scholarly journals Refinement of the Maxwell formula for a composite reinforced by circular cross-section fibres. Part II: using Padé approximants

2020 ◽  
Vol 231 (12) ◽  
pp. 5145-5157
Author(s):  
Igor I. Andrianov ◽  
Jan Awrejcewicz ◽  
Galina A. Starushenko ◽  
Vladimir A. Gabrinets
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
The Novel ◽  
High Contrast ◽  
Asymptotic Results ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity

Abstract The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repeated cell problem the Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S. Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow, especially for nondilute high-contrast composite materials. For improving this drawback we used Padé approximations for various forms of SAP solutions with the following additive matching of obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and convenient form. They can be used even for a volume fraction of inclusion very near the physically possible maximum value as well as for high-contrast composite constituents. The results are confirmed by comparison with known numerical and asymptotic results.

scholarly journals Refinement of the Maxwell formula for composite reinforced by circular cross-section fibers. Part I: using the Schwarz alternating method

2020 ◽  
Vol 231 (12) ◽  
pp. 4971-4990 ◽  
Author(s):  
Igor I. Andrianov ◽  
Jan Awrejcewicz ◽  
Galina A. Starushenko ◽  
Vladimir A. Gabrinets
Keyword(s):  
Cross Section ◽  
Effective Properties ◽  
Circular Cross Section ◽  
Principal Term ◽  
The Novel ◽  
Asymptotic Results ◽  
Asymptotic Homogenization ◽  
Schwarz Alternating Method ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity

Abstract The effective properties of the fiber-reinforced composite materials with fibers of circular cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For analytical solution of the periodically repeated cell problem, the Schwarz alternating process is employed. The principal term of the refined formula coincides with the classical Maxwell formula. On the other hand, the refined formula can be used far beyond the area of applicability of the Maxwell formula. It can be used for dilute and non-dilute composites. It is confirmed by comparison with known numerical and asymptotic results.

scholarly journals An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170080 ◽  
Author(s):  
Duncan Joyce ◽  
William J. Parnell ◽  
Raphaël C. Assier ◽  
I. David Abrahams
Keyword(s):  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
Rational Functions ◽  
High Volume ◽  
Cross Sectional ◽  
Antiplane Elasticity ◽  
Unidirectional Fibre ◽  
Explicit Expressions

In Parnell & Abrahams (2008 Proc. R. Soc. A 464 , 1461–1482. ( doi:10.1098/rspa.2007.0254 )), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme.

Refinement of the Maxwell Formula for Fiber-Reinforced Composites

2019 ◽  
Vol 11 (01) ◽  
pp. 1950001
Author(s):  
Alexander Kalamkarov ◽  
Igor Andrianov ◽  
Galina Starushenko
Keyword(s):  
Thermal Conductivity ◽  
Physical Properties ◽  
Effective Properties ◽  
Principal Term ◽  
The Novel ◽  
Fiber Reinforced ◽  
Reinforced Composite ◽  
Coefficient Of Thermal Conductivity ◽  
Shape Perturbation ◽  
Limiting Values

The effective properties of the fiber-reinforced composite materials with fibers of square cross-section are investigated. The novel formula for the effective coefficient of thermal conductivity refining the classical Maxwell formula (MF) is derived. The methods of asymptotic homogenization, boundary shape perturbation and Schwarz alternating process are applied. It is shown that the principal term of the asymptotic expansion of the refined formula in powers of small size of inclusions coincides with the classical MF. The corrections to the MF are obtained for different values of geometrical and physical properties of the constituents of the composite material. The analytical and numerical analyses are carried out and illustrated graphically. In particular, the derived refined formula and the MF are compared for the limiting values of the geometric dimensions and physical properties of the composite. It is shown that the refined formula is applicable for the inclusions with any conductivity in the entire range of the geometric sizes of inclusions, including the limiting cases of inclusions with zero thermal conductivity and maximally large inclusions.

scholarly journals Eco-friendly technology of manufacturing complex products made of composites

2019 ◽  
Vol 140 ◽  
pp. 02004
Author(s):  
Aleksey Ignatov ◽  
Rustam Subkhankulov
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Manufacturing Process ◽  
Volume Fraction ◽  
Turbine Blades ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Technological Parameters ◽  
Technological Support ◽  
The Impact

Numerous studies in application of modern composite materials show that their advantages can be successfully implemented in manufacturing «smart» products. This study proposes an improved technological method of manufacturing multilayer environmentally friendly products with a variable cross section, which allows us to expand the possibilities of using modern polymer composite materials (PCM). The technology allows manufacturing products of the most complex geometric shapes, such as wind turbine blades. The aim of the study is the technological support of engineering production in the manufacture of multilayer products of variable cross section made from PCM. Scientific novelty consists in identifying the patterns of implementation and management of the manufacturing process of multilayer products of variable cross-section, and establishing the influence of structural and technological parameters of the manufacturing process on their operational characteristics. The relationship between the pressure of a hot directed air stream and the volume fraction of pores in the hardened material of a multilayer composite product with a variable cross section during layer-by-layer application is investigated. During the study, fundamental and applied principles of mechanical engineering technology, material resistance, adhesion theory, mathematical statistics tools and software were used to process the results of the experiment. Based on the results of laboratory studies, a methodology has been developed for effective prediction of pore content in the manufacturing of composite products. The introduction of the presented technology and the corresponding original methodology into production will reduce the complexity and energy costs of manufacturing composite products, improve their quality and reduce the impact of toxic components from composite materials on workers.

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

scholarly journals The investigation of the cavitation processes in the radial labyrinth pump

2018 ◽  
Vol 8 (1) ◽  
pp. 322-328
Author(s):  
Moloshnyi Oleksandr ◽  
Szulc Przemyslaw
Keyword(s):  
Numerical Simulation ◽  
Cross Section ◽  
Volume Fraction ◽  
Mechanical Energy ◽  
Circular Cross Section ◽  
Back Side ◽  
Numerical Investigations ◽  
Numerical Research ◽  
The Moment ◽  
Velocity Pressure

Abstract The paper concerns the analysis of the cavitation processes in the flow passages of the radial labyrinth pump. The object of the analysis contains the active (moving) and the passive (stationary) discs with straight channels trajectory and semi-circular cross-section. The conversion of the mechanical energy into hydraulic based on the exchange of the momentum between the liquid remaining in the moving and the stationary areas of the discs as well as on the centrifugal increase of the moment of momentum. The analysis of the cavitation processes was realized by the experimental research and the numerical simulation. In the article, the comparison of the cavitation characteristics was carried out. The numerical simulation had given similar results to the experimental one, the process of the cavitation was visualized. Furthermore, numerical investigations helped to describe the cavitation development. The results of the numerical research such as the distributions of the velocity, pressure and vapor volume fraction in the passages were presented. At first, cavitation starts on the back side and on the top of the wall between channels of the active disc. Further, the cavitation areas are growing along the axis of the channels. Eventually, they separation was observed and vortices of the vapour-gas mixture in the middle of the channels were formed. This phenomenon is so-called super cavitation vortices.

scholarly journals Thermomechanical nonlinear stability of pressure-loaded CNT-reinforced composite doubly curved panels resting on elastic foundations

2019 ◽  
Vol 8 (1) ◽  
pp. 582-596 ◽  
Author(s):  
Le Thi Nhu Trang ◽  
Hoang Van Tung
Keyword(s):  
Nonlinear Stability ◽  
Volume Fraction ◽  
Effective Properties ◽  
Geometrical Nonlinearity ◽  
Nonlinear Load ◽  
Elastic Foundations ◽  
Thermal Environments ◽  
Reinforced Composite ◽  
Distribution Type ◽  
Curved Panels

Abstract Nonlinear stability of nanocomposite spherical and cylindrical panels reinforced by carbon nanotubes (CNTs), resting on elastic foundations and subjected to uniform external pressure in thermal environments is investigated in this paper. CNTs are embedded into matrix phase through uniform distribution (UD) or functionally graded (FG) distribution, and effective properties of CNT-reinforced composite are estimated through an extended rule of mixture. Governing equations are based on classical shell theory taking geometrical nonlinearity, initial geometrical imperfection and panel-foundation interaction into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain nonlinear load-deflection relation. Numerical examples show the effects of volume fraction and distribution type of CNTs, in-plane condition of edges, curvature of panel, thermal environments, elastic foundations and imperfection size on the nonlinear response and snap-through instability of the curved panels. The present study reveals that efficiency of CNT distribution type depends on curvature of panel and in-plane behavior of boundary edges, and bifurcation type buckling response of pressure-loaded panels may occur at elevated temperature.

CHAOTIC VIBRATIONS OF CLOSED CYLINDRICAL SHELLS IN A TEMPERATURE FIELD

2008 ◽  
Vol 18 (05) ◽  
pp. 1515-1529 ◽  
Author(s):  
A. V. KRYSKO ◽  
J. AWREJCEWICZ ◽  
E. S. KUZNETSOVA ◽  
V. A. KRYSKO
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Novel ◽  
Fourier Methods ◽  
Constant Stiffness ◽  
Chaotic Vibrations ◽  
Qualitative Changes ◽  
Shell Dynamics

A closed cylindrical shell with circular cross-section having constant stiffness and density and subjected to sign changeable loading and embedded into a temperature field is analyzed. Both Bubnov–Galerkin (with a higher approximation) and Fourier methods are applied to solve the derived nonlinear nondimensional partial differential equations. Among others, the novel scenario of transition from shell harmonic to chaotic vibrations via the collapse of quasi-periodic vibrations with one independent frequency and Hopf bifurcation is detected, illustrated and discussed. In addition, it is shown how for various intensities of the temperature field (including its absence) the increase of the loading yields qualitative changes in the investigated shell dynamics, and how chaotic zones are transmitted into periodic ones and vice versa.

Numerical Investigation of Turbulent Magnetic Nanofluid Flow inside Straight Channels

2016 ◽  
Vol 819 ◽  
pp. 382-391 ◽  
Author(s):  
Nor Azwadi Che Sidik ◽  
Mohammed Raad Abdulwahab
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Section ◽  
Volume Fraction ◽  
Numerical Study ◽  
Circular Cross Section ◽  
Average Diameter ◽  
Turbulent Regime ◽  
Reynolds Number Increase ◽  
Number Increase

A numerical study using computational fluid dynamics method with an approach of single phase has been presented in order to determine the effects of the concentration of the nanoparticles and flow rate on the convective heat transfer and friction factor in turbulent regime flowing through three different straight channels (straight, circular and triangular) with different Reynolds number (5000 ≤ Re ≤ 20000) using constant applied heat flux. The nanofluid was used consist of Fe3O4 magnetic nanoparticles with average diameter of (13nm) dispersed in water with four volume fraction (0, 0.2, 0.4, 0.6%). The results revealed that as volume fraction and Reynolds number increase Nusselt number increase and the heat transfer rate in circular cross section tube is better than that in square and triangular cross section channels.

Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure

2016 ◽  
Vol 07 (03) ◽  
pp. 1650006 ◽  
Author(s):  
Alexander L. Kalamkarov ◽  
Igor V. Andrianov ◽  
Pedro M. C. L. Pacheco ◽  
Marcelo A. Savi ◽  
Galina A. Starushenko
Keyword(s):  
Thermal Conductivity ◽  
Composite Materials ◽  
Asymptotic Analysis ◽  
Circular Cross Section ◽  
Homogenization Method ◽  
Hexagonal Structure ◽  
Unit Cell ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.

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