research & reviews: journal of physics vol 7 issue 3

(RRJoPHY)

ISSN 2278-2265 (Online)

ISSN 2347-9973 (Print)

September–December 2016

Research & Reviews Journal of Physics

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STM JOURNALS

1. A Review Study of Advances in the Science and Technology of Carbon Nanotubes Sufiyan Nudrat, Yadav Archana, Saeed S. Hasan 1

2. Stress Analysis of Rotating Cylindrical Pressure Vessel of Functionally Graded Material by Element Based Material Gradation Amit Kumar Thawait 7

3. Chemical Potential of Water from Monte Carlo Simulation: The Fundamentals H. Bashir, Y. Wang, A.J. Abbas 16

4. Strength and Stability of Copper in (100) Loading using EAM Vikram Singh, Gitam Singh 28

5. Free Vibration of Cross-ply Composite Plates by a High-Order Shear Deformable Finite Element Mihir Chandra Manna, Mainak Manna 36

6. On the Role of Surface Roughness in Ankle Joint Replacements Puneet Katyal 48

ContentsResearch & Reviews : Journal of Physics

RRJoPHY (2016) 1-6 © STM Journals 2016. All Rights Reserved Page 1

Research and Reviews: Journal of Physics ISSN: 2278–2265(online), ISSN: 2347-9973(print)

Volume 5, Issue 3 www.stmjournals.com

A Review Study of Advances in the Science and

Technology of Carbon Nanotubes

Sufiyan Nudrat, Yadav Archana*, Saeed S. Hasan Department of Electronics and Communication Engineering, Integral University, Lucknow,

Uttar Pradesh, India

Abstract In this paper, we are presenting a brief literature review of present and future carbon nano tubes applications in different fields. Carbon nanotubes are the allotropes of carbon present as wires of pure carbon with nanometer diameters and lengths of many microns. There are several carbon nanotubes applications, which take full advantage of CNTs unique properties of mechanical strength, electrical and thermal conductivity. Many developments on fabrication of carbon nanotubes (CNTs) have been made to fulfill the demands on better performance including response time and higher sensitivity. In the very near future, carbon nanotubes will play a significant role in a wide range of commercial applications. Keywords: Carbon nanotube, electronics, current, graphene

INTRODUCTION Carbon Nanotubes

Carbon nanotubes (CNTs) are the recently discovered allotrope of carbon, which take the form of cylindrical carbon molecules and have novel properties that make them potentially useful in a wide variety of applications in nanotechnology, electronics, optics, and other fields of material science. They exhibit extraordinary strength and unique electrical properties and are efficient conductors of heat [1]. Carbon nanotubes are wires of pure carbon with nanometer diameters and lengths of many microns. The carbon nanotubes have a unique property called chirality, an emergence of the vertically twisting (Figure 1).

Carbon nanotubes types are categorized into two types: single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs). A single-walled carbon nanotube (SWNT) may be thought of as a single atomic layer thick sheet of graphite (called graphene) rolled into

a seamless cylinder. Multi-walled carbon nanotubes (MWNT) consist of several concentric nanotube shells. Graphene is a zero-gap semiconductor; for most directions in the graphene sheet, there is a bandgap, and electrons are not free to flow along those directions unless extra energy is given. However, in certain special directions, graphene is metallic, and electrons flow easily along those directions. This property is not obvious in bulk graphite, since there is always a conducting metallic path, which can connect any two points, and the graphite conducts electricity. When graphene is rolled up to make the nanotube, a special direction is selected, the direction along the axis of the nanotube. Single-walled carbon nanotubes can be formed in three different designs: armchair, chiral, and zigzag. The design depends on the way the graphene is wrapped into a cylinder. For example, imagine rolling a sheet of paper from its corner, which can be considered one design, and a different design can be formed by rolling the paper from its edge. There are


Research and Reviews: Journal of Physics ISSN: 2278–2265(online), ISSN: 2347-9973(print)


Stress Analysis of Rotating Cylindrical Pressure Vessel of

Functionally Graded Material by Element Based Material

Gradation

Amit Kumar Thawait* Department of Mechanical Engineering, Shri Shankaracharya Group of Institutes, Bhilai,

Chhattisgarh, India

Abstract The present study aims at the elastic analysis of rotating cylindrical pressure vessels made of functionally graded materials (FGMs), by element based gradation. Material properties of the shells vary in radial direction according to exponential distribution law. Ceramic-metal and metal-ceramic, both the types of FGM are considered and the effects of gradation of material properties on stress and deformation behavior of the shells are investigated. Further, a comparison of deformation and stresses for different values of thickness parameters in ceramic-metal and metal-ceramic shell is made. Results obtained show that there is a significant variation in stresses and deformation behavior of the FGM shells for different values of thickness parameter. Keywords: Functionally graded material (FGM), elastic stress analysis, cylindrical pressure vessel, rotating shell, element based material gradation

INTRODUCTION Functionally graded materials (FGMs) are special composite materials that have continuous and smooth spatial variations of physical and mechanical properties. The gradation of material properties in FGMs is achieved by varying the volume fractions of the constituents. Functionally graded shells are widely used in space vehicles, aircrafts, nuclear power plants and many other engineering applications [1]. The total stresses due to internal pressure and centrifugal load have effects on their strength and safety. Thus, control and optimization of total stresses and displacement fields is an important task, which is achieved by varying the material property in FGM pressure vessels. Many researchers have worked on elastic analysis of rotating conical shells, cylindrical shells, disks etc. by analytical as well as approximate methods such as finite element method. Tutuncu et al. reported closed form solution for stresses and displacements in functionally graded cylindrical and spherical vessels subjected to internal pressure, using the infinitesimal theory of elasticity [2]. The

material stiffness obeying a power law is assumed to vary through the wall thickness and Poisson’s ratio is assumed constant. Abrinia et al. have analyzed FGM thick cylinders under combined pressure and temperature loading [3]. Nejad et al. reported work on stresses analysis in isotropic rotating thick-walled cylindrical pressure vessels made of functionally graded materials [4]. The pressure, inner radius and outer radius are considered constant. Material properties are considered as a function of the radius of the cylinder to a power law function and the Poisson’s ratio is assumed as constant. Finite element method based on Rayleigh-Ritz energy formulation is applied to obtain the elastic behavior of functionally graded thick truncated conical shell by Asemi et al. [5]. Using this method, the effects of semi-vertex angle of the cone and the power law exponent on distribution of different types of displacements and stresses are considered. In a recent work, Sadrabadi et al. studied thick walled cylindrical tanks or tubes made of functionally graded material, under internal pressure and temperature gradient [6].


Research & Reviews: Journal of Physics ISSN: 2278-2265(online), ISSN: 2347-9973(print)


Chemical Potential of Water from Monte Carlo

Simulation: The Fundamentals

H. Bashir1,*, Y. Wang

2, A.J. Abbas

1

1Gas Engineering Division, School of Science, Computing and Engineering, University of Salford, Manchester, UK

2Civil Engineering Department, School of Science, Computing and Engineering, University of Salford, Manchester, England

Abstract

Monte Carlo simulation was conducted using the Towhee software to calculate the chemical potential of water. The implementation is made simple and provides a clear demonstration of the concept of Monte Carlo simulation. This paper is targeted to new researchers interested in molecular modelling and can be used as a guide for beginners in the art of molecular modelling, specifically Monte Carlo simulation. The purpose of carrying out the calculation of the water chemical potential is that the value obtained can be implemented in the Grand Canonical (𝜇𝑉𝑇) ensemble or Gibbs ensemble for further research. The result obtained from the Monte Carlo simulation for the chemical potential of water are in agreement with published water potential values, therefore validating the SPC water model and MCCCS Towhee software [1]. Keywords: Monte Carlo simulation, molecular modelling, water chemical potential

INTRODUCTION Molecular modelling is a set of techniques, which predict the properties of matter at the molecular level, which in turn can be used to determine macroscopic data. These include structural, thermodynamics and thermochemical properties [2]. Model systems, which are representative of the bulk system of interest, are studied. The efficiency of these models lies in the fact that a small number of particles can be representative of the bulk system [3]. These methods are now becoming innovative tools used by researchers due to the advancement and mass production of computers, which have made them accessible. It is now possible to run computer simulation using both, desktops and laptops. Soft wares are now available that can be used for visualisation, with a ready-made force field and data banks of ready-made models of molecules for running a simulation of choice. Furthermore, molecular modelling is now being used more frequently to construct virtual experiments in cases where controlled laboratory experiments are difficult, too dangerous, impossible or expensive to perform

[4, 5]. They are also used to check the reliability of analytical methods. The vision for molecular modelling was conceived long ago even before the advent of computers as reported by Jabbarzadeh et al. [6]. They pointed out that Laplace described the idea as “Given for one instant an intelligent being which could comprehend all the forces by which, nature is animated and the respective situation of the beings who compose it, an intelligence sufficiently vast to submit these data to analysis; it would embrace in the same formula, the movements of the greatest bodies of the universe and those of the lightest atoms, nothing would be uncertain and the future, as the past, would be present in its eyes”. Rapport points out that a philosophical concept by Greek theorist in the 5th century BC, in which the universe is believed to be composed of tiny indivisible particles, which are the basis for the foundation of molecular dynamics [7]. The earliest work in atomic scale simulation was accomplished by Metropolis et al. [8]. This work was fundamental to the so-called Monte Carlo (MC) method. Early models were idealised




Strength and Stability of Copper in (100)

Loading using EAM

Vikram Singh1,*, Gitam Singh

2

1Department of Physics, Agra College, Agra, Uttar Pradesh, India 2Department of Physics, Raja Balwant Singh College, Agra, Uttar Pradesh, India

Abstract

Numerical computations of strength and stability of copper in case of (100) loading are carried out by taking new embedded atom method (EAM). New EAM contains three adjustable parameters and four unknown parameters, which have calculated using experimental values of lattice constant, second order elastic constants. Computed value of theoretical strength of Cu is same order in magnitude of the results of other investigators. Second unstable phase found in compression. Keywords: Strength, stability, EAM, stress

INTRODUCTION Calculations of theoretical strength of cubic metals have been active field in research. Many workers have been calculated theoretical strength of cubic metals in various modes of deformations by taking various types of interaction between atoms [1–16]. The ideal (theoretical) strength was originally defined as stress or strain at which perfect crystal lattice became mechanically unstable with respect to arbitrary homogeneous infinitesimal deformation. Many applications of this problem are presents in literature. Cerney and coworkers studied mechanical stability of cubic metals (Ni, Ir, Fe, Cr) in hydrostatic loading and uniaxial loading using simulation technique [17–23]. Based on Born-Hill-Milstein elastic stability theory Ho et al. investigates the effect of transverse loading on ideal tensile strength of six FCC materials using molecular statics and density function theory simulation [24]. Recently Mouhat et al. gives necessary and sufficient stability conditions for noncubic and lower symmetry classes crystals and Ogata et al. gives review article on this topic [25, 26]. Recently by taking embedded atom method (EAM), many workers have estimated theoretical strength and stability of cubic metal in various loading conditions [1–5]. In this paper, we developed new EAM which contain three adjustable parameters and four unknown parameters. Potential parameters of this EAM

have been calculated using experimental values of lattice constant and second order elastic constants as an input data. We have estimated strength of Cu in (100) loading using this analytic EAM. EMBEDDED ATOM METHOD The original method was subsequently expended by Bakes to treat solids with highly directional distributions of valance electron densities that is, covalent bonding, allowing for much more wider scope of applications [27]. The fundamentals of the method have been discussed in the literature in detail (see for example review [28]), so only some important aspects necessary for discussion of the present work will be given here. In the EAM format, the cohesive energy per atom Ea of a homogeneous monatomic crystal can be written as

𝐸𝑎 = F (ρ) + 1

2∑ ∅(𝑟𝑖𝑗) (1)

With 𝜌 = ∑ 𝑓(𝑟𝑖𝑗) (2)

where, F() is the embedded function, is the total electron density at the reference atomic site, (rij) is the electron density function, (rij) is the pair potential function, and rij is the distance between atoms i and j. From review of literature, we conclude that many type of functions have been used for (r), (r) and

RRJoPHY (2016) 36-47© STM Journals 2016. All Rights Reserved Page 36



Free Vibration of Cross-ply Composite Plates by a High-

Order Shear Deformable Finite Element

Mihir Chandra Manna

1,*, Mainak Manna

2

1Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, India

2Department of Computer Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, India

Abstract

Free vibration analysis of composite rectangular plates with different thickness ratios, different boundary conditions and different aspect ratios has been investigated using a high-order shear flexible triangular plate element. The first order shear deformation theory (FOSDT) is used to include the effect of transverse shear deformation. The element has eighteen nodes on the sides and seven internal nodes. Element geometry is expressed in terms of three linear shape functions of area coordinates. The formulation is displacement type. The element has seventy-one degrees of freedom, which has been reduced to fifty-seven degrees of freedom by Guyan reduction scheme for the degrees of freedom associated with the internal nodes. Rotary inertia has been included in the consistent mass matrix. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Keywords: Shear deformation, Guyan reduction scheme, rotary inertia, consistent mass matrix

INTRODUCTION Thick and thin isotropic and composite plates and shells have wide applications in ships, aircrafts, bridges, etc. A thorough study of their dynamic behavior and characteristics is essential to assess and use their full potentials. Different techniques like RBF-pseudo-spectral method, differential quadrature method, boundary characteristic orthogonal polynomials and pseudo-spectral method have been used in recent years [1–4]. More recently Kansa’s nonsymmetric radial basis function (RBF) collocation method was applied by Ferreira for free vibration analysis of Timoshenko beams, Mindlin plates and composite plates [5, 6]. Other methods which have been very recently used for the aforementioned purposes are meshless method and discrete singular convolution (DSC) method [7, 8]. Shufrin et al. have investigated the free vibration of rectangular thick plates with variable thickness and different boundary conditions by using the extended Kantorovich method [9]. Kang et al.

have proposed a practical analytical method for the free vibration analysis of a simply supported rectangular plate with unidirectional arbitrary thickness variation [10]. But, since early sixties, Finite Element Method (FEM) has been proved to be more versatile tool in engineering fields [11, 12]. Plate bending is one of the first problems where the application of finite element was done in the early sixties. Initial attempts were made for bending and free vibration analyses with Kirchoff’s hypothesis which showed a number of problems. These are mostly associated with the satisfaction of normal slope continuity on the interfaces between various elements. Above-mentioned slope continuity problem has been eliminated by applying well-known Reissner-Mindlin’s hypothesis for thick plates. In Reissner-Mindlin’s hypothesis the transverse displacement (w) and rotations of normal (x and y) are expressed as independent field variables. A large number of published works on plate vibration are available as may be seen by inspection of the




On the Role of Surface Roughness in Ankle Joint

Replacements

Puneet Katyal* Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology,

Hisar, Haryana, India

Abstract Research efforts in biomechanics have geared towards the long-term effectiveness and survival of total joint replacements, because of osteoarthritis causes loosening, instability, wear of articulating components and finally loss of function. Surface roughness of articulating components significantly influences their tribological behavior. Other factors affecting the wear of articulating surfaces include material and geometrical properties. In this work, the human ankle joint is represented by an equivalent ellipsoid-on-plane model to study the effect of surface roughness on the pressure profile, film shape, minimum film thickness, lambda ratio ( λ ) and coefficient of friction in total joint replacements under steady-state conditions. The main purpose here is to promote fluid film lubrication and therefore, reduce wear in ankle joint replacements. Keywords: EHL, Surface roughness, film thickness

INTRODUCTION In recent years, total joint replacements for osteoarthritis joints have received considerable attention as an effective alternative. However, these artificial joints suffer from almost unavoidable complications due to loosening, instability and wear of articulating components. This has inspired several researchers to develop new and improved implant designs over the last few decades. The focus of experimental and theoretical research investigations pertaining to biomechanics has shifted to long-term effectiveness and survival of total joint replacements. It is well-known that mathematical modeling of a synovial joint problem serves not only to predict the performance parameters, which are difficult to measure experimentally, but also to simulate the system behavior under varying physiological conditions. The wear of articulating components—one of the major causes of synovial joint failure—can be reduced significantly by improving the lubrication characteristics. Therefore, lubrication modeling is an effective tool employed in research projects aimed at enhancing the clinical performance and life expectancy of artificial human joints. Most of the theoretical studies pertaining to artificial human joints focus on hip and knee

joints. As a comprehensive review of the subject matter is beyond the scope of this paper, some of the pertinent papers are cited in the following text. Goenka formulated and solved Reynolds equation in spherical coordinates by means of finite element approach [1]. This work established the basis to investigate lubrication of soft-on-hard couples with a realistic ball-in-socket scheme. Kothari et al. and Cheng et al. studied the influence of nonspherical bearing surfaces under steady-state conditions [2, 3]. In a later work, Jin and Dowson presented a full transient hydrodynamic lubrication analysis using more realistic working conditions [4]. Wang and Jin investigated the effects of the cup inclination angle and the combined flexion–extension and internal–external rotation on the lubrication characteristics pertaining to artificial hip joints [5]. Jalali-Vahid et al. employed elastohydrodynamic lubrication (EHL) model for ball-in-socket configuration to predict the lubricant film thickness in natural and artificial hip joints [6–9]. Moreover, numerical simulations carried out for ball-in-socket and ball-on-plane

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