Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
13
5
2015
GENERAL INTEGRAL EQUATIONS OF STOKES FLOW THROUGH THE RANDOM STRUCTURE POROUS MEDIA
375-392
10.1615/IntJMultCompEng.2015013278
Valeriy A.
Buryachenko
Civil Engineering Department, University of Akron, Akron, Ohio 44325-3901, USA and Micromechanics and Composites LLC, 2520 Hingham Lane, Dayton, Ohio 45202, USA
porous media
boundary integral methods
Stokesian dynamics
One considers a slow linear flow through a fixed random bed of rigid particles. The general integral equations (GIEs) connecting the fields of velocities and pressures of fluid in a point being considered and the fields in the surrounding points are obtained for the random (statistically homogeneous and inhomogeneous, so-called graded) structures containing the particles of arbitrary shape and orientation. The new GIEs are presented in a general form of perturbations introduced by the heterogeneities. The mentioned perturbations can be found by any available numerical method which has advantages and disadvantages; if it is crucial for the analyst to be aware of their range of applications. The method of obtaining GIEs is based on a centering procedure of subtraction from both sides of a new initial integral equation, their statistical averages obtained without any auxiliary asymptotic assumptions, which are exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs and establishes an advantage with the known GIEs.
DYNAMIC CHARACTERISTICS OF SINGLE-LAYERED GRAPHENE SHEETS DUE TO ATOMIC VACANCY DEFECT USING MULTISCALE ANALYSIS TECHNIQUE INCORPORATING TERSOFF-BRENNER POTENTIAL
393-412
10.1615/IntJMultCompEng.2015013313
Sachin O.
Gajbhiye
Department of Mechanical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
S. P.
Singh
Department of Mechanical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
multiscale analysis
atomic vacancy
graphene sheet
Tersoff-Brenner potential
molecular dynamics
atomistic finite element method
This paper deals with the eigenvalues extraction and steady-state forced vibration response of single-layered graphene sheets (SLGSs) with and without atomic vacancy defect using atomistic finite element method. The multi-body interatomic TersoffBrenner potential is used to represent the energy between two adjacent carbon atoms. Based on the Tersoff-Brenner potential, a new set of force constant parameters is established for graphene sheet, and the equivalent geometric and elastic properties of the space frame element to represent carboncarbon bond are derived which are consistent with the material constitutive relations. Different values of aspect ratio and contours of SLGS are considered along with clamped, bridged, and cantilevered boundary conditions. A computational sine sweep test is carried out on the atomic structure of SLGSs with and without atomic vacancy defect within the frequency range of 0 to 10 THz. The vibration characteristics of SLGSs are also investigated under an impulse excitation. The response of SLGSs to the harmonic and impulse load over an applied frequency range is calculated. The response of SLGSs with an atomic vacancy defect is also compared with that of without defect to study its effect on the vibration characteristics. The results have been validated using molecular dynamics simulation and with those available in the literature.
A CONTINUUM MECHANICAL SURROGATE MODEL FOR ATOMIC BEAM STRUCTURES
413-442
10.1615/IntJMultCompEng.2015013568
Marcus G.
Schmidt
AICES Graduate School, RWTH Aachen University, Aachen, Germany
Ahmed E.
Ismail
AICES Graduate School, RWTH Aachen University, Aachen, Germany; Aachener Verfahrenstechnik: Molecular Simulations and Transformations, Faculty of Mechanical Engineering, RWTH Aachen University, Aachen, Germany
Roger A.
Sauer
AICES Graduate School, RWTH Aachen University, Aachen, Germany
geometrically exact beams
molecular dynamics
multiscale
constitutive models
contact mechanics
Starting from a fully atomistic system, we outline a general approach to obtain an approximate continuum surrogate model incorporating specific kinematic state variables. The continuum mechanical system is furnished with a hyperelastic material model. We then adapt the procedure to slender structures with beam-like character, such as silicon nanowires or carbon nanotubes. The surrogate model can be described as a geometrically exact beam, which can be treated numerically using finite elements. Based on molecular dynamics simulations, we show how to obtain for a given atomistic beam system both a set of suitable deformed states as well as generalized stress and strain measures. Finally, we benchmark the obtained continuum model by assessing its accuracy for a beam coming into contact with an infinite Lennard-Jones wall.
ELECTRO-THERMO-MECHANICAL VIBRATION ANALYSIS OF EMBEDDED SINGLE-WALLED BORON NITRIDE NANOTUBES BASED ON NONLOCAL THIRD-ORDER BEAM THEORY
443-461
10.1615/IntJMultCompEng.2015013784
Majid
Ghadiri
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran
Farzad
Ebrahimi
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran
E.
Salari
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran
S. A. H.
Hosseini
Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran
G. R.
Shaghaghi
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran
SWBNNT
electro-thermo-mechanical vibration
Winkler foundation
third-order shear deformation theory
differential transform method
In this article, single-walled boron nitride nanotube (SWBNNT) vibration behavior is investigated based on nonlocal elasticity theory. The SWBNNT is analyzed as a nanobeam based on higher order shear deformation theory. Loading is composed of temperature change and axially external electric potential field. SWBNNT is embedded in a Winkler foundation. The governing equation and boundary conditions are derived by using the Hamilton principle. The analytical and differential transform (DT) methods are applied to determind natural frequency of the SWBNNT with different boundary conditions. The obtained results show good agreement with these cited in the literature. Also, comparison between the results of DT and analytical methods reveals the accuracy of the DT method. At the end, it is shown that temperature change, slenderness ratio, electric potential field, elastic foundation constant, and nonlocal parameters have a significant effect on natural frequency values.