Труды сотрудников ИВМ СО РАН

/ V. M. Sadovskii, O. V. Sadovskaya ; ed. by T.E.Simos [et al.] // NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B. Ser. AIP Conference Proceedings : AMER INST PHYSICS, 2012. - Vol. 1479: International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) (SEP 19-25, 2012, Kos, GREECE). - pp. 1611-1614, DOI 10.1063/1.4756474. - Cited References: 4 . - ISBN 0094-243X. - ISBN 978-0-7354-1091-6РУБ Mathematics, Applied + Physics, Applied

Аннотация: Parallel program systems for numerical solution of 2D and 3D problems of the dynamics of deformable media with constitutive relationships of rather general form on the basis of universal mathematical model describing small strains of elastic, elastic-plastic and granular materials are worked out. Some computations of dynamic problems with and without taking into account the moment properties of a material were performed on supercomputers with cluster architecture.

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Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович; Sadovskaya, O.V.; Садовская, Оксана Викторовна; Simos, T.E. \ed.\; Psihoyios, G. \ed.\; Tsitouras, C. \ed.\

[Text] / O.V. Sadovskaya, V.M. Sadovskii // Acoust. Phys. - 2010. - Vol. 56, Is. 6. - P942-950, DOI 10.1134/S1063771010060199. - Cited References: 19. - This study was supported by the Russian Foundation for Basic Research (project no. 08-01-00148), Complex Fundamental Research Program no. 2 of the Presidium of the Russian Academy of Sciences, and Siberian Division of the Russian Academy of Sciences (Interdisciplinary Integration Project no. 40). . - 9. - ISSN 1063-7710РУБ Acoustics

Аннотация: Oscillatory processes in media with microstructure under the action of concentrated impulse and time-periodic perturbations are analyzed within the Cosserat elasticity theory. According to the results of computations, such media are characterized by a resonance frequency equal to the frequency of natural oscillations of particle rotational motion. This frequency is a phenomenological parameter of a material. It was established that the oscillatory rotation of particles changes for monotone rotational motion with increasing intensity of shear strains.


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

[Text] / M.P. Varygina, O.V. Sadovskaya, V.M. Sadovskii // J. Appl. Mech. Tech. Phys. - 2010. - Vol. 51, Is. 3. - pp. 405-413, DOI 10.1007/s10808-010-0055-5. - Cited References: 9. - This work was supported by the Russian Foundation for Basic Research (Grant No. 08-01-00148), the Complex Program of Basic Research of the Presidium of the Russian Academy of Sciences No. 2 Intelligent information technologies, mathematical modeling, system analysis and automation, and the interdisciplinary Integration project of the Siberian Division of the Russian Academy of Sciences No. 40. . - ISSN 0021-8944РУБ Mechanics + Physics, Applied

Аннотация: Using highly effective parallel calculations, it is shown that in a moment elastic medium, there is a resonant frequency which corresponds to the eigenfrequency of rotational motion of particles and does not depend on the size of the region studied.


Доп.точки доступа:
Varygina, M.P.; Варыгина, Мария Петровна; Sadovskaya, O.V.; Садовская, Оксана Викторовна; Sadovskii, V.M.; Садовский, Владимир Михайлович

/ O. V. Sadovskaya // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2013. - Vol. 8236 LNCS: 5th International Conference on Numerical Analysis and Applications, NAA 2012 (15 June 2013 through 20 June 2013, Lozenetz. - P471-478, DOI 10.1007/978-3-642-41515-9_53 . -
Аннотация: Parallel program systems for numerical solution of 2D and 3D problems of the dynamics of deformable media with constitutive relationships of rather general form on the basis of universal mathematical model describing small strains of elastic, elastic-plastic and granular materials are worked out. Computational algorithm is based on the splitting methods with respect to physical processes and spatial variables. Some computations of dynamic problems with and without taking into account the moment properties of a material were performed on clusters. В© 2013 Springer-Verlag.

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Institute of Computational Modeling SB RAS, Akademgorodok 50/44, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskaya, O.V.; Садовская, Оксана Викторовна

/ V. M. Sadovskii, O. V. Sadovskaya // Wave Mot. - 2015. - Vol. 52. - P138-150, DOI 10.1016/j.wavemoti.2014.09.008 . - ISSN 0165-2125
Аннотация: Based on the equations of the dynamics of piecewise-homogeneous elastic material, parallel computational algorithms are developed to simulate the process of stress and strain wave propagation in amedium consisting of alarge number of blocks interacting through compliant interlayers. Computations of waves caused by localized impulse perturbations show that such amedium can be considered as isotropic only in the case of sufficiently thin interlayers. In the case of relatively thick interlayers, the anisotropy effects are observed which consist in the appearance of elongated wave fronts along the coordinate directions and characteristic oscillations of velocities and stresses because of the rotational motion of blocks. For the description of waves in ablocky medium with thin interlayers, the equations of the isotropic Cosserat continuum are applicable. As the thickness of interlayers increases, the orthotropic Cosserat continuum theory which takes into account the symmetry of elastic properties relative to the coordinate planes can be applied. By comparing the elastic wave velocities in the framework of piecewise-homogeneous model and continuum model, a simple method is obtained to estimate the mechanical parameters of the orthotropic Cosserat continuum modeling ablocky medium. In two-dimensional formulation of the orthotropic model the computational algorithm and the program system are worked out for the analysis of propagation of elastic waves. The comparison showed good qualitative agreement between the results of computations of waves caused by localized impulses, in the framework of the model of ablocky medium with compliant interlayers and the model of orthotropic Cosserat continuum.

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Держатели документа:
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V.M.; Sadovsky V.M.; Sadovskaya, O.V.; Садовская, Оксана Викторовна

[Text] / O. V. Sadovskaya, V. M. Sadovskii, M. P. Varygina // ECCOMAS Thematic Conference - COMPDYN 2013: 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Proceedings - An IACM Special Interest Conference. - 2013. - P4578-4592
Аннотация: In the framework of mathematical model of a block medium with elastic blocks interacting through compliant viscoelastic interlayers and its approximation on the basis of equations of the Cosserat continuum, the problems of periodic perturbation of a layer and of a half-space under the action of distributed and localized surface loads are solved numerically. The simple formulas are suggested to determine the elasticity coefficients of the moment continuum by given characteristics of the materials of blocks and interlayers, which provide a good correspondence of the wave fields received by means of the exact and approximate models. Parallel computational algorithms, based on models of the inhomogeneous elasticity theory and the Cosserat elasticity theory, are applied to the analysis of propagation of elastic waves in geomaterials with layered and block microstructure. These algorithms are realized as parallel program systems for GPUs (using CUDA technology) and for multiprocessor computers of the cluster type (using MPI library). Monotone grid-characteristic schemes with a balanced number of time steps in elastic layers or blocks and in viscoelastic interlayers are used. By the analysis of numerical solutions it is shown that the multiblock medium has a resonant frequency of rotational motion of blocks, and this frequency does not depend on the size of a massif and on the boundary conditions at its surface.

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Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович; Varygina, M.P.; Варыгина, Мария Петровна; Садовская, Оксана Викторовна

[Text] / O. V. Sadovskaya, V. M. Sadovskii // AIP Conference Proceedings. - 2015. - Vol. 1648: International Conference on Numerical Analysis and Applied Mathematics (SEP 22-28, 2014, Rhodes, GREECE). - Ст. UNSP 630006, DOI 10.1063/1.4912864. - Cited References:5 . - ISSN 0094-243XРУБ Mathematics, Applied + Physics, Applied

Аннотация: Wave processes in blocky media with a large number of elastic blocks, interacting through compliant interlayers, are described by the equations of a piecewise-homogeneous isotropic elastic medium and by the equations of an orthotropic Cosserat continuum. Parallel program systems for numerical implementation of 2D dynamic problems on wave propagation in blocky media are worked out. Computations demonstrating the anisotropy of a blocky medium even for a sufficiently small thickness of interlayers were performed on supercomputers with cluster architecture.

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Держатели документа:
SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia

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

/ O. V. Sadovskaya, V. M. Sadovskii, M. A. Pokhabova // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2015. - Vol. 9045: 6th International Conference on Finite Difference Methods, FDM 2014; Lozenetz; Bulgaria; 18 June 2014 through 23 June 2014; Code 156479. - P340-347, DOI 10.1007/978-3-319-20239-6_37 . -
Аннотация: Based on the equations of the dynamics of a piecewisehomogeneous elastic material, parallel computational algorithms are developed to simulate the process of stress and strain wave propagation in a medium consisting of a large number of blocks, interacting through compliant interlayers. For the description of waves in a block medium with thick interlayers the orthotropic couple-stress continuum theory, taking into account the symmetry of elastic properties relative to the coordinate planes, can be applied. By comparing the elastic wave velocities in the framework of piecewise-homogeneous model and continuum model, the simple method is obtained to estimate mechanical parameters of an orthotropic Cosserat continuum, modeling a block medium. In two-dimensional formulation of the orthotropic model, the computational algorithm and the program system are worked out for the analysis of propagation of elastic waves. The comparison showed good qualitative agreement between the results of computations of waves, caused by localized impulses, by the model of a block medium with compliant interlayers and the model of an orthotropic Cosserat continuum. © Springer International Publishing Switzerland 2015.

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Держатели документа:
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V. M.; Садовский, Владимир Михайлович; Pokhabova, M. A.; Похабова М.А.; Садовская, Оксана Викторовна

[Текст] : статья / В. М. Садовский, О. В. Садовская, М. П. Варыгина // Параллельные вычислительные технологии (ПаВТ'2012) : ЮУрГУ, 2012. - С. 662-672 . - ISBN 978-5-696-04237-4
Аннотация: Разработан комплекс параллельных прикладных программ, представляющий собой набор инструментальных средств, предназначенных для решения задач динамики деформируемых сред с определяющими уравнениями достаточно общего вида на основе явных разностных схем сквозного счета. Созданы компьютерные приложения 2Dyn_Granular, 2Dyn_Cosserat и 3Dyn_Granular, 3Dyn_Cosserat для численного исследования процессов распространения упругопластических волн в структурно неоднородных средах с учетом и без учета моментных свойств материала на многопроцессорных вычислительных системах кластерного типа.

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Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Садовская, Оксана Викторовна; Sadovskaya O.V.; Варыгина, Мария Петровна; Varygina M.P.; Sadovskii V.M.; ПАРАЛЛЕЛЬНЫЕ ВЫЧИСЛИТЕЛЬНЫЕ ТЕХНОЛОГИИ 2012 (ПаВТ'2012) (2012 ; 26.03 - 30.03 ; Новосибирск)

[Текст] : статья / В. М. Садовский // Дальневосточный математический журнал. - 2016. - Т. 16, № 2. - С. 209-222 . - ISSN 1608-845X
   Перевод заглавия: Thermodynamically consistent equations of the couple stress elasticity

УДК

539.371

Аннотация: Для описания движения микрополярной среды, в которой наряду с поступательными степенями свободы реализуются независимые вращения частиц, выбирается естественная мера кривизны, представляющая собой характеристику деформированного состояния, не зависящую от пути его достижения. Показано, что часто используемая лагранжева мера кривизны со скоростью изменения, равной тензору градиентов угловой скорости, корректна только в геометрически линейном приближении. Методом внутренних термодинамических параметров состояния строятся нелинейные определяющие уравнения моментной теории упругости. В результате линеаризации этих уравнений в изотропном случае получаются уравнения континуума Коссера, в которых сопротивление материала изменению кривизны характеризуется не тремя независимыми коэффициентами, как в классической теории, а одним. Полная система уравнений динамики моментной среды при конечных деформациях и поворотах частиц приводится к термодинамически согласованной системе законов сохранения. С помощью этой системы получены интегральные оценки решений задачи Коши и краевых задач с диссипативными граничными условиями, гарантирующие единственность и непрерывную зависимость от начальных данных.
To describe motion in a micropolar medium, with the concurrent translational degrees of freedom and independent particle rotations, it is chosen to use natural measure of curvature that is a strain state characteristic independent of deformation method. It is shown that the common Lagrangian curvature measure with the rate of change equal to a tensor of angular velocity gradients is only applicable under geometrically linear approximation. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against the three independent coefficients of the classical theory. The complete system of equations for the dynamics of a medium with couple stresses under finite strains and particle rotations reduces to a thermodynamically consistent system of laws of conservation. This system allows to obtain the integral estimates that guarantee the uniqueness and continuous dependence on the initial data of solutions of the Cauchy problems and the boundary-value problems with dissipative boundary conditions.

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Держатели документа:
Институт вычислительного моделирования СО РАН

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

/ V. M. Sadovskii // Eng. Trans. - 2017. - Vol. 65, Is. 1. - P201-208 . - ISSN 0867-888X
Аннотация: To describe motion in a micropolar medium a special measure of curvature is used that is a strain state characteristic independent of deformation process. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against three independent coefficients of the classical theory. So, it turns out that the developed variant of the model gives an adequate description of generalized plane stress state in an isotropic micropolar medium, while the classical one describes this state only at a certain case. The complete system of nonlinear equations for the dynamics of a medium with couple stresses reduces to a thermodynamically consistent system of laws of conservation, which allows obtaining integral estimates that guarantee the correctness of the Cauchy problem and boundary-value problems with dissipative boundary conditions. © 2017, Polish Academy of Sciences. All rights reserved.

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Держатели документа:
Institute of Computational Modeling SB RAS, Krasnoyarsk, Russian Federation

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

/ V. M. Sadovskii, E. P. Chentsov // (15 June 2016 through 22 June 2016 : Springer Verlag, 2017. - Vol. 10187 LNCS. - P583-590, DOI 10.1007/978-3-319-57099-0_66 . -
Аннотация: Resonance phenomena in inhomogeneous layered and blocky media are investigated on the basis of the discrete model of transverserotational oscillations in linear monoatomic chain. To analyze the behavior of the system in near-resonance region, spectral portraits are built. It allows to visualize resonant frequencies and to analyze alteration of an amplitude vector. Using mentioned model, a set of resonant frequencies are found. It is shown that there exists one specific frequency, which does not depend on the number of particles in the chain. In passing to the limit as the chain length tends to infinity, this frequency, related to rotational particles vibration, is the unique resonant frequency. The discussed property is associated with the previously studied property of the Cosserat continuum, where the resonant frequency of rotational motion exists, which does not depend on the specimen size and on the conditions of loading at its boundary. © Springer International Publishing AG 2017.

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Держатели документа:
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Chentsov, E.P.; Ченцов, Евгений Петрович; Садовский, Владимир Михайлович

/ M. Varygina // (15 June 2016 through 22 June 2016 : Springer Verlag, 2017. - Vol. 10187 LNCS. - P690-697, DOI 10.1007/978-3-319-57099-0_79 . -
Аннотация: System of equations describing micropolar elastic thin plates is written in symmetric hyperbolic form. For the solution of dynamic problems in the framework of micropolar thin plates the numerical algorithm is proposed. The algorithm based on the two-cyclic splitting method in combination with monotone finite-difference 1D schemes is proposed. The results of computations of problems on distributed impulse action loads are shown. © Springer International Publishing AG 2017.

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Держатели документа:
Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Варыгина, Мария Петровна

[Текст] : научное издание / Ирина Владимировна Смолехо, Оксана Викторовна Садовская, Владимир Михайлович Садовский // Вычислительные технологии. - 2017. - Т. 22, № S1. - С. 87-98 . - ISSN 1560-7534
   Перевод заглавия: Numerical modeling of acoustic waves in a liquid crystal using CUDA technology
Аннотация: В рамках акустического приближения математической модели, описывающей термомеханическое поведение жидкого кристалла с учетом моментных свойств, получена система уравнений второго порядка для касательного напряжения и угловой скорости. Разработан алгоритм численного решения этой системы при заданных начальных данных и граничных условиях, который реализован в виде параллельной программы на языке Си с использованием технологии CUDA для вычислительных систем с графическими ускорителями.
One of the approaches to mathematical modeling for deformation of a liquid crystal is based on the assumption that a liquid crystal is a fine-dispersed continuum, at each point of which the elongated particles - molecules or domains of co-oriented molecules - can move according to laws of the viscous fluid dynamics and can rotate relative to a fluid. In this approach the Cosserat continuum theory is applicable, where along with translational motion, characterized by the velocity vector, the rotational degrees of freedom for particles with the angular velocity vector are considered and, along with the stress tensor with nonsymmetrical components, the nonsymmetrical tensor of couple stresses is introduced. Within the framework of acoustic approximation of the model, which describes thermomechanical behavior of a liquid crystal taking into account the couple stresses, the system of two differential equations of the second-order was obtained for the tangential stress and angular velocity in two-dimensional case. The algorithm for numerical solution of the obtained system of equations under given initial data and boundary conditions is considered. This system is solved using the explicit finite-difference scheme “cross” of the second-order approximation. The stability condition for the scheme is obtained. The algorithm is realized as a parallel program in the C language using the CUDA technology for computing systems with graphics accelerators. A series of computations of acoustic waves in a liquid crystal was performed to demonstrate the efficiency of proposed program. The comparison of numerical solution and the exact solution was carried out.

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Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Смолехо, Ирина Владимировна; Smolekho Irina Vladimirovna; Садовская, Оксана Викторовна; Sadovskaya Oxana Viktorovna; Садовский, Владимир Михайлович; Sadovskii Vladimir Mikhailovich

/ V. M. Sadovskii, O. V. Sadovskaya // Russ. J. Numer. Anal. Math. Model. - 2018. - Vol. 33, Is. 2. - P111-121, DOI 10.1515/rnam-2018-0010. - Cited References:21 . - ISSN 0927-6467. - ISSN 1569-3988РУБ Engineering, Multidisciplinary + Mathematics, Applied

Аннотация: Dynamic processes in block-structured media are described within the framework of a mathematical model where elastic blocks interact with each other through pliable interlayers possessing complex mechanical properties. The case of elastic interaction is considered, the effects of plasticity and viscoelastic shear in block interlayers are taken into account. We use the model of porous fluid-saturated material in interlayers in which pores collapse during sudden or prolonged application of compressive stresses. An implicit difference scheme is constructed for numerical implementation of the model based on principles for construction of Ivanov's schemes with controlled energy dissipation. UsingMPI (Message Passing Interface), we developed parallel software for modelling wave motion in a two-dimensional formulation. The results of numerical analysis are presented for the waves initiated by rotation of blocks, which indicates a strong anisotropy of the blocky medium.

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Держатели документа:
RAS, Inst Computat Modelling, Siberian Branch, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Sadovskii, Vladimir M.; Sadovskaya, Oxana V.

/ I. E. Petrakov, V. M. Sadovskii // AIP Conference Proceedings : American Institute of Physics Inc., 2019. - Vol. 2164: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2019 (20 June 2019 through 25 June 2019, ) Conference code: 153460. - Ст. 090004, DOI 10.1063/1.5130834 . -
Аннотация: Generalized rheological method is used to construct constitutive equations of fiber composite materials with the fibers having high tensile stiffness and low stiffness upon compression. Polymer-based composite reinforced by thin carbon fibers, used in the aerospace industry, was chosen as the material for research. The method for determining the effective moduli of elasticity, based on the analysis of the bending state of a thin rod, was implemented to check the material's moduli. Photos of the bent rod with cantilever bending were processed to obtain a plane projection, and then digitized using computer programs. The deflection data along the rod length was used further in solving the inverse problem of determining flexural stiffness (it was considered constant) using the least squares method. By means of Matlab functions, the problem of minimizing the standard deviation of the calculated deflection from the digitized one was solved on a discrete system of points along the axis of the rod. The deflection was computed by the finite difference method based on the generalized equation of the Euler elastic line which takes into account the flexural stiffness, deformation along the rod, Timoshenko effect (the effect of shear deformation) and Cosserat effect (the effect of independent turns of the reinforcing fibers relative to the matrix). Young's modulus upon tension was measured experimentally using standard technique. Young's modulus upon compression was calculated using the value of flexural stiffness corresponding to the best approximation of calculated deflection to the digitized deflection. As a result, it was shown that the ratio of moduli for the material under consideration is in the range of 50-60% and, if the calculation of flexural stiffness is made with Young's modulus under tension, then it is possible to obtain a relative error in the deflection up to 30% with the increased thickness of the rod. © 2019 Author(s).

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Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Petrakov, I. E.; Sadovskii, V. M.

/ B. D. Annin [et al.] // J. Sib. Fed. Univ. Math. Phys. - 2019. - Vol. 12, Is. 5. - P533-542, DOI 10.17516/1997-1397-2019-12-5-533-542 . - ISSN 1997-1397
Аннотация: For the analysis of bending of a thin rod made of fiber composite, the generalized Euler elastic equation is used, taking into account different resistance of the material to tension and compression, the influence of transverse shear, elongation of the axis and independent rotations of the reinforcing elements relative to the matrix. Based on Newton’s method, a computational algorithm has been developed for solving the static bending problem. A method for determining phenomenological parameters of the composite has been implemented, including photographing the bending state of the rod under the action of a system of forces and couple forces, digital processing of the photography and solving the inverse coefficient problem. The method was validated by comparing the results of computations with a laboratory physical experiment. It is shown that the moduli of elasticity in tension and compression of carbon fiber composite used in the experiment, essentially differ, and that the use of equal moduli in determining bending stiffness results in a significant error in the deflection calculations. © Siberian Federal University. All rights reserved.

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Lavrentyev Institute of Hydrodynamics RAS SB, Lavrentуeva, 15, Novosibirsk, 630090, Russian Federation
Institute of Computational Modelling RAS SB, Akademgorodok, 50/44, Krasnoyarsk, 660036, Russian Federation
Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russian Federation
Reshetnev Siberian State University of Science and Technology, Semafornaya, 433/1, Krasnoyarsk, 660059, Russian Federation

Доп.точки доступа:
Annin, B. D.; Sadovskii, V. M.; Petrakov, I. E.; Vlasov, A. Y.

/ B. D. Annin, V. M. Sadovskii, I. E. Petrakov, A. Y. Vlasov // J. Sib. Fed. Univ.-Math. Phys. - 2019. - Vol. 12, Is. 5. - P533-542, DOI 10.17516/1997-1397-2019-12-5-533-542. - Cited References:10. - The work was supported by the Russian Foundation for Basic Research (grant no. 19-01-00511) and by the Ministry of Education and Science of the Russian Federation (contract no. 02.G25.31.0147). The presented calculations were performed on the Flagman computer of the Institute of Computational Modeling of the SB RAS. . - ISSN 1997-1397. - ISSN 2313-6022РУБ Mathematics

Аннотация: For the analysis of bending of a thin rod made of fiber composite, the generalized Euler elastic equation is used, taking into account different resistance of the material to tension and compression, the influence of transverse shear, elongation of the axis and independent rotations of the reinforcing elements relative to the matrix. Based on Newton's method, a computational algorithm has been developed for solving the static bending problem. A method for determining phenomenological parameters of the composite has been implemented, including photographing the bending state of the rod under the action of a system of forces and couple forces, digital processing of the photography and solving the inverse coefficient problem. The method was validated by comparing the results of computations with a laboratory physical experiment. It is shown that the moduli of elasticity in tension and compression of carbon fiber composite used in the experiment, essentially differ, and that the use of equal moduli in determining bending stiffness results in a significant error in the deflection calculations.

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Держатели документа:
Lavrentyev Inst Hydrodynam RAS SB, Lavrentyeva 15, Novosibirsk 630090, Russia.
Inst Computat Modelling RAS SB, Akademgorodok 50-44, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Inst Math & Comp Sci, Svobodny 79, Krasnoyarsk 660041, Russia.
Reshetnev Siberian State Univ Sci & Technol, Semafornaya 433-1, Krasnoyarsk 660059, Russia.

Доп.точки доступа:
Annin, Boris D.; Sadovskii, Vladimir M.; Petrakov, Igor E.; Vlasov, Anton Yu; Sadovskii, Vladimir; Petrakov, Igor; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-01-00511]; Ministry of Education and Science of the Russian FederationMinistry of Education and Science, Russian Federation [G25.31.0147]