTS

УДК

621.757

Аннотация: Практически все изделия различных отраслей промышленного производства состоят из комплектующих деталей, часть из которых соединяется в узлы и механизмы с помощью различных способов и средств. Такие соединения могут выполняться как в подвижном, так и в неподвижном вариантах, которые, в свою очередь, могут быть выполнены как разъемными, так и неразъемными, а применяемые для этого способы и технологии выбираются в зависимости от технических возможностей обеспечения безопасности собираемого изделия в эксплуатации, стоимости и других показателей. В ряде случаев выгоднее собрать узел/механизм или изделие именно из соединяемых с помощью крепежа комплектующих деталей, чем изготовлять его из «цельного» материала (monolithic bulk material). При изготовлении сложных изделий, относящихся, например, к аэрокосмической технике, для обеспечения точности и надежности сборки применяется широкий диапазон технологий соединения деталей, особенно из разнородных материалов, включая холодную сварку (cold welding), которая выполняется без нагрева соединяемых деталей, плотное соединение происходит в результате их сжатия до появления пластических деформаций; сварку трением с перемешиванием (friction stir welding); окантовывание с помощью штампа (mechanical clinching); клепальную технологию (self-pierce riveting) и др. Приводятся конкретные примеры выполнения соединения деталей при изготовлении изделий аэрокосмической отрасли, такие как сварка (корпуса летательных аппаратов), пайка (камера сгорания), соединение с натягом (головка цилиндра), соединение при помощи шпилек (корпус турбонасосного агрегата), штифтов (лопатки спрямляющего аппарата вентилятора газотурбинного двигателя) и др.
Almost all products of various branches of industrial production consist of components, some of which are connected in the nodes and the mechanisms through various ways and means. Such connections can be made, both in the mobile and fixed variants, which, in turn, may be made detachable and non-detachable, and used methods and technologies which are chosen depending on the technical capabilities, security, collect the product in operation, cost and other factors. In some cases it is more profitable to collect node/mechanism or product originating from connected via fastener components than manufacturing it from a “solid” material (monolithic bulk material). In the manufacture of complex products, for example, related to aerospace engineering, to ensure the accuracy and reliability of assembly a wide range of technologies of details connection, especially of dissimilar materials, including: cold welding, which is performed without heating the joined parts, a tight coupling occurs as a result of their compression until plastic deformation, friction welding with stirring, mechanical clinching, riveting technology and other, is applied. The article provides the specific examples of the connection parts in the manufacture of products of aerospace industry, such as welding (case aircraft), soldering (combustion chamber), the connection tightness (cylinder head), the connection with bolts (case turbo-pump assembly), pins (blades directing vanes of the fan gas turbine engine) and other.

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Держатели документа:
Институт вычислительного моделирования СО РАН
Сибирский государственный аэрокосмический университет имени академика М. Ф. Решетнева

Доп.точки доступа:
Кукушкин, И.В.; Kukushkin I.V.; Krushenko G.G.

[Текст] : статья / Борис Григорьевич Тарасов, Владимир Михайлович Садовский, Оксана Викторовна Садовская // Вычислительная механика сплошных сред. - 2016. - Т. 9, № 1. - С. 38-51, DOI 10.7242/1999-6691/2016.9.1.4 . - ISSN 1999-6691
   Перевод заглавия: Analysis of fan waves in a laboratory model simulating the propagation of shear ruptures in rocks

УДК

539.374

Аннотация: Анализируется веерный механизм передачи вращательного движения в системе упруго связанных пластин на плоском основании, имитирующий распространение сдвиговых трещин в горной породе с аномально высокой хрупкостью. Такие трещины возникают в земной коре на глубинах сейсмической активности. Они продвигаются за счет формирования множественных наклонных микротрещин отрыва, приводящих к образованию веерной домино-структуры в головной части трещины. Создана лабораторная физическая модель, которая наглядно демонстрирует процесс распространения веерных волн. Получены уравнения динамики вращательного движения пластин как механической системы с конечным числом степеней свободы. На основе метода Мерсона решения задачи Коши для систем обыкновенных дифференциальных уравнений разработан вычислительный алгоритм, учитывающий контактное взаимодействие пластин. В рамках упрощенной математической модели динамического поведения веерной системы в приближении сплошной среды оценены зависимости длины веера от скорости движения. Показано, что в отсутствие трения веер может двигаться по инерции с любой скоростью, не превосходящей критическое значение, которое определяется размером, моментом инерции и начальным по отношению к плоскому основанию углом пластин, а также коэффициентом упругости связей. При наличии трения веер останавливается. С помощью дискретной и непрерывной моделей исследованы основные качественные закономерности поведения веера, движущегося под действием приложенных касательных усилий, величина которых в лабораторной физической модели регулируется изменением угла наклона основания. Установлено, что результаты расчетов хорошо согласуются с наблюдениями и данными измерений по лабораторной модели.
The fan-shaped mechanism of rotational motion transmission in the system of elastically connected plates on a plane base is analyzed. This mechanism governs the propagation of shear ruptures in super brittle rocks of the Earth’s crust at seismogenic depths. A laboratory physical model was created which demonstrates the process of fan wave propagation. Equations of the dynamics of a fan system as a mechanical system with a finite number of degrees of freedom are obtained. A computational algorithm taking into account contact interaction between plates is worked out. Within the framework of a simplified continuous model, the approximate estimates of the length of a fan depending on the velocity of its propagation are obtained. It is shown that in the absence of friction a stationary fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of plates, the initial angle and the coefficient of elasticity of connection, and that the length of a fan decreases with increasing velocity. In the absence of distributed shear stress, when the system of plates is in a horizontal position, the fan stops due to the friction forces. The action of distributed shear stress leads to the incomplete disclosure of a fan, and besides the angle of opening decreases with increasing friction. In a system with friction the velocity of a traveling fan is uniquely determined by the opening angle, and in the case of neglecting friction it can take any value within an allowable range. On the basis of a discrete model, the computations demonstrating the incomplete disclosure of fans with different opening angles due to rapid or slow change in the velocity of rotation of the first plate are performed. Comparison of the results of computations of the length and velocity of the fan by means of a discrete model with computations based on analytical formulas and laboratory observations showed a good correspondence between the results.

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Держатели документа:
University of Western Australia
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Садовский, Владимир Михайлович; Sadovskii V.M.; Садовская, Оксана Викторовна; Sadovskaya O.V.; Tarasov Boris Grigorievich

/ B. G. Tarasov, V. M. Sadovskii // (15 June 2016 through 22 June 2016 : Springer Verlag, 2017. - Vol. 10187 LNCS. - P648-656, DOI 10.1007/978-3-319-57099-0_74 . -
Аннотация: The main goal of this paper is to analyze the fan-mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating growth of shear ruptures in super brittle rocks. A physical model recently designed demonstrates that the fan-structure formation can be stable at the absence of distributed shear stress applied. The action of distributed shear stress causes the fan propagation as a wave representing the rupture head. The developed mathematical model of a fan-structure as a continuous system establishes the relation between the fan velocity and the fan length. It is shown that in the absence of friction the fan velocity may be arbitrary, but not greater than the limit velocity which is determined by the moment of inertia of slabs, the initial angle of their orientation and the elastic coefficient of bonds. In a system with friction the velocity of traveling fan is solely determined by the opening angle. The action of distributed shear stress leads to the instability start before the fan-structure completion. The fan length decreases with increasing velocity. © Springer International Publishing AG 2017.

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Держатели документа:
University of Western Australia, Stirling Highway 35, Perth, WA, Australia
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович

/ B. G. Tarasov [et al.] // Int. J. Fract. - 2017. - Vol. 207, Is. 1. - P87-97, DOI 10.1007/s10704-017-0223-1. - Cited References:30. - The authors acknowledge the support provided by the Centre for Offshore Foundation Systems (COFS) at the University of Western Australia. . - ISSN 0376-9429. - ISSN 1573-2673РУБ Materials Science, Multidisciplinary + Mechanics

Аннотация: Experiments on frictional stick-slip instability in brittle materials and natural observations show that friction falls towards zero in the head of shear ruptures propagating with extreme velocities (up to supershear levels). Although essential for understanding earthquakes, fracture mechanics and tribology the question of what physical processes determine how weakening occurs is still unclear. Here, using a mathematical model, we demonstrate that the extremely low friction can be caused by a fan-like fault structure formed on the basis of a tensile-cracking process observed in all extreme ruptures. The mathematical model visualises and describes the fan-structure as a mechanical system during rupture propagation. It explains some features observed in laboratory experiments.

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Держатели документа:
Univ Western Australia, Ctr Offshore Fdn Syst, Stirling Highway 35, Perth, WA 6009, Australia.
Russian Acad Sci, Inst Appl Math, Far Eastern Branch, Radio St 7, Vladivostok 690041, Russia.
Russian Acad Sci, Inst Computat Modelling, Siberian Branch, Akademgorodok 50-44, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Tarasov, Boris G.; Guzev, Mikhail A.; Sadovskii, Vladimir M.; Cassidy, Mark J.; Centre for Offshore Foundation Systems (COFS) at the University of Western Australia

/ B. G. Tarasov, V. M. Sadovskii, O. V. Sadovskaya // J. Appl. Mech. Tech. Phys. - 2017. - Vol. 58, Is. 7. - P1139-1152, DOI 10.1134/S0021894417070100. - Cited References:23. - This research was partially supported by the Centre for Offshore Foundation Systems (the University of Western Australia) and the Complex Fundamental Research Program no. II.2P "Integration and Development" of Siberian Branch of the Russian Academy of Sciences (grant no. 0356-2016-0728). . - ISSN 0021-8944. - ISSN 1573-8620РУБ Mechanics + Physics, Applied

Аннотация: The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth's crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

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Держатели документа:
Univ Western Australia, Ctr Offshore Fdn Syst, Perth, WA 6009, Australia.
Inst Computat Modeling SB RAS, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Tarasov, B. G.; Sadovskii, V. M.; Sadovskaya, O. V.; Centre for Offshore Foundation Systems (the University of Western Australia); Complex Fundamental Research Program [II.2P, 0356-2016-0728]

/ V. M. Sadovskii, O. V. Sadovskaya, B. G. Tarasov // AIP Conference Proceedings : American Institute of Physics Inc., 2018. - Vol. 2025: 10th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2018 (20 June 2018 through 25 June 2018, ) Conference code: 141497, DOI 10.1063/1.5064918 . -
Аннотация: In our research, we analyze the laboratory physical model of the system of rotating bonded slabs on inclined plane, which was created to imitate the process of fan waves formation and propagation in hard rocks at the depths of seismic activity in the Earth's crust. Mathematical model of the dynamics of this system as a mechanical system with a finite number of degrees of freedom is realized by means of the Merson method for numerical solution of ordinary differential equations. We consider two approaches describing the resistance to separation of slabs in a fan-structure. In the first of them, a nonlinear tension diagram for the bonds between the slabs with a characteristic tooth simulating the initial strength of the bonds is determined. In the second one, the value of limiting force is assumed to be given. Comparison of the computational results by these two approaches shows a good qualitative and quantitative correspondence. The influence of dry friction on the process of motion of a fan as well as the dependence of the speed of a fan on the geometrical and mechanical parameters of a system are analyzed. © 2018 Author(s).

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Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation
University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia

Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.; Tarasov, B. G.

[Текст] : статья / Е. Н. Васильев, В. А. Деревянко, Д. П. Емельянов // Решетневские чтения. - 2018. - Т. 1, № 22. - С. 231-233 . - ISSN 1990-7702
   Перевод заглавия: INVESTIGATION OF TEMPERATURE REGIME OF BEARING

УДК

621.822

Аннотация: Проведены экспериментальные и расчетные исследования температурного режима подшипника качения электронасосного агрегата.
Experimental and computational studies of the temperature regime of the rolling bearing of the electric pump unit are carried out.

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Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Васильев, Е.Н.; Vasil'ev E.N.; Деревянко, В.А.; Derevyanko V.A.; Емельянов, Д.П.; Emel'yanov D.P.

[Текст] / В. М. Садовский [и др.]. - [Б. м. : б. и.], 1998. - Б. ц.
Перевод заглавия: Development of numerical methods for the solution of contact elastic-plastic problems
   Перевод заглавия: Development of numerical methods for the solution of contact elastic-plastic problems
Аннотация: При помощи формулировки граничных условий контактного взаимодействия деформируемых тел с учетом трения Кулона в виде квазивариационного неравенства разработаны оригинальные алгоритмы численного решения динамических контактных задач, обладающие вычислительной устойчивостью и гарантирующие выполнение геометрических ограничений в заранее неизвестной зоне контакта, условия неотрицательности нормального давления и противоположную направленность векторов касательной скорости и касательного напряжения при проскальзывании. Построены и обоснованы новые разностные схемы решения одномерных и двумерных задач динамики слоисто-неоднородных упругих и упругопластических сред, преимущества которых перед известными схемами выражаются в высокой точности описания разрывов, монотонности, отсутствии иных нефизичных эффектов. Разработан математический аппарат для исследования точности приближенных решений задач динамики упругопластических тел на основе алгоритмов корректировки решения.
Original methods are worked out for numerical analysis of a dynamic contact interaction between deformable bodies taking account of Kulon's friction by means of the formulation of suitable boundary conditions in the form of quasi-variational inequalities. The application of this formulation makes possible to construct iterative procedures, having computational stability and guaranteeing the implementation of geometric constraints in a priori unknown, changing in process of deformation contact zone, and also conditions of nonnegativity of the normal pressure, opposite directedness of tangent velocity and tangent stress vectors for slipping. New finite difference schemes are constructed for the solution of one-dimensional and two-dimensional problems of dynamics of laminated inhomogeneous elastic and elastoplastic media. Such properties as multiple precision of discontinuous solutions description, monotonicity and absence of other nonphysical effects are related to advantages of these schemes. Mathematical approach is suggested for analysis of precision of approximate solutions of dynamic problems by means of special algorithms of solution correction.

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Держатели документа:
Институт вычислительного моделирования СО РАН (ИВМ СО РАН)

Доп.точки доступа:
Садовский, В.М.; Sadovskii V.M.; Бычек, О.В.; Sadovskaya O.V.; Блинов, А.Н.; Богульский, И.О.
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