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.

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.

A new integral equation approach to elastodynamic homogenization

2008 ◽  
Vol 464 (2094) ◽  
pp. 1461-1482 ◽  
Author(s):  
William J Parnell ◽  
I. David Abrahams
Keyword(s):  
Integral Equation ◽  
Volume Fraction ◽  
Effective Properties ◽  
Order Approximation ◽  
High Volume ◽  
Leading Order ◽  
Cross Sectional ◽  
Integral Equation Approach ◽  
Order Scheme ◽  
Sectional Shape

A new theory of elastodynamic homogenization is proposed, which exploits the integral equation form of Navier's equations and relationships between length scales within composite media. The scheme is introduced by focusing on its leading-order approximation for orthotropic, periodic fibre-reinforced media where fibres have arbitrary cross-sectional shape. The methodology is general but here it is shown for horizontally polarized shear (SH) wave propagation for ease of exposition. The resulting effective properties are shown to possess rich structure in that four terms account separately for the physical detail of the composite (associated with fibre cross-sectional shape, elastic properties, lattice geometry and volume fraction). In particular, the appropriate component of Eshelby's tensor arises naturally in order to deal with the shape of the fibre cross section. Results are plotted for circular fibres and compared with extant methods, including the method of asymptotic homogenization. The leading-order scheme is shown to be in excellent agreement even for relatively high volume fractions.

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 Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

2019 ◽  
Vol 32 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Czesław Szymczak ◽  
Marcin Kujawa
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Torsional Vibration ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Vibration Frequencies ◽  
Cross Sectional ◽  
First Order ◽  
Thin Walled ◽  
Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

Velocity Field and Energy Dissipation in Viscoplastic Flow in Tubes of Non-Circular Cross-Section

2014 ◽  
Author(s):  
Mario F. Letelier ◽  
Dennis A. Siginer ◽  
Felipe Godoy
Keyword(s):  
Energy Dissipation ◽  
Velocity Field ◽  
Yield Stress ◽  
Cross Section ◽  
Mechanical Energy ◽  
Longitudinal Velocity ◽  
Circular Cross Section ◽  
Viscoplastic Flow ◽  
Entire Cross Section ◽  
Cross Sectional

An analytical method for determining the velocity field, shear stress and energy dissipation in viscoplastic flow in non-circular straight tubes is presented. Bingham’s model of fluid is used for the case of tubes with several cross-sectional contours that can be arbitrarily chosen through a shape factor imposed in the solution for the longitudinal velocity. The analysis is extended to steady flow in tubes in which the cross-section contour exhibits sharp corners. In these cases three flow zones are distinguished: stagnant, non-zero deformation, and plug zones. The method provides the expressions for determining the boundaries and characteristics of those three zones for a wide variety of cross-section shapes. In particular the dynamics of plug-zones for large values of the yield stress and for contours that markedly differ from circumferences is analyzed. Energy dissipation is determined throughout the entire cross-section, so that the effect of shape on mechanical energy loss is assessed in terms of the yield stress and viscosity of the fluid. Some general expressions that help understand energy dissipation mechanisms are derived by using natural coordinates for the velocity field and related variables. These results draw on several recent works from other researchers and the present authors, which have highlighted the significant difficulty of determining the zones of zero deformation in viscoplastic flow when the related solid boundaries are not elementary.

scholarly journals Cross-Sectional Geometry and the Intermetallics Structure in a High Pressure Die Cast Mg-Al Alloy

2010 ◽  
Vol 638-642 ◽  
pp. 1579-1584 ◽  
Author(s):  
A.V. Nagasekhar ◽  
Carlos H. Cáceres ◽  
Mark Easton
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Al Alloy ◽  
Cross Sectional ◽  
The Core ◽  
Die Cast ◽  
Increased Strength ◽  
Scanning Electron

Specimens of rectangular and circular cross section of a Mg-9Al binary alloy have been tensile tested and the cross section of undeformed specimens examined using scanning electron microscopy. The rectangular cross sections showed three scales in the cellular intermetallics network: coarse at the core, fine at the surface and very fine at the corners, whereas the circular ones showed only two, coarse at the core and fine at the surface. The specimens of rectangular cross section exhibited higher yield strength in comparison to the circular ones. Possible reasons for the observed increased strength of the rectangular sections are discussed.

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.

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation

2005 ◽  
Vol 363 (1832) ◽  
pp. 1551-1571 ◽  
Author(s):  
Shiva P Pudasaini ◽  
Yongqi Wang ◽  
Kolumban Hutter
Keyword(s):  
Numerical Simulation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Mass ◽  
Governing Equations ◽  
Cross Sectional ◽  
Variation Diminishing ◽  
Cross Sectional Profile ◽  
Sectional Profile

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495 , 193–208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.

On Thermal Interface Materials With Polydisperse Fillers: Packing Algorithm and Effective Properties

2018 ◽  
Author(s):  
Piyas Chowdhury ◽  
Kamal Sikka ◽  
Anuja De Silva ◽  
Indira Seshadri
Keyword(s):  
Thermal Conductivity ◽  
Elastic Modulus ◽  
Volume Fraction ◽  
Effective Properties ◽  
Material Design ◽  
High Volume ◽  
Thermal Interface Materials ◽  
Thermal Interface ◽  
Packing Algorithm ◽  
Interface Materials

Thermal interface materials (TIMs), which transmit heat from semiconductor chips, are indispensable in today’s microelectronic devices. Designing superior TIMs for increasingly demanding integration requirements, especially for server-level hardware with high power density chips, remains a particularly coveted yet challenging objective. This is because achieving desired degrees of thermal-mechanical attributes (e.g. high thermal conductivity, low elastic modulus, low viscosity) poses contradictory challenges. For instance, embedding thermally conductive fillers (e.g. metallic particles) into a compliant yet considerably less conductive matrix (e.g. polymer) enhances heat transmission, however at the expense of overall compliance. This leads to extensive trial-and-error based empirical approaches for optimal material design. Specifically, high volume fraction filler loading, role of filler size distribution, mixing of various filler types are some outstanding issues that need further clarification. To that end, we first forward a generic packing algorithm with ability to simulate a variety of filler types and distributions. Secondly, by modeling the physics of heat/force flux, we predict effective thermal conductivity, elastic modulus and viscosity for various packing cases.

The Structure and Function of the Basement Membrane Muscle System in Amphiporus lactifloreus (Nemertea)

1952 ◽  
Vol s3-93 (21) ◽  
pp. 1-15
Author(s):  
J. B. COWEY
Keyword(s):  
Basement Membrane ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Minimum Length ◽  
Muscle Fibres ◽  
Body Volume ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Sectional Shape

The body wall of A. lactifloreus has the following structure from the outside inwards. (i) A basement membrane of five to six layers immediately underlying the epithelium. Each layer consists of right-hand and left-hand geodesic fibres making a lattice, whose constituent parallelograms have a side length of from 5 to 6µ. The fibres are attached to one another where they cross; so there can be no slipping relative to one another. (ii) A layer of circular muscle-fibres running round the animal containing two systems of argyrophil fibres--one of fibres at intervals of 10µ. running parallel to the muscle-fibres and the other of fibres running radially through the layer from the basement membrane to the myoseptum. (iii) A myoseptum which is identical in structure with a single layer of the basement membrane (iv) A layer of longitudinal muscle, whose fibres are arranged in layers on each side of a series of longitudinal radial membranes. Membranes identical in structure with the basement membrane invest the nerve cords, the gut, the gonads, and the proboscis. The interrelations of argyrophil and muscle-fibres in the muscle layers is described and their functioning discussed. The system of inextensible geodesic fibres is analysed from a functional standpoint. The maximum volume enclosed by a cylindrical element (cross-section circular), of such a length that the geodesic makes one complete turn round it, varies with the value of the angle θ between the fibres and the longitudinal axis. When θ is 0° the volume is zero; it increases to a maximum when θ is 54° 44' and decreases again to zero when θ is 90°. The length of the element under these conditions varies from zero when θ is 90° to a maximum (the length of one turn of the geodesic) when θ is 0°. The body-volume of the worm is constant. Thus it has a maximum and minimum length when its cross-section is circular, and at any length between these values its cross-section becomes more or less elliptical. It is maximally elliptical when θ is 54° 44', i.e. when the volume the system could contain, at circular cross-section, is maximal. From measurements of the ratio of major to minor axes of this maximally elliptical cross-section, the maximum and minimum lengths of the worm relative to the relaxed length and values of θ at maximum and minimum length are calculated. The worm is actually unable to contract till its cross-section is circular; but measurements of its cross-sectional shape at the minimum length it can attain, permit calculation of the theoretical length and value of θ for this cross-sectional shape. Calculated values of length and the angle 6 agree well with the directly observed values.

Sign in / Sign up

Export Citation Format

Share Document