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2017 year, number 3

Fluid Flow Simulation in a Random Elliptical Porous Medium by using the Lattice Boltzmann Method

M. Ezzatabadipour1, H. Zahedi2, M. M. Keshtkar3
1Sirjan Jahan Steel Complex, Kerman, Iran
2University of Isfahan, Isfahan, Iran
3Islamic Azad University, Kerman, Iran
Keywords: решеточный метод Больцмана, условия на криволинейной границе, хаотичное распределение, пористая среда, частицы эллиптической формы, проницаемость, lattice Boltzmann method, curved boundary conditions, random distribution, porous medium, elliptical particles, permeability

Abstract >>
A fluid flow through an isotropic porous medium with randomly arranged elliptical particles is simulated by the lattice Boltzmann method. The dimensionless pressure drop and the dimensionless permeability are evaluated as functions of the Reynolds number. The effect of the aspect ratio of the major to minor semi-axis of the ellipse on the dimensionless permeability is considered for different values of porosity. The pressure drop is thoroughly investigated as a function of fluid viscosity for different values of the aspect ratio and porosity. The influence of various parameters of the problem on the mean tortuosity of the medium is considered.

Numerical Simulation of Cerebrospinal Fluid Hydrodynamics in the Healing Process of Hydrocephalus Patients

S. Gholampou1, N. Fatouraee2, A. S. Seddighi3,4, A. Seddighi3,4
1Islamic Azad University, Tehran, Iran
2Amirkabir University of Technology, Tehran, Iran
3Shahid Beheshti, Tehran, Iran
4University of Medical Sciences, Tehran, Iran
Keywords: сильвиев канал, давление спинно-мозговой жидкости, взаимодействие жидкости и твердого тела, число Рейнольдса, шунтирование, aqueduct of sylvius, CSF pressure, fluid-solid interactions, Reynolds number, shunting

Abstract >>
Three-dimensional computational models of the cerebrospinal fluid (CSF) flow and brain tissue are presented for evaluation of their hydrodynamic conditions before and after shunting for seven patients with non-communicating hydrocephalus. One healthy subject is also modeled to compare deviated patients data to normal conditions. The fluid-solid interaction simulation shows the CSF mean pressure and pressure amplitude (the superior index for evaluation of non-communicating hydrocephalus) in patients at a greater point than those in the healthy subject by 5.3 and 2 times, respectively.

Numerical Analysis of the Flow Pattern and Vortex Breakdown over a Pitching Delta wing at Supersonic Speeds

M. Hadidoolabi, H. Ansarian
Malek Ashtar University of Technology, Tehran, Iran
Keywords: дельтовидное крыло, структура течения, сверхзвуковой поток, отрыв вихрей, delta wing, flow pattern, supersonic flow, vortex breakdown

Abstract >>
A supersonic compressible flow over a 600 swept delta wing with a sharp leading edge undergoing pitching oscillations is computationally studied. Numerical simulations are performed by the finite volume method with the use of the k -w turbulence model for various Mach numbers and angles of attack. Variations of flow patterns in a crossflow plane, hysteresis loops associated with the vortex core location, and vortex breakdown positions during a pitching cycle are investigated. Trends for various Mach numbers, mean angles of attack, pitching amplitudes, and pitching frequencies are illustrated.

Numerical Estimation of Heterogeneous Reaction Constants in the Flow of Diluted Gas Through a Cylindrical Channel

M. Yu. Plotnikov1, E. V. Shkarupa2
1Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: разреженный газ, константы гетерогенных реакций, цилиндрический канал, прямое статистическое моделирование}, rarefied gas, heterogeneous reaction constants, cylindrical channel, direct statistical modeling

Abstract >>
The direct statistical modeling method is used to study the influence of the coefficients of heterogeneous dissociation and recombination reactions on the flow of rarefied gas through a cylindrical channel. It is established that the degree of dissociation of the flow coming out of the channel is significantly dependent on the relationship between the dissociation and recombination coefficients. The technique for determining the dissociation and recombination coefficients on the basis of the experimental data is proposed.

Axisymmetric Flow and Heat Transfer of the Carreau Fluid due to a Radially Stretching Sheet: Numerical Study

M. Khan, Hashim
Quaid-i-Azam University, Islamabad, 44000, Pakistan
Keywords: осесимметричное течение, жидкость Карро, теплоперенос, растяжение листа, метод стрельбы, axisymmetric flow, Carreau fluid, heat transfer, radially stretching sheet, shooting technique

Abstract >>
The prime objective of this article is to study the axisymmetric flow and heat transfer of the Carreau fluid over a radially stretching sheet. The Carreau constitutive model is used to discuss the characteristics of both shear thinning and shear thickening fluids. The momentum equations for the two-dimensional flow field are first modeled for the Carreau fluid with the aid of the boundary layer approximations. The essential equations of the problem are reduced to a set of nonlinear ordinary differential equations by using local similarity transformations. Numerical solutions of the governing differential equations are obtained for the velocity and temperature fields by using the fifth-order Runge-Kutta method along with the shooting technique. These solutions are obtained for various values of physical parameters. The results indicate substantial reduction of the flow velocity as well as the thermal boundary layer thickness for the shear-thinning fluid with an increase in the Weissenberg number, and the opposite behavior is noted for the shear-thickening fluid. Numerical results are validated by comparisons with already published results.

Thermal Radiation Effect on a Mixed Convection Flow and Heat Transfer of the Williamson Fluid Past an Exponentially Shrinking Permeable Sheet with a Convective Boundary Condition

A. Zaib1, K. Bhattacharyya2, M. Khalid1, S. Shafie3
1Federal Urdu University of Arts, Science & Technology, Gulshan-e-Iqbal Karachi, Pakistan
2Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
3Universiti Teknologi Malaysia, JB, 81310 Skudai, Johor, Malaysia
Keywords: излучение, смешанная конвекция, жидкость Вильямсона, экспоненциальный закон сжатия пленки, конвективные граничные условия, radiation effect, mixed convection flow, Williamson fluid, exponentially shrinking sheet, convective boundary condition

Abstract >>
The thermal radiation effect on a steady mixed convective flow with heat transfer of a nonlinear (non-Newtonian) Williamson fluid past an exponentially shrinking porous sheet with a convective boundary condition is investigated numerically. In this study, both an assisting flow and an opposing flow are considered. The governing equations are converted into nonlinear ordinary differential equations by using a suitable transformation. A numerical solution of the problem is obtained by using the Matlab software package for different values of the governing parameters. The results show that dual nonsimilar solutions exist for the opposing flow, whereas the solution for the assisting flow is unique. It is also observed that the dual nonsimilar solutions exist only if a certain amount of mass suction is applied through the porous sheet, which depends on the Williamson parameter, convective parameter, and radiation parameter.

Effect of the Grid Step of the Vector Displacement Field on the Strain Estimate in the Digital Image Correlation Method

S. V. Panin1,2, V. V. Titkov1, P. S. Lyubutin1,2
1Institute of Strength Physics and Material Science, Siberian Branch, Russian Academy of Sciences, Tomsk, 634055, Russia
2National Research Tomsk Polytechnical University, Tomsk, 634050, Russia
Keywords: поле векторов перемещений, шаг сетки, корреляция цифровых изображений, погрешность оценки деформации, текстура, шум Гаусса, displacement vector field, grid step, digital image correlation, strain error estimate, texture, Gaussian noise

Abstract >>
The influence of the grid step of the displacement vector field on the strain estimate in the digital image correlation method is considered. The reasons for the emergence and the magnitude of the strain estimate error in processing optical images of material surfaces with different textures are analyzed. The dependence of the grid step for strain estimation on the magnitude of displacements and also on the presence and size of the discontinuity region in the strain field is studied. An adapted algorithm for choosing the grid step is proposed, which allows the strain calculation error to be reduced by a factor of 1.9 with simultaneous reduction of computational expenses by a factor of 2.1.

Cyclic Pressing of Ultra-High-Molecular-Weight Polyethylene Powder

B. S. Zlobin1, A. A. Shtertser1, V. V. Kiselev1, S. D. Shemelin1, V. A. Poluboyarov2, A. A. Zhdanok2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Institute of Solid State Chemistry and Mechanochemistry, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630128, Russia
Keywords: сверхвысокомолекулярный полиэтилен, циклическое ударное прессование, компакт, прочностные свойства, микро- и наноразмерные добавки, ultra-high-molecular-weight polyethylene, cyclic shock pressing, compact, strength properties, micro- and nanosized additives

Abstract >>
Bulk samples of GUR 4150 ultra-high-molecular-weight polyethylene with a molar mass of 9.2 х 106 g/mol are obtained by cyclic impact compaction. During compaction, the material remains in a solid state, which ensures the preservation of the crystalline phase with a volume fraction of up to 66%. The strength properties of the samples are not inferior to those of the products obtained using industrial hot pressing. It is shown that the method described here is suitable for obtaining compacts with micro- and nanosized additives.

Effect of the Silicon-Carbide Microand Nanoparticle Size on the Thermo-Elastic and Time-Dependent Creep Response of a Rotating Al-SiC Composite Cylinder

A. Loghman, M. Hammami, E. Loghman
University of Kashan, Kashan, I.R.Iran
Keywords: вращающийся цилиндр, установившаяся ползучесть, композит Al-SiC, микро- и наноразмерные частицы, rotating cylinder, time-dependent creep, Al-SiC composite, micro- and nanoparticles

Abstract >>
The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby's constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 m. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertial body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl-Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.

Properties of an Al/(Al2O3+TiB2+ZrB2) Hybrid Composite Manufactured by Powder Metallurgy and Hot Pressing

F. Farhadinia, A. Sedghi, M.T. Nooghani
Imam Khomeini international university, Qazvin, Iran
Keywords: композит с металлической матрицей, гибридный композит, порошковая металлургия, механические свойства, микроструктура, metal matrix composites, hybrid, powder processing, mechanical properties, microstructure

Abstract >>
The properties and microstructure of an Al/(Al2O3 + TiB2 + ZrB2) hybrid composite made by using hot pressing of aluminum combined with different amounts of TiB2, ZrB2, and Al2O3 powders are studied. The mechanical properties of the composites are investigated on the basis of microhardness and compression tests. The results show that the microstructure of the composites is uniform and the particles are well distributed in the matrix.

Numerical Simulation of Plastic Deformation and Damage Accumulation in Structural Materials under Various Low-Cycle Loading Conditions

V. A. Gorokhov, S. A. Kapustin, Yu. A. Churilov
Lobachevsky National Research Nizhny Novgorod State University, Nizhny Novgorod, 603950, Russia
Keywords: пластическое деформирование, малоцикловое нагружение, накопление повреждений, численное моделирование, пластическое деформирование, малоцикловое нагружение, накопление повреждений, численное моделирование, plastic deformation, low-cycle loading, damage accumulation, numerical modeling

Abstract >>
This paper presents the results of a finite-element study of elastic-plastic deformation and damage accumulation in structural materials under various cyclic loading conditions. Material behavior is described by the relations of damage mechanics and using thermoplastic model which takes into account the plastic deformation of the material under cyclic loading and the kinetic equations of the energy theory of damage accumulation. The basic laws of plastic deformation and development of damage in materials under hard, soft, symmetric, and asymmetric low-cycle loading.

Symmetry Classes of Anisotropy Tensors of Quasielastic Materials and the Generalized Kelvin Approach

N. I. Ostrosablin
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: линейно-упругие материалы, квазиупругость, упругость по Коши, анизотропия, классы симметрии, собственные модули и состояния, linearly elastic materials, quasielasticity, Cauchy elasticity, anisotropy, symmetry classes, proper modes and states

Abstract >>
The anisotropy matrices (tensors) of quasielastic (Cauchy-elastic) materials were obtained for all classes of crystallographic symmetries in explicit form. The fourth-rank anisotropy tensors of such materials do not have the main symmetry, in which case the anisotropy matrix is not symmetric. As a result of introducing of various bases in the space of symmetric stress and strain tensors, the linear relationship between stresses and strains is written in invariant form similar to the form in which generalized Hooke’s law is written for the case of anisotropic hyperelastic materials and contains six positive Kelvin proper modules. It is shown that the introduction of modified rotation deformations in the strain space can cause a transition to the symmetric anisotropy matrix observed in the case of hyperelasticity. For the case of transverse isotropy, there are examples of the determination of the Kelvin proper modules and proper bases and the rotation matrix in the strain space. It is shown that there is a possibility of existence of quasielastic media with a skew-symmetric anisotropy matrix with no symmetric part. Some techniques for the experimental testing of the quasielasticity model are proposed.

Chaotic Interaction Dynamics of Three Structures: Two Cylindrical Shells Nested into Each Other and Their Reinforcing Local Rib

V. A. Krysko, S. S. Vetsel', V. V. Dobriyan, O. A. Saltykova
Gagarin Saratov State Technical University, Saratov, 410054 Russia
Keywords: хаотическая динамика, метод конечных элементов, замкнутая цилиндрическая оболочка, балка, контактное взаимодействие, хаотическая синхронизация, chaotic dynamics, finite element method, closed cylindrical shell, beam, contact interaction, chaotic synchronization

Abstract >>
This paper studies the chaotic dynamics of two cylindrical shells nested into each other with a gap and their reinforcing beam, also with a gap, which is subjected to a distributed alternating load. The problem is using methods of nonlinear dynamics and qualitative theory of differential equations. The basic equations are the Novozhilov equations for equations geometrically nonlinear structures. Contact pressure is determined by Kantor's method. Using finite elements in the spatial variables, the partial differential equations for the beam and shells are reduced to the Cauchy problem, which is solved by explicit integration (Euler's method). The chaotic synchronization of this system is studied.

Esign of Corrugated Plates with Extreme Stiffnesses

A. G. Kolpakov
Siberian State University of Telecommunications and Informatics, Novosibirsk, 630108, Russia
Keywords: гофрированные пластины, эффективные жесткости, задача проектирования, corrugated plate, effective stiffness, design problem

Abstract >>
The maximum (minimum) effective stiffnesses of a corrugated plate with varying corrugation shape are determined.

Determination of Uniaxial Stresses in Steel Structures by the Laser-Ultrasonic Method

A. A. Karabutov1,2, N. B. Podymova3,2, E. B. Cherepetskaya2
1International Laser Center, Moscow, 119991, Russia
2Moscow State Mining University, Moscow, 119991, Russia
3M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
Keywords: механические напряжения, эффект акустоупругости, лазерно-ультразвуковой преобразователь, скорость головных ультразвуковых волн, mechanical stresses, acoustoelasticity effect, laser-ultrasound transducer, the velocity of head ultrasonic waves

Abstract >>
This paper describes the experimental implementation of the laser-ultrasonic method for diagnosing mechanical compression and tensile stresses in steel structures, based on the acoustoelasticity effect. The special laser-ultrasonic transducer that ensures the laser excitation and highly sensitive piezoelectric recording of head (longitudinal subsurface) ultrasonic waves. It is shown on the example of R65 rail samples of various quality that, regardless of the structural phase state of the rail, there is one and the same linear relationship between the relative variation of the velocity of head ultrasonic waves and the absolute value of uniaxial compression and tensile stresses acting in the rail.

Study of Strength Orthotropic Cylindrical Panels with Account for Geometric Nonlinearity

A. A. Semenov
St. Petersburg State Architectural and Construction University, St. Petersburg, 190005, Russia
Keywords: оболочки, прочность, устойчивость, геометрическая нелинейность, цилиндрические панели, углепластик, shells, strength, stability, geometric nonlinearity, cylindrical panels, carbon plastic

Abstract >>
This paper describes the influence of geometric nonlinearity in the analysis of the strength of orthotropic cylindrical panels. The values of maximum permissible loads in the linear and nonlinear versions of calculations of structures made of unidirectional carbon plastics are given, and the loads at which stability loss occurs are determined. The mathematical models accounts for transverse shifts and geometric nonlinearity and stated as the full potential strain energy functional. The calculations are carried out on the basis of the method of solution continuation with respect to the parameter. The strength is estimated by using the maximum stress criterion.

Accounting for the Frequency-Dependent Dynamic Modulus of Elasticity of Duralumin in Deformation Problems

V. N. Paimushin1,2, V. A. Firsov1, I. Gunal1, V. M. Shishkin3
1Tupolev Kazan National Research Technical University, Kazan, 420111 Russia
2Kazan Federal University, Kazan, 420008 Russia
3Vyatka State University, Kirov, 610000 Russia
Keywords: образец, динамический модуль упругости, частотная зависимость, идентификация, конечный элемент, sample, dynamic elastic modulus, frequency dependence, identification, finite element

Abstract >>
The bending vibrations of D16AT Duralumin samples are investigated, and a significant frequency dependence of the dynamic modulus of elasticity of D16AT Duralumin is detected. It is shown that in the frequency range 0-20 Hz, the dynamic elastic modulus is significantly reduced and at high frequencies, it is practically unchanged. A general method has been developed to determine the form and frequency of free vibrations of the structure taking into account the dependence of the dynamic modulus of elasticity of the material on the frequency of its deformation. Numerical experiments on pulsed loading of an elongated plate have been determined, and the need to consider the frequency dependence of the dynamic modulus of elasticity of Duralumin in structural analysis has been shown.

Influence of Rigid Constraints on the Deformation of a Hydrostatically Compressed Shell

V. V. Kiselev, D. V. Dolgikh
Mikheev Institute of Metal Physics, Ekaterinburg, 620990 Russia
Keywords: оболочки, деформация, гидростатическое давление, нелинейная теория упругости, shells, deformation, hydrostatic pressure, nonlinear theory of elasticity

Abstract >>
The change in the cross section of a shell with external and internal constraints is analyzed by analytical and numerical methods using simplified nonlinear models. It is shown that an appropriate choice of constraints eliminates unwanted wrinkles and imparts the shape of a regular hollow polyhedron to a circular shell.

Simulation of Dynamic Processes in Three-Dimensional Layered Cracked Media with the Use of the Grid-Characteristic Numerical Method

V. I. Golubev1, R. I. Gilyazutdinov1, I. B. Petrov1, N. I. Khokhlov1, A. V. Vasyukov2
1Moscow Institute of Physics and Technology, Dolgoprudny, 141700, Russia
2Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia
Keywords: трещиноватые среды, математическое моделирование, численные методы, параллельные алгоритмы, прямые задачи сейсмической разведки, композитные материалы, cracked media, mathematical simulation, numerical methods, parallel algorithms, direct seismic prospecting tasks, composite materials

Abstract >>
This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer cracked media. The dynamic processes are described using the defining system of equations in partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic method on curvilinear structural grids. The cracked nature of the medium is accounted for by explicitly selecting the boundaries of individual cracks and setting special boundary conditions in them. The various models of the heterogeneous deformed medium having a cracked structure are considered: a homogeneous medium, a medium with horizontal boundaries, and media with inclined and curvilinear boundaries. The wave fields detected on the surface are obtained, and their structure is analyzed. It is demonstrated that it is possible to detect waves propagating from a cracked medium even in the case of nonparallel (inclined and curvilinear) boundaries of geological layers.

T-Stress Estimation by the Two-Parameter Approach for a Specimen with a V-Shaped Notch

O. Bouledroua1, A. Elazzizi1,2, M. Hadj. Meliani1,3, G. Pluvinage3, Y. G. Matvienko4
1Hassiba BenBouali University of Chlef, Esalem City, Chlef, 02000, Algeria
2Mohamed Boudiaf University of Sciences and Technology, Oran, 31000, Algeria
3Universitе Paul Verlaine de Metz, France
4Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, 101990. Russia
Keywords: стесненная деформация, T-напряжения, эффективное расстояние, надрез, метод конечных элементов, constraint, T-stress, effective distance, notch, finite element analysis

Abstract >>
In the present research, T-stress solutions are provided for a V-shaped notch in the case of surface defects in a pressurised pipeline. The V-shaped notch is analyzed with the use of the finite element method by the Castem2000 commercial software to determine the stress distribution ahead of the notch tip. The notch aspect ratio is varied. In contrast to a crack, it is found that the T-stress is not constant and depends on the distance from the notch tip. To estimate the T-stress in the case of a notch, a novel method is developed, inspired by the volumetric method approach proposed by Pluvinage. The method is based on averaging the T-stress over the effective distance ahead of the notch tip. The effective distance is determined by the point with the minimum stress gradient in the fracture process zone. This approach is successfully used to quantify the constraints of the notch-tip fields for various geometries and loading conditions. Moreover, the proposed T-stress estimation creates a basis for analyzing the crack path under mixed-mode loading from the viewpoint of the two-parameter fracture mechanics.

Nonlinear Dynamic Analysis of an Elastically Restrained Cantilever Tapered Beam

M. Akbarzade, A. Farshidianfar
Ferdowsi University of Mashhad, Mashhad, Iran
Keywords: нелинейные осцилляции, аналитические методы, периодическое решение, nonlinear oscillation, analytical methods, periodic solution

Abstract >>
An analytical simulation of an elastically restrained tapered cantilever beam is performed. Five different analytical methods are applied to solve the dynamic model of the nonlinear oscillation equation. Analytical relationships between the natural frequency and the initial amplitude are obtained. The present solutions are compared with the exact solution, and excellent agreement is noted.

Numerical Study of the Effect of Reinforcing Elements in the Pole Field on the Strength of Non-Spherical Shells under a Pulse Load

Yu. P. Meshcheryakov
Lavrent'ev Institute of Hydrodynamics Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: прочность, несферическая оболочка, численное моделирование, импульсная нагрузка, strength, non-spherical shell, numerical simulation, pulse load

Abstract >>
This paper describes the study of the stress-strain state in the elements of a non-spherical shell of variable thickness arising during pulse action. The effect of the radii of inserts used as reinforcing elements on the magnitude of stresses in the non-spherical bottoms is investigated. The relationship between the stress-strain state in the shell pole and the radius of the inserts is studied. It is shown that the use of an insert of an optimum radius allows creating an equally strong explosion chamber.