2015
7
1
1
120
1

MixedMode Stress Intensity Factors for Surface Cracks in Functionally Graded Materials Using Enriched Finite Elements
http://jsm.iauarak.ac.ir/article_514619.html
1
Threedimensional enriched finite elements are used to compute mixedmode stress intensity factors (SIFs) for threedimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixedmode loading. The method, which advantageously does not require special mesh configuration/modifications and postprocessing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two and threedimensional mixedmode fracture problems are selected from the literature for comparison. Twodimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain loading and an edge crack in a finitesize plate under shear traction load. The threedimensional example models a deflected surface crack in a finitesize FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed threedimensional enriched finite elements are capable of accurately computing mixedmode fracture parameters for cracks in FGMs.
0

1
12


J
Sheikhi
Civil Engineering, Imam Hossein University
Iran


M
Poorjamshidian
Department of Mechanical Engineering, Imam Hossein University
Iran


S
Peyman
Instructor, Department of Mechanical Engineering, Imam Hossein University
Iran
Mixedmode
Surface crack
Enriched finite elements
[[1] Ozturk M., Erdogan F., 1996, Axisymmetric crack problem in bonded materials with a graded interfacial region, International Journal of Solids and Structures 33(2):193219.##[2] Delale F., Erdogan F., 1983, The crack problem for a nonhomogeneous plane, Journal of Applied Mechanics 50(3): 609614.##[3] Eischen j.w., 1987, Fracture of nonhomogeneous materials, International Journal of Fracture 34: 322.##[4] Konda N., Erdogan F., 1994, The mixedmode crack problem in a nonhomogeneous elastic medium, Engineering Fracture Mechanics 47(3): 533545.##[5] Erdogan F., Wu B.H., 1997, The surface crack problem for a plate with functionally graded properties, Journal of Applied Mechanics 64(1): 449456.##[6] Honein T., Herrmann G., 1997, Conservation laws in nonhomogeneous plane elastostatics, Journal of Mechanics and Physics of Solids 45(5): 789805.##[7] Gu P., Dao M., Asaro R.J., 1999, A simplified method for calculating the cracktip field of functionally graded materials using the domain integral, Journal of Applied Mechanics 66(1): 101108.##[8] Santare M.H., Lambros J., 2000, Use of graded finite elements to model the behavior of nonhomogeneous materials, Journal of Applied Mechanics 67(4): 819822.##[9] Kim J.H., Paulino G.H., 2002, Finite element evaluation of mixed mode stress intensity factors in functionally graded materials, International Journal for Numerical Methods in Engineering 53(6): 19031935.##[10] Dolbow J.E., Gosz M., 2002, On the computation of mixedmode stress intensity factors in functionally graded materials, International Journal of Solids and Structures 39(2): 25572574.##[11] Kim J.H., Paulino G.H., 2002, Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials, Journal of Applied Mechanics 69(4): 502514.##[12] Anlas G., Lambros J., Santare M.H., 2002, Dominance of asymptotic crack tip fields in elastic functionally graded materials, International Journal of Fracture 115(4): 193204.##[13] Shim D.J., Paulino G.H., Dodds R.H., 2006, Effect of material gradation on Kdominance of fracture specimens, Engineering Fracture Mechanics 73(4): 643648.##[14] Walters M.C., Paulino G.H., Dodds R.H., 2004, Stressintensity factors for surface cracks in functionally graded materials under modeI thermomechanical loading, International Journal of Solids and Structures 41(5): 10811118.##[15] Yildirim B., Dag S., Erdogan F., 2005, Threedimensional fracture analysis of FGM coatings under thermomechanical loading, International Journal of Fracture 132 (4): 369395.##[16] Walters M.C., Paulino G.H., Dodds R.H., 2004, Computation of mixedmode stress intensity factors for cracks in threedimensional functionally graded solids, Journal of Engineering Mechanics 132 (1): 115.##[17] Ayhan A.O., 2007, Mixedmode stress intensity factors for deflected and inclined surface cracks in finitethickness plates, Engineering Fracture Mechanics 71 (7):10591079.##[18] Ayhan A.O., Nied H.F., 2002, Stress intensity factors for threedimensional surface cracks using enriched finite elements, International Journal for Numerical Methods in Engineering 54 (6): 899921.##[19] Hartranft R.J., Sih G.C., 1969, The use of eigenfunction expansions in the general solution of threedimensional crack problems, Journal of Mathematics and Mechanics 19:123138.##]
1

Frequency Analysis of Embedded Orthotropic Circular and Elliptical Micro/NanoPlates Using Nonlocal Variational Principle
http://jsm.iauarak.ac.ir/article_514620.html
1
In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nanoplates. The nanoplate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nanoplate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method are applied to obtain a Quadratic Functional. The Ritz functions are used to form an assumed expression for transverse displacement which satisfies the kinematic boundary conditions. The Ritz functions eliminate the need for mesh generation and thus large degrees of freedom arising in discretization methods such as Finite Element Method (FEM). Effects of nonlocal parameter, lengths of nanoplate, aspect ratio, mode number, material properties and foundation parameters on the nanoplate natural frequencies are investigated. It is shown that the natural frequencies depend on the nonlocality of the micro/nanoplate, especially at small dimensions.
0

13
27


A
Anjomshoa
Department of Mechanical Engineering, Isfahan University of Technology
Iran


A.R
Shahidi
Department of Mechanical Engineering, Isfahan University of Technology
Iran


S.H
Shahidi
Department of Mechanical Engineering, Isfahan University of Technology
Iran


H
Nahvi
Department of Mechanical Engineering, Isfahan University of Technology
Iran
hnahvi@cc.iut.ac.ir
Nonlocal elasticity theory
Frequency Analysis
Elliptical nanoplate
Variational principle
[[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 5658.##[2] Stankovich S., Dikin D.A., Dommet G., Zimney E., Stach E., Piner R., Nguyen S., Ruoff R., Nahvi B.A., 2006, Graphenebased composite materials, Nature 442: 282286.##[3] Mylvaganam K., Zhang L., 2004, Important issues in a molecular dynamics simulation for characterising the mechanical properties of carbon nanotubes, Carbon 42(10): 20252032.##[4] Sears A., Batra R.C., 2004, Macroscopic properties of carbon nanotubes from molecularmechanics simulations, Physical Review B 69(23): 235406.##[5] Sohi A.N., Naghdabadi R., 2007, Torsional buckling of carbon nanopeapods, Carbon 45: 952957.##[6] Popov V.N., Doren V.E.V., Balkanski M., 2000, Elastic properties of singlewalled carbo nanotubes, Physical Review B 61: 30783084.##[7] Sun C., Liu K., 2008, Dynamic torsional buckling of a doublewalled carbon nanotube embedded in an elastic medium, Journal of Mechanics ASolids 27: 4049.##[8] Behfar K., Seifi P., Naghdabadi R., Ghanbari J., 2006, An analytical approach to determination of bending modulus of a multilayered graphene sheet, Thin Solid Films 496(2): 475480.##[9] Wong E.W., Sheehan P.E., Lieber C.M., 1997, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes, Science 277: 19711975.##[10] Liew K.M., He X.Q., Kitipornchai S., 2006, Predicting nanovibration of multilayered graphene sheets embedded in an elastic matrix, Acta Materialia 54: 42294236.##[11] Eringen A.C., 1972, Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science 10(5): 425435.##[12] Eringen A.C, 2002, Nonlocal Continuum Field Theories, Springer, New York.##[13] Wang C.M., Zhang Y.Y., He X.Q., 2007, Vibration of nonlocal Timoshenko beams, Nanotechnology 18(10):105401.##[14] Civalek Ö., Akgöz B., 2010, Free vibration analysis of microtubules as cytoskeleton components: nonlocal EulerBernoulli beam modeling, Scientia Iranica 17(5): 367375.##[15] Civalek Ö., Çigdem D., 2011, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling 35: 20532067.##[16] Murmu T., Adhikari S., 2010, Nonlocal transverse vibration of doublenanobeamsystems, Journal of Applied Physics 108: 083514.##[17] Khademolhosseini F., Rajapakse R.K.N.D., Nojeh A., 2010, Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models, Computational Materials Science 48: 736742.##[18] Wang Q., Varadan V.K., 2006, Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Materials and Structures 15: 659666.##[19] Reddy J.N., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45: 288307.##[20] Luo X., Chung D.D.L., 2000, Vibration damping using flexible graphite, Carbon 38: 15101512.##[21] Zhang L., Huang H., 2006, Young’s moduli of ZnO nanoplates: Ab initio determinations, Applied Physics Letters 89: 183111.##[22] Freund L.B., Suresh S., 2003, Thin Film Materials, Cambridge University Press, Cambridge.##[23] Scarpa F., Adhikari S., Srikantha Phani A., 2009, Effective elastic mechanical properties of single layer grapheme sheets, Nanotechnology 20(6):065709.##[24] SakhaeePour A., 2009, Elastic properties of singlelayered graphene sheet, Solid State Communications 149: 9195.##[25] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206223.##[26] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A 37: 10621069.##[27] Aydogdu M., Tolga A., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954959.##[28] Jomehzadeh E., Saidi A.R., 2011, A study on large amplitude vibration of multilayered graphene sheets, Computational Materials Science 50: 10431051.##[29] Jomehzadeh E., Saidi A.R., 2011, Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nanoplates, Composite Structures 93: 10151020.##[30] Duan W.H., Wang C.M., 2007, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18(38) :385704.##[31] Farajpour A., Mohammadi M., Shahidi A.R., Mahzoon M., 2011, Axisymmetric buckling of the circular grapheme sheets with the nonlocal continuum plate model, Physica E 43: 18201825.##[32] Babaie H., Shahidi A.R., 2011, Smallscale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method, Archive of Applied Mechanics 81: 10511062.##[33] Malekzadeh P., Setoodeh A.R., Alibeygi Beni A., 2011, Small scale effect on the vibration of orthotropic arbitrary straightsided quadrilateral nanoplates, Composite Structures 93: 16311639.##[34] Malekzadeh P., Setoodeh A.R., Alibeygi B. A., 2011, Small scale effect on the thermal buckling of orthotropic arbitrary straightsided quadrilateral nanoplates embedded in elastic medium, Composite Structures 93: 20832089.##[35] Shahidi A.R., Mahzoon M., Saadatpour M.M., Azhari M., 2005, Very large deformation analysis of plates and folded plates by Finite Strip method, Advances in Structural Engineering 8(6): 547560.##[36] Liew K.M., Wang C.M., 1993, Pb2 RayleighRitz method for general plate analysis, Engineering Structures 15(1): 5560.##[37] Azhari M., Shahidi A.R., Saadatpour M.M., 2005, Local and postlocal buckling of stepped and perforated thin plates, Applied Mathematical Modelling 29(7): 633652.##[38] Ceribasi S., Altay G., 2009, Free vibration of super elliptical plates with constant and variable thickness by Ritz method, Journal of Sound and Vibration 319: 668680.##[39] Adali S., 2009, Variational principle for transversely vibrating multiwalled carbon nanotubes based on nonlocal EulerBernoulli beam model, Nano Letters 9: 17371741.##[40] Adali S., 2011, Variational principle and natural boundary conditions for multilayered orthotropic grapheme sheets undergoing vibrations and based on nonlocal elasticity theory, Journal of Theoretical and Applied Mechanics 49(3): 621639.##[41] Phadikar J.K, Pradhan S.C., 2010, Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates, Computational Materials Science 49: S492S499.##[42] Aksencer T., Aydogdu M., 2012, Forced transverse vibration of nanoplates using nonlocal elasticity, Physica E 44: 17521759.##[43] Akgoz B., Civalek O., 2013, Modeling and analysis of microsized plates resting on elastic medium using the modified couple stress theory, Mechanica 48: 863873.##[44] HosseiniHashemi S., Zare M., Nazemnezhad R., 2013, An exact analytical approach for free vibration of Mindlin rectangular nanoplates via nonlocal elasticity, Composite Structures 100: 290299.##[45] Mohammadi M., Goodarzi M., Ghayour M., Alivand S., 2012, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial inplane preload via nonlocal elasticity theory, Journal of Solid Mechanics 4(2): 128143.##[46] Mohammadi M., Farajpour A., Goodarzi M., Heydarshenas R., 2013, Levy type solution for nonlocal thermomechanical vibration of orthotropic monolayer graghene sheet embedded in an elastic medium, Journal of Solid Mechanics 5(2): 116132.##[47] Mohammadi M., Goodarzi M., Ghayour M., Farajpour A., 2013, Influence of inplane preload on the vibration frequency of circular grapheme sheet via nonlocal continuum theory, Composites Part B: Engineering 51: 121129.##[48] Wang C.M, Wang L., 1994, Vibration and buckling of super elliptical plates, Journal of Sound and Vibration 171: 301314.##[49] Lam K.Y., Liew K.M., Chow S.T., 1992, Use of twodimensional orthogonal polynomials for vibration analysis of circular and elliptical plates, Journal of Sound and Vibration 154(2): 261269.##]
1

Exact 3D Solution for Free Bending Vibration of Thick FG Plates and Homogeneous Plate Coated by a Single FG Layer on Elastic Foundations
http://jsm.iauarak.ac.ir/article_514621.html
1
This paper presents new exact 3D (threedimensional) elasticity closedform solutions for outofplane free vibration of thick rectangular single layered FG (functionally graded) plates and thick rectangular homogeneous plate coated by a functionally graded layer with simply supported boundary conditions. It is assumed that the plate is on a WinklerPasternak elastic foundation and elasticity modulus and mass density of the FG layer vary exponentially through the thickness of the FG layer, whereas Poisson’s ratio is constant. In order to solve the equations of motion, a proposed displacement field is used for each layer. Influences of stiffness of the foundation, inhomogeneity of the FG layer and coating thicknesstototal thickness ratio on the natural frequencies of the plates are discussed. Numerical results presented in this paper can serve as benchmarks for future vibration analyses of single layered FG plates and coated plates on elastic foundations.
0

28
40


H
Salehipour
School of Mechanical Engineering, Isfahan University of Technology
Iran


R
Hosseini
School of Mechanical Engineering, University of Tehran
Iran


K
Firoozbakhsh
School of Mechanical Engineering, Sharif University of Technology
Iran
firoozbakhsh@sharif.ir
Free bending vibration
Exact 3D solution
Thick FG plates
Homogeneous plate coated by a single FG layer
WinklerPasternak elastic foundation
[[1] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, Functionally gradient materials forum, Proceedings of First International Symposium on Functionally Gradient Materials, Sendai, Japan.##[2] Koizumi M., 1993, Functional gradient material, Ceramic Transactions 34:310.##[3] Tarn J.Q., Wang Y. M., 1994, A three dimensional analyses of anisotropic inhomogeneous and laminated plates, Journal of Thermal Stresses 31:497515.##[4] Tarn J.Q., Wang Y. M., 1995, Asymptotic thermoelastic analyses of anisotropic inhomogeneous and laminated plates, Journal of Thermal Stresses 18:3538.##[5] Chen W.Q., Ding H. J., 2000, Bending of functionally graded piezoelectric rectangular plates, Acta Mechanica Solida Sinica 13:312319.##[6] Chen W.Q., Lee K.Y., Ding H. J., 2005, On free vibration of nonhomogeneous transversely isotropic magnetoelectroelastic plates, Journal of Sound and Vibration 279:237251.##[7] Reddy J.N., Cheng Z.Q., 2001, Threedimensional solutions of smart functionally graded plates, Journal of Applied Mechanics 68:234241.##[8] Vel S.S., Batra R.C.,2002, Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, American Institute of Aeronautics and Astronautics 40:14211433.##[9] Vel S.S., Batra R.C.,2003, Threedimensional analysis of transient thermal stresses in functionally graded plates, International Journal of Solids and Structures 40:71817196.##[10] Vel S.S., Batra R.C., 2004, Threedimensional exact solution for the vibration of functionally graded rectangular plates, Journal of Sound and Vibration 272:703730.##[11] Zhong Z., Shang E.T., 2003, Threedimensional exact analysis of a simply supported functionally gradient piezoelectric plate, International Journal of Solids and Structures 40:53355352.##[12] Zhong Z., Yu T., 2006, Vibration of simply supported functionally graded piezoelectric rectangular plate, Smart Materials and Structures 15:14041412.##[13] Kashtalyan M., Menshykova M., 2007, Threedimensional elastic deformation of a functionally graded coating/substrate system, International Journal of Solids and Structures 44:52725288.##[14] Kashtalyan M., Menshykova M., 2009, Effect of a functionally graded interlayer on threedimensional elastic deformation of coated plates subjected to transverse loading, Composite Structures 89:167176.##[15] Kashtalyan M., 2004, Threedimensional elasticity solution for bending of functionally graded rectangular plates, European Journal of Mechanics  A/Solids 23:853864.##[16] Huang Z.Y., Lu C.F., Chen W.Q., 2008, Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations, Composite Structures 85:95104.##[17] Lu C.F., Chen W.Q., Shao J.W., 2008, Semianalytical threedimensional elasticity solutions for generally laminated composite plates, European Journal of Mechanics  A/Solids 27:899917.##[18] Lu C.F., Lim C.W., Chen W.Q., 2009, Exact solutions for free vibration of functionally graded thick plates on elastic foundations, Mechanics of Advanced Materials and Structures 16:576584.##[19] Li Q., Iu V.P., Kou K.P., 2008, Threedimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration 311:498515.##[20] Li Q., Iu V.P., Kou K.P., 2009, Threedimensional vibration analysis of functionally graded material plates in thermal environment, Journal of Sound and Vibration 324:733750.##[21] Amini M.H., Soleimani M., Rastgoo A., 2009, Threedimensional free vibration analysis of functionally graded material plates resting on an elastic foundation, Smart Materials and Structures 18:19.##[22] Alibeigloo A., 2010, Exact solution for thermoelastic response of functionally graded rectangular plates, Composite Structures 92:113121.##[23] HosseiniHashemi S.h., Salehipour H., Atashipour S.R., 2012, Exact threedimensional free vibration analysis of thick homogeneous plates coated by a functionally graded layer, Acta Mechanica 223:21532166.##[24] HosseiniHashemi S.h., Salehipour H., Atashipour S.R., Sburlati R., 2013, On the exact inplane and outofplane free vibration analysis of thick functionally graded rectangular plates: Explicit 3D elasticity solutions, Composites Part B 46:108115.##[25] Levinson M., 1984, A novel approach to thick plate theory suggested by studies in foundation theory, International Journal of Mechanical Sciences 26:427436.##[26] Levinson M., 1985, The simply supported rectangular plate: an exact, three dimensional, linear elasticity solution, Journal of Elasticity 15:283291.##[27] Levinson M., 1985, Free vibrations of a simply supported, rectangular plate: an exact elasticity, Journal of Sound and Vibration 98:289298.##]
1

Buckling Analysis of Rectangular Functionally Graded Plates with an Elliptic Hole Under Thermal Loads
http://jsm.iauarak.ac.ir/article_514622.html
1
This paper presents thermal buckling analysis of rectangular functionally graded plates (FG plates) with an eccentrically located elliptic cutout. The plate governing equations derived by the first order shear deformation theory (FSDT) and finite element formulation is developed to analyze the plate behavior subjected to a uniform temperature rise across plate thickness. It is assumed that the nonhomogenous material properties vary through the plate thickness according to a power function. The developed finite element (FE) code with an extended mesh pattern is written in MATLAB software. The effects of aspect ratio of the plate, ellipse radii ratio, position and orientation of the cutout, boundary conditions (BCs) and volume fraction exponent are investigated in details. The results of present code are compared with those available in the literature and some useful designorientated conclusions are achieved.
0

41
57


R
Rezae
Faculty of Mechanical Engineering, University of Shahrood
Iran


A.R
Shaterzadeh
Faculty of Mechanical Engineering, University of Shahrood
Iran
ar.shaterzadeh@gmail.com


S
Abolghasemi
Faculty of Mechanical Engineering, University of Shahrood
Iran
FG plates
Thermal buckling
Finite Element Analysis
Elliptic hole
[[1] Bodaghi M., Saidi A.R., 2010, Levytype solution for buckling analysis of thick functionally graded rectangular plates based on the higherorder shear deformation plate theory, Applied Mathematical Modelling 34: 36593673.##[2] Samsam Shariat B.A., Eslami M.R., 2006, Thermal buckling of imperfect functionally graded plates, International Journal of Solids and Structures 43: 40824096.##[3] Weibgraebera P., Mittelstedtb C., Beckera W., 2012, Buckling of composite panels: A criterion for optimum stiffener design, Aerospace Science and Technology 16(1):1018.##[4] Zhao X., Lee Y.Y., Liew K.M., 2009, Mechanical and thermal buckling analysis of functionally graded plates, Composite Structures 90: 161171.##[5] Ghosh M.K., Kanoria M., 2009, Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green–Lindsay theory, Acta Mechanica 207: 5167.##[6] Mahdavian M., 2009, Buckling analysis of simplysupported functionally graded rectangular plates under nonuniform inplane compressive loading, Journal of Solid Mechanics 1(3):213225.##[7] Samsam Shariat B.A., Eslami M.R., 2007, Buckling of thick functionally graded plates under mechanical and thermal loads, Composite Structures 78: 433439.##[8] Xiang S., Kang G., 2013, A nthorder shear deformation theory for the bending analysis on the functionally graded plates, European Journal of Mechanics A/Solids 37:336343.##[9] Mozafaria H., Ayob A., 2012, Effect of thickness variation on the mechanical buckling load in plates made of functionally graded materials, Procedia Technology 1: 496504.##[10] Raki M., Alipour R., Kamanbedast A., 2012, Thermal buckling of thin rectangular FGM plate, World Applied Sciences Journal 16(1): 5262.##[11] Avci A., Sahin O.S., Uyaner M., 2005, Thermal buckling of hybrid laminated composite plates with a hole, Composite Structures 68: 247254.##[12] Zhen W., Wanji C., 2009, Stress analysis of laminated composite plates with a circular hole according to a singlelayer higherorder model, Composite Structures 90: 122129.##[13] Kiani Y., Eslami M.R., 2013, An exact solution for thermal buckling of annular FGM plates on an elastic medium, Composites: Part B 45:101110.##[14] Thai H.T., Choi D.H., 2012, An efficient and simple refined theory for buckling analysis of functionally graded plates, Applied Mathematical Modelling 36: 10081022.##[15] Saji D., Varughese B., 2008, Finite element analysis for thermal buckling behaviour in functionally graded plates with cutouts, Proceedings of the International Confrence on Aerospace Science and Technology, Bangalore India.##[16] Natarajan S., Chakraborty S., Ganapathi M., Subramanian M., 2014, A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method, European Journal of Mechanics  A/Solids 44: 136147.##[17] Zenkour A. M., Mashat D. S., 2010, Thermal buckling analysis of ceramicmetal functionally graded plates, Natural Science 2(9):968978.##[18] Saidi A. R., Baferani A. H., 2010, Thermal buckling analysis of moderately thick functionally graded annular sector plates, Composite Structures 92:17441752.##[19] Park J.S., Kim J.H., 2006, Thermal post buckling and vibration analyses of functionally graded plates, Journal of Sound and Vibration 289: 7793.##[20] Yang J., Shen H.S., 2002, Vibration characteristics and transient response of sheardeformable functionally graded plates in thermal environments, Journal of Sound and Vibration 255:579602.##[21] Reddy J. N., 2006, Theory and Analysis of Elastic Plates and Shells, Second edition, CRC press.##[22] Efraim E., Eisenberger M., 2007, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration 299:720738.##[23] Logan D. L., 2010, A First Course in the Finite Element Method, Fourth edition.##]
1

Nonlinear Vibration Analysis of the FluidFilled Single Walled Carbon Nanotube with the Shell Model Based on the Nonlocal Elacticity Theory
http://jsm.iauarak.ac.ir/article_514623.html
1
Nonlinear vibration of a fluidfilled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on VonKarman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing into the ordinary differential equations of motion. To achieve an analytical solution, the method of averaging is successfully applied to the nonlinear governing equation of motion. The SWCNT is assumed to be filled by the fluid (water) and the fluid is presumed to be an ideal non compression, non rotation and in viscid type. The fluidstructure interaction is described by the linear potential flow theory. An analytical formula was obtained for the nonlinear model and the effects of an internal fluid on the coupling vibration of the SWCNTfluid system with the different aspect ratios and the different nonlinear parameters are discussed in detail. Furthermore, the influence of the different nonlocal parameters on the nonlinear vibration frequencies is investigated according to the nonlocal Eringen’s elasticity theory.
0

58
70


P
Soltani
Department of Mechanical Engineering, Semnan branch, Islamic Azad university
Iran
payam.soltani@gmail.com


R
Bahramian
Department of Mechanical Engineering, Semnan branch, Islamic Azad university
Iran


J
Saberian
Department of Mechanical Engineering, Semnan branch, Islamic Azad university
Iran
Nonlinear vibration
Fluidfilled SWCNT
Donnell’s shell model
Nonlocal parameter
[[1] Lee S.M., An K.H., Lee Y.H., Seifert G., Frauenheim T., 2001, A hydrogen storage mechanism in singlewalled carbon nanotubes, Journal of the American Chemical Society 123: 50595063.##[2] Hummer G., Rasaiah J. C., Noworyta J.P., 2001, Water conduction through the hydrophobic channel of carbon nanotubes, Nature 414: 188190.##[3] Liu J., Rinzler A. G., Dai H.J., 1998, Fulleren pipes, Science 280: 12531256.##[4] Yakobson B.I., Brabec C.J., Bernholc J., 1996, Nanomechanics of carbon tubes: instabilities beyond linear response, Physical Review Letters 76: 25112514.##[5] Yoon J., Ru C. Q., Mioduchowski A., 2005, Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technology 65: 13261336.##[6] Yan Y., Huang X.Q., Zhang L.X., Wang Q., 2007, Flowinduced instability of doublewalled carbon nanotubes based on an elastic shell model, Journal of Applied Physics 102: 044307.##[7] Yan Y., Wang W.Q., Zhang L.X., He X.Q., 2009, Dynamical behaviors of fluid conveyed multiwalled carbon nanotubes, Applied Mathematical Modelling 33: 14301440.##[8] Wang L., Ni Q., 2008, On vibration and instability of carbon nanotubes conveying fluid, Computational Materials Science 43: 399402.##[9] khosravian N., RafiiTabar H., 2008, Computational modelling of a nonviscous fluid flow in a multiwalled carbon nanotube modelled as a Timoshenko beam, Nanotechnology 19: 275703.##[10] Khadem S.E., Rasekh M., 2009, Nonlinear vibration and stability analysis of axially loaded embedded carbon nanotubes conveying fluid, Applied Physics 42: 135112.##[11] Ghavanloo E., MasoudRafiei F., 2010, Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Physica E 42: 22182224.##[12] Dong K., Liu B.Y., Wang X., 2008, Wave propagation in fluidfilled multiwalled carbon nanotubes embedded in elastic matrix, Computational Materials Science 42: 139148.##[13] Yan Y., Wang W.Q., Zhang L.X., 2010, Noncoaxial vibration of fluidfilled multiwalled carbon nanotubes, Applied Mathematical Modelling 34: 122128.##[14] Yan Y., Wang W.Q., Zhang L.X., 2009, Nonlinear vibration chara cristics of fluid filled doublewalled carbon nanotubes, Modern Physics Letters B 23: 26252636.##[15] Eringen A.C., 2002, Nonlocal Continuum Field Theories, New York, Springer.##[16] Eringen A.C., 1976, Nonlocal Polar Field Models, New York, Academic Press.##[17] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 47034710.##[18] Gupta S.S., Bosco F.G., Batra R.C., 2010, Wall thickness and elastic moduli of singlewalled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration, Computational Materials Science 47: 10491059.##[19] Amabili M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press.##[20] Karagiozisa K.N., Amabili M., Paı¨doussisa M.P., Misra A.K., 2005, Nonlinear vibrations of fluidfilled clamped circular cylindrical shells, Journal of Fluids and Structures 21: 579595.##[21] Pellicano F., Amabili M., 2003, Stability and vibration of empty and fluidfilled circular cylindrical shells under static and periodic axial loads, International Journal of Solids and Structures 40: 32293251.##[22] Goncalves P.B., Batista R.C, 1998, Nonlinear vibration analysis of fluidfilled cylindrical shells, Journal of Sound and Vibration 127: 133143.##[23] Amabili M., 2005, Nonlinear vibrations of doubly curved shallow shells, International Journal of NonLinear Mechanics 40: 683710.##[24] Amabili M., Pellicano F., Paidoussis M.P., 1998, Nonlinear vibrations of simply supported circular cylindrical shells, coupled to quiescent fluid, Journal of Fluids and Structures 12: 883918.##[25] Evensen D.A.,1967, Nonlinear Flexural Vibrations of ThinWalled Circular Cylinders, National Aeronautics and Space Administration, Spring field.##[26] Nayfeh A.H., Mook D.T., 1995, Nonlinear Oscillations, Wiley.##[27] Liu D.K., 1998, Nonlinear Vibrations of Imperfect ThinWalled Cylindrical Shells.##[28] Yan Y., Wang W., Zhang L.,2012, Free vibration of the fluidfilled singlewalled carbon nanotube based on a double shellpotential flow model, Applied Mathematical Modeling 36: 61466153.##[29] Narendar S. , Roy Mahapatra D., Gopalakrishnan S., 2011, Prediction of nonlocal scaling parameter for armchair and zigzag singlewalled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation, International Journal of Engineering Science 49: 509522.##]
1

Modifying StressStrain Curves Using Optimization and Finite Elements Simulation Methods
http://jsm.iauarak.ac.ir/article_514624.html
1
Modifying stressstrain curves is one of the important topics in mechanical engineering and materials science. Real stressstrain curves should be modified after necking point as stress becomes threedimensional after creation of throat, and consequently, equivalent stress should be used instead of axial one. Also, distribution of triple stresses across throat section is not uniform anymore, and it is not possible to calculate the stress through dividing force value by surface area. Methods presented to modify these curves mainly have some defects which enter the error resulting from simplifying assumptions into the results. Entrance of stress analysis softwares into mechanical engineering has caused use of finite elements methods in order to modify stressstrain curves. As you know, being as an input for stress analysis software, as one of the applications of these curves, has a direct effect on simulation results. Optimization methods have been developed and extended in engineering sciences. Modifying stressstrain curves may be an application of these methods. Considering the sample shape resulting from tension test as the basis in this research, we have changed the modified stressstrain curved in a way that the shape resulting from simulation coincides with the sample resulting from the test. Accordingly, the stressstrain curve has been modified, and the results have been verified, using results obtained from normal methods such as Bridgeman method.
0

71
82


A
Rezaei Pour Almasi
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Iran
almasiamir67@yahoo.com


F
Fariba
Department of Mechanical Engineering ,Hamedan Branch ,Islamic Azad University
Iran


S
Rasoli
Young Researchers and Elite Club, Hamedan Branch, Islamic Azad university
Iran
StressStrain Curve
Modification factor
Optimization
Material model
[[1] Bridgeman P.W., 1944, The stress distribution at the neck of a tension specimen, Transactions of American Society for Metal 32: 553574.##[2] Davidenkov N.N., Spiridonova N.I., 1947, Mechanical method of testing analysis of the state of stress in the neck of a tension test speciement, Proceedings American Society for Testing Material 46: 11471158.##[3] Siebel E., Schwaigere S., 1948, Mechanics of tensile test (in German), Arch Eisenhuttenwes 19: 145152.##[4] Leroy G., Embury J., Edwards G., Ashby M.F., 1981, A model of ductile fracture based on the nucleation and growth of voids, Acta Metallurgica 29: 15091522.##[5] Needleman A., 1972, A numerical study of necking in circular cylindrical bars, Journal of the Mechanics and Physics of Solids 20: 111127.##[6] Brunig M., 1998, Numerical analysis and modeling of large deformation and necking behavior of tensile Specimens, Finite Elements in Analysis and Design 28: 303319.##[7] Niordson C.F., Redanz P., 2004, Size effects in plane strain sheetnecking , Journal of the Mechanics and Physics of Solids 52: 24312454.##[8] Koc P., Stok B., 2004, Computeraided identification of the yield curve of a sheet metal after onset of necking, Computational Materials Science 31: 155168.##[9] Tang C.Y., Lee T.C., 2003, Simulation of necking using a damage coupled finite element method, Journal of Materials Processing Technology 139: 510513.##[10] Yung L., 1996, Uniaxial true stress strain after necking, Journal of Technology 5: 3748.##[11] Giuseppe M., 2004, A new model for the elastoplastic characterization and the stress – strain determination on the necking section of a tensile specimen, International Journal of Solid and Structures 41: 35453564.##[12] HungYang Y., JungHo C., 2003, NDE of metal damage ultrasonic whit a damage mechanics model, International Journal of Solids and Structures 40: 72857298.##[13] ASTM, E8, Standard Methods of Tension Testing of Metallic Materials, Annual book of ASTM standard, American society for testing and materials.##[14] Majzoobi G.H. , FreshtehSaniee F., FarajZadehKhosroshahi S., BeikMohhamadloo H., Determination of material parameter under dynamic loading part I:Experiments and simulation, Computational Materials Science 49(2):192200.##]
1

Free Vibration Analysis of Moderately Thick Functionally Graded Plates with Multiple Circular and Square Cutouts Using Finite Element Method
http://jsm.iauarak.ac.ir/article_514632.html
1
A simple formulation for studying the free vibration of sheardeformable functionally graded plates of different shapes with different cutouts using the finite element method is presented. The aim is to fill the void in the available literature with respect to the free vibration results of functionally graded plates of different shapes with different cutouts. The material properties of the plates are assumed to vary according to a power law distribution in terms of the volume fraction of the constituents. Validation of the formulation is done with the help of convergence studies with respect to the number of nodes and the results are compared with those from past investigations available only for simpler problems. In this paper rectangular, trapezoidal and circular plates with cutouts are studied and the effects of volume fraction index, thickness ratio and different external boundary conditions on the natural frequencies of plates are studied.
0

83
95


J
Vimal
Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India
Iran
jyoti_vimal@yahoo.com


R.K
Srivastava
Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India
Iran


A.D
Bhatt
Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India
Iran


A.K
Sharma
Department of Mechanical Engineering, Madhav Institute of Technology & Science Gwalior, India
Iran
Functionally Graded Materials
Free vibration
Circular/square/trapezoidal plates
Circular/square cutouts
[[1] Jha D.K., Kant T., Singh R.K., 2013, A critical review of recent research on functionally graded plates, Composite Structures 96: 833849.##[2] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering 47(1–3): 663684.##[3] Reddy J.N., 1984, A simple higherorder theory for laminated composite plates, Journal of Applied Mechanics 51: 745752.##[4] Xiang S., Kang G.W., 2013, A nthorder shear deformation theory for the bending analysis on the functionally graded plates, European Journal of Mechanics  A/Solids 37: 336343.##[5] Xiang S., Jin Y.X., Bi Z.Y., Jiang S.X., Yang M.S., 2011, A norder shear deformation theory for free vibration of functionally graded and composite sandwich plates, Composite Structures 93(11): 28262832.##[6] Huang X. L., Shen S. H., 2004, Nonlinear vibration and dynamic response of functionally graded plates in thermal environments, International Journal of Solids and Structures 41: 24032427.##[7] Yang J., Sheen S. H., 2003, Free vibration and parametric response of shear deformable functionally graded cylindrical panels, Journal of Sound and Vibration 261: 871893.##[8] Jiu Hui W., Liu A.Q., Chen H. L., 2007, Exact solutions for free vibration analysis of rectangular plate using bessel functions, Journal of Applied Mechanics 74: 12471251.##[9] Zhao X., Lee Y. Y., Liew K. M., 2009, Free vibration analysis of functionally graded plates using the elementfree KpRitz method, Journal of Sound and Vibration 319: 918939.##[10] Hiroyuki M., 2008, Free vibration and stability of functionally graded plates according to a 2D higherorder deformation theory, International Journal of Composite Structures 82: 499512.##[11] Hosseini Hashemi A.h., Fadaee M., Atashipour S. R., 2011, Study on the free vibration of thick functionally graded rectangular plates according to a new exact closedform procedure, International Journal of Composite Structures 93: 722735.##[12] Chai B. G., 1996, Free vibration of laminated plates with a central circular hole , International Journal of Composite Structures 35: 357368.##[13] Sakiyama T., Huang M., 1996, Free vibration analysis of rectangular plates with variously shapehole, Journal of Sound and Vibration 226: 769786.##[14] Liu G. R., Zhao X., Dai K.Y., Zhong Z.H., Li G. Y., Han X., 2008, Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method, International Journal of Composites Science and Technology 68: 354366.##[15] Bathe K. J., 1971, Solution Methods for Large Generalized Eigen Value Problems in Structural Engineering, Department of Civil Engineering, University of California, Berkeley.##[16] Maziar J., Iman R., 2012, Free vibration analysis of functionally graded plates with multiple circular and noncircular cutouts, Chinese Journal of Mechanical Engineering 25(2):277284.##[17] Huang M., Sakiyama T., 1999, Free vibration analysis of rectangular plates with various shape hole, Journal of Sound and Vibration 226: 769786.##[18] Maziar J., Amin Z., 2011, Thermal effect on free vibration analysis of functionally graded arbitrary straightsided plates with different cutouts, Latin American Journal of Solids and Structures 8: 245 257.##[19] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York.##]
1

Nonlinear Instability of Coupled CNTs Conveying Viscous Fluid
http://jsm.iauarak.ac.ir/article_514633.html
1
In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal EulerBernoulli beam (EBB) theory. CNTs are embedded in a viscoelastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are derived. The differential quadrature (DQ) method is applied to obtain the nonlocal frequency of coupled viscoCNTs system. The effects of various parameters such as the longitudinal magnetic field, viscoPasternak foundation, Knudsen number, surface effect, aspect ratio and velocity of conveying viscous are specified. It is shown that the longitudinal magnetic field is responsible for an up shift in the frequency and an improvement of the instability of coupled system. Results also reveal that the surface effect and internal conveying fluid plays an important role in the instability of nano coupled system. Also, it is found that trend of figures have good agreement with previous researches. It is hoped that the nonlinear results of this work could be used in design and manufacturing of nano/micro mechanical system in advanced nanomechanics applications where in this study the magnetic field is a controller parameter.
0

96
120


A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Iran
aghorban@kashanu.ac.ir


S
Amir
Faculty of Mechanical Engineering, University of Kashan
Iran
Nonlinear vibration
Coupled system
magnetic field
Conveying fluid
Surface stress
Knudsen Number
[[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 5658.##[2] Lim C.W., Li C., Yu J.L., 2010, Dynamic behavior of axially moving nanobeams based on nonlocal elasticity approach, Acta Mechanica Sinica 26: 755265.##[3] Zhen Y., Fang B., 2010, Thermal–mechanical and nonlocal elastic vibration of singlewalled carbon nanotubes conveying fluid, Computational Materials Science 49: 276282.##[4] Fang B., Xin Y., Zhen C., Ping Z., Tang Y., 2013, Nonlinear vibration analysis of doublewalled carbon nanotubes based on nonlocal elasticity theory, Applied Mathematical Modelling 37: 10961107.##[5] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications 36:833837.##[6] Soltani P., Farshidianfar A., 2012, Periodic solution for nonlinear vibration of a fluidconveying carbon nanotube, based on the nonlocal continuum theory by energy balance method, Applied Mathematical Modelling 36: 37123724.##[7] Ghorbanpour Arani A., Shajari A.R., Amir S., Loghman A., 2012, Electrothermomechanical nonlinear nonlocal vibration and instability of embedded microtube reinforced by BNNT, conveying fluid, Physica E 45: 109121.##[8] Mirramezani M., Mirdamadi H.R., 2012, The effects of Knudsendependent flow velocity on vibrations of a nanopipe conveying fluid, Archive of Applied Mechanics 82: 879890.##[9] Rashidi V., Mirdamadi H.R., Shirani E., 2012, A novel model for vibrations of nanotubes conveying nano flow, Computational Materials Science 51: 347352.##[10] Wang L., 2010, Vibration analysis of fluidconveying nanotubes with consideration of surface effect, Physica E 43: 437439.##[11] Gurtin M.E., Murdoch A.I., 1975, A continuum theory of elastic material surface, Archive for Rational Mechanics and Analysis 57(4): 291323.##[12] Gurtin M.E., Murdoch A.I., 1978, Surface stress in solids, International Journal of Solids and Structures 14(6): 431440.##[13] Lei Y., Adhikari S., Friswell M.I., 2013, Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams, International Journal of Engineering Science 66/67: 113.##[14] Ghavanloo E., Fazelzadeh S.A., 2011, Flowthermo elastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid, Physica E 44: 1724.##[15] Murmu T., McCarthy M.A., Adhikari S., 2012, Vibration response of doublewalled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach, Journal of Sound and Vibration 331: 50695086.##[16] Wang H., Dong K., Men F., Yan Y.J., Wang X., 2010, Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix, Applied Mathematical Modelling 34: 878889.##[17] Murmu T., McCarthy M.A., Adhikari S., 2013, Inplane magnetic field affected transverse vibration of embedded singlelayer graphene sheets using equivalent nonlocal elasticity approach, Composite Structures 96: 5763.##[18] Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystems, Physics Letters A 375: 601608.##[19] Murmu T., Adhikari S., 2010, Nonlocal transverse vibration of doublenanobeamsystems, Journal of Applied Physics 108: 083514.##[20] Murmu T., Adhikari S., 2010, Nonlocal effects in the longitudinal vibration of doublenanorod systems, Physica E 43: 415422.##[21] Murmu T., Adhikari S., 2011, Nonlocal vibration of bonded doublenanoplatesystems, Composites Part B: Engineering 42:19011911.##[22] Ghorbanpour Arani A., Amir S., 2013, Electrothermal vibration of viscoelastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradiant theory, Physica B 419: 16.##[23] Eringen A.C., Edelen D.G.B., 1972, On nonlocal elasticity, International Journal of Engineering Science 10: 233248.##[24] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface wave, Journal of Applied Physics 54: 47034710.##[25] Reddy J.N., 2002, Energy Principles and Variational Methods in Applied Mechanics, John Willey & Sons.##[26] Reddy J.N., Wang C.M., 2004, dynamics of fluid conveying beams, Centre for Offshore Research and Engineering National University of Singapore.##[27] Khodami Maraghi Z., Ghorbanpour Arani A., Kolahchi R., Amir S., Bagheri M.R., 2013, Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid, Composites Part B: Engineering 45: 423432.##[28] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications 36: 833837.##[29] Paidoussis M.D., 1998, FluidStructure Interactions: Slender Structures and Axial Flow, Academic Press, London.##[30] Beskok A., Karniadakis G.E., 1999, Report: a model for flows in channels, pipes, and ducts at micro and nano scales, Microscale Thermophysical Engineering 3: 4377.##[31] Ghorbanpour Arani A., Loghman A., Shajari A.R., Amir S., 2010, Semianalytical solution of magnetothermoelastic stresses for functionally graded variable thickness rotating disks, Journal of Mechanical Science and Technology 24: 21072117.##[32] Bellman R.E., Kashef B.G., Casti J., 1972, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10: 4052.##[33] Hu L.C., Hu C., 2013, Identification of rate constants by differential quadrature in partly measurable compartmental models, Mathematical Biosciences 21: 7176.##[34] Civan F., Sliepcevich C.M., 1984, Application of differential quadrature to transport processes, Journal of Mathematical Analysis and Applications 101: 423443.##[35] Striz A.G., Jang S.K., Bert C.W., 1988, Nonlinear bending analysis of thin circular plates by differential quadrature, Thinwalled structures 6: 5162.##[36] Bozdogan K.B., 2012, Differential quadrature method for free vibration analysis of coupled shear walls, Structural Engineering & Mechanics 41: 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Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technology 65: 13261336.##[44] Wang L., Ni Q., Li M., Qian Q., 2008, The thermal effect on vibration and instability of carbon nanotubes conveying fluid, Physica E 40: 31793182.##]