2016
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Reliability Analysis of Nanocomposite Beams Reinforced with CNTs under Buckling Forces Using the Conjugate HLRF
2
2
In this paper, the nonlinear conjugate map is applied based on the conjugate HasoferLind and Rackwitz Fiessler (CHLRF) method to evaluate the reliability index using the first order reliability method of the embedded nanocomposite beam, which is made of a polymer reinforced with carbon nanotubes (CNTs). The structure is simulated with the Timoshenko beam model. The MoriTanaka model is applied for calculating the effective material properties of the nanocomposite beam and the surrounding elastic medium is considered as spring and shear constants. The governing equations are derived based on the energy method and the Hamilton's principle. Moreover, using an analytical method, the buckling performance function of the structure is obtained. The effects of the basic random variables including the lengthtothickness ratio of the beam (L/h), the spring constant, and the shear constant of the foundation with respect to the volume fraction of CNTs are investigated based on the reliability index of the nanocomposite beam which is subjected to an axial force of 20 GPa. The results indicate that the failure probabilities of the studied nanocomposite beams are sensitive to the lengthtothickness ratio of the beam (L/h) and the spring constant of the foundation variables.
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200
207


Behrooz
Keshtegar
Department of Civil Engineering, University of Zabol,
Zabol, 9861335856, Iran, Bkeshtegar@uoz.ac.ir
Department of Civil Engineering, University
Iran
bkeshtegar@uoz.ac.ir


Abbasali
Ghaderi
Department of Civil Engineering, University of Sistan and Baluchestan,
Zahedan, 98798155, Iran
Department of Civil Engineering, University
Iran


Ahmed
ElShafie
Department of Civil Engineering, Faculty of Engineering, University Malaya,
Kuala Lumpur, 50603, Malaysia
Department of Civil Engineering, Faculty
Iran
elshafie@um.edu.my
Nanocomposite beam
Conjugate HLRF
first order reliability method
Timoshenko beam model
[[1] Engesser, F., Über Die Knickfestigkeit Gerader Stäbe, Z. Archit. Ing. Ver. Hann., Vol. 35, pp. 455–462, 1889. ##[2] Shanley, F.R., Inelastic Column Theory, J. Aeronaut. Sci., Vol. 14, Pp. 261–264, 1947. ##[3] Mau, S.T., Effect of Tie Spacing Oninelastic Buckling of Reinforcing Bars, ACI Struct. J., Vol. 87, No. 6, pp. 617677, 1990. ##[4] Mau, S.T. and ElMabsout, M., Inelastic Buckling of Reinforcing Bars, J. Eng. Mech., Vol. 115, No. 1, pp. 117, 1989. ##[5] Pantazopoulou, S.J., Detailing for Reinforcement Stability in RC Members, J. Struct. Eng., Vol. 124, No. 6, pp. 6236321998. ##[6] Dhakal, R.P. and Maekawa, K., Modeling for Postyield Buckling of Reinforcement, J. Struct. Eng., Vol. 128, No.9, pp. 11391147, 2002. ##[7] Bae, S., Mieses, A.M. and Bayrak, O., Inelastic Buckling of Reinforcing Bars, J. Struct. Eng., Vol. 131, No. 2, pp. 314321, 2005. ##[8] Dhakal, R.P. and Maekawa, K., Reinforcement Stability and Fracture of Cover Concrete in Reinforced Concrete Members, J. Struct. Eng., Vol. 128, No. 10, pp. 12531262, 2002. ##[9] Krauberger, N., Saje, M., Planinc, I. and Bratina, S., Exact Buckling Load of a Restrained RC Column, Struct. Eng. Mech., Vol. 27, pp. 293–310, 2007. ##[10] Lou, T., Lopes, S.M.R. and Lopes, A.V. (2015), “Numerical Modelling of Nonlinear Behaviour of Prestressed Concrete Continuous Beams”, Comput. Concrete, 15, 391410. ##[11] Bajc, U., Saje, M., Planinc, I. and Bratina, S., Semianalytical Buckling Analysis of Reinforced Concrete Columns Exposed to Fire, Fire Safety J., Vol. 71, pp. 110–122, 2015. ##[12] Vijai, K., Kumutha, R. and Vishnuram, B.G., Flexural Behaviour of Fibre Reinforced Geopolymer Concrete Composite Beams, Comput. Concrete, Vol. 15, pp. 437459, 2015. ##[13] Keshtegar, B. and Miri, M., Reliability Analysis of Corroded Pipes Using Conjugate HL–RF Algorithm Based on Average Shear Stress Yield Criterion, Engineering Failure Analysis, Vol. 46, pp. 104–117, 2014. ##[14] Keshtegar B. and Hao P., A Hybrid Loop Approach Using the Sufficient Descent Condition for Accurate, Robust and Efficient ReliabilityBased Design Optimization, Journal of Mechanical Design, Vol. 138, No. 12: pp. 12140111 ##[15] Keshtegar, B. (2016), A Modified Mean Value of Performance Measure Approach for ReliabilityBased Design Optimization, Arab J Sci Eng. 19, doi:10.1007/s13369016232202016 ##[16] Keshtegar, B., Chaotic Conjugate Stability Transformation Method for Structural Reliability Analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 310, pp. 866885, 2016. ##[17] Keshtegar, B., Stability Iterative Method for Structural Reliability Analysis Using a Chaotic Conjugate Map, Nonlinear Dyn., Vol. 84, No. 4, pp. 21612174, 2016. ##[18] Keshtegar, B., Limited Conjugate Gradient Method for Structural Reliability Analysis, Engineering with Computers, doi:10.1007/s0036601604937, pp. 19, 2016. ##[19] Keshtegar, B. and Miri, M., Introducing Conjugate Gradient Optimization for Modified HLRF Method, Engineering Computations, Vol. 31, pp. 775790, 2014. ##[20] Fletcher, R. and Reeves, C., Function minimization by conjugate gradients, J. Comput. Vol. 7, pp. 149–154, 1964. ##[21] Gong, J.X. and Yi, P., A Robust Iterative Algorithm for Structural Reliability Analysis, Struct. Multidisc. Optim., Vol. 43, pp. 519–527, 2011. ##[22] Meng, Z., Li, G., Yang, D. and Zhan, L., A New Directional Stability Transformation Method of Chaos Control for First Order Reliability Analysis, Struct. Multidiscipl. Optim., DOI: 10.1007/s001580161525z, pp. 112, 2016.##]
Nonlinear Vibration Analysis of SingleWalled Carbon Nanotube Conveying Fluid in Slip Boundary Conditions Using Variational Iterative Method
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2
In this paper, nonlinear dynamic behaviour of the carbon nanotube conveying fluid in slip boundary conditions is studied using the variation iteration method. The developed solutions are used to investigate the effects of various parameters on the nonlinear vibration of the nanotube. The results indicate that an increase in the slip parameter leads to a decrease in the frequency of vibration and the critical velocity, while the natural frequency and the critical fluid velocity increase as the stretching effect increases. Also, as the nonlocal parameter increases, the natural frequency and the critical velocity decreases. The analytical solutions help to have better insights and understand the relationship between the physical quantities of the problem.
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208
221


Gbeminiyi
Sobamowo
Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
Department of Mechanical Engineering, University
Iran
mikegbeminiyi@gmail.com
Nonlinear vibration
Slip boundary Condition
Fluidconveying Nanotube
Variational iteration method
[Iijima, S. Helical microtubules of graphitic carbon. Nature, London, Vol. 354, no. 6348, pp. 56–58, 1991. ##Yoon, G., Ru, C.Q., Mioduchowski, A. Vibration and instability of carbon nanotubes conveying fluid. Journal of Applied Mechanics, Transactions of the ASME, Vol. 65, no. 9, 1326–1336, 2005. ##Yan, Y., Wang, W.Q. and Zhang, L.X. Nonlocal effect on axially compressed buckling of triplewalled carbon nanotubes under temperature field. Journal of Applied Math and Modelling, Vol. 34, pp. 3422–3429, 2010. ##Murmu, T., and Pradhan, S. C. Thermomechanical vibration of Singlewalled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Computational Material Science, Vol. 46, pp. 854–859, 2009. ##Yang, H. K. and Wang, X. Bending stability of multiwall carbon nanotubes embedded in an elastic medium. Modeling and Simulation in Materials Sciences and Engineering, Vol. 14, pp. 99–116, 2006. ##Yoon, J. Ru, C.Q., Mioduchowski, A. Vibration of an embedded multiwall carbon nanotube. Composites Science and Technology, Vol. 63, no. 11, pp. 1533–1542, 2003. ##Lu, P. Lee, H.P., Lu, C. Zhang, P.Q. Application of nonlocal beam models for carbon nanotubes. International Journal of Solids and Structures, Vol. 44, no. 16, pp. 5289–5300, 2007. ##Zhang, Y., Liu, G., Han, X. Transverse vibration of doublewalled carbon nanotubes under compressive axial load. Applied Physics Letter A, Vol. 340, no. 14, pp. 258–266, 2005. ##GhorbanpourArani, M.S. Zarei, M. Mohammadimehr, A. Arefmanesh, M.R. Mozdianfard. The thermal effect on buckling analysis of a DWCNT embedded on the Pasternak foundation”, Physica E, Vol. 43, pp. 1642–1648, 2011. ##Sobamowo, M. G. Thermal analysis of longitudinal fin with temperaturedependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering Vol. 99, pp.1316–1330, 2016. ##Rafei, M. Ganji, D. D. Daniali, H., Pashaei. H. The variational iteration method for nonlinear oscillators with discontinuities. J. Sound Vib. Vol. 305, pp. 614–620, 2007. ##S. S. Ganji, D. D. Ganji, D. D., H. Ganji, Babazadeh, Karimpour, S.: Variational approach method for nonlinear oscillations of the motion of a rigid rod rocking back and cubicquintic duffing oscillators. Prog. Electromagn. Res. M Vol. 4, pp. 23–32, 2008. ##Liao, S. J. The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,Ph. D. dissertation, Shanghai Jiao Tong University, 1992 ##Zhou, J. K. Differential Transformation and its Applications for Electrical Circuits. Huazhong University Press: Wuhan, China, 1986. ##Fernandez, A. On some approximate methods for nonlinear models. Appl Math Comput., Vol. 21., pp. 16874, 2009 ##Eringen, A. C. “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves”, Journal of Applied Physics, Vol. 54, no. 9, pp.4703–4710, 1983. ##Eringen, A. C. “Linear theory of nonlocal elasticity and dispersion of plane waves”, Inter national Journal of Engineering Science, Vol. 10, no. (5), pp. 425–435, 1972. ##Eringen, A. C. and Edelen, D. G., B. “On nonlocal elasticity”, International Journal of Engineering Science, Vol. 10(3), pp. 233–248, 1972. ##Eringen, A. C. “Nonlocal continuum field theories”, Springer, New York 2002. ##AliAsgari, M., Mirdamadi, H. R. and Ghayour, M. Coupled effects of nanosize, stretching, and slip boundary conditions on nonlinear vibrations of nanotube conveying fluid by the homotopy analysis method.Physica E, Vol. 52, pp. 77–85, 2013. ##Shokouhmand, H. Isfahani, A. H. M. and Shirani, E. “Friction and heat transfer coefficient in micro and nano channels with porous media for wide range of Knudsen number”, International Communication in Heat and Mass Transfer, Vol. 37, pp. 890894, 2010. ##]
Magnetic Field Effects on the Elastic Behavior of Polymeric Piezoelectric Cylinder Reinforced with CNTs
2
2
In the present study, the magnetic field effects of the elastic response of the polymeric piezoelectric cylinder reinforced with the carbon nanotubes (CNTs) are studied. The cylinder is subjected to an internal pressure, a constant electric potential difference at the inner and outer surfaces, and the thermal and magnetic fields. The MoriTanaka model is used for obtaining the equivalent material properties of the cylinder. The governing differential equation of the cylinder is derived and solved analytically based on the charge and equilibrium relations. The main purpose of this paper is to investigate the effects of the magnetic field on the stresses, the electric potential, and the radial displacement distributions of the polymeric piezoelectric cylinder. The presented results indicate that the existence of the magnetic field can reduce the stresses of the nanocomposite cylinder.
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222
229


Ali
Cheraghbak
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Faculty of Mechanical Engineering, University
Iran
ali.cheraghbeyk@gmail.com


Abbas
Loghman
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Faculty of Mechanical Engineering, University
Iran
aloghman@kashanu.ac.ir
Magnetic field
CNT
Piezoelectric cylinder
MoriTanak model
Electric filed
[[1] Ghorbanpour, A., Golabi, S. and Saadatfar, M., “Stress and electric potential fields in piezoelectric smart spheres”, Journal of Mechanical Science and Technology, Vol. 20, pp. 19201933, 2006. ##[2] Saadatfar, M. and Razavi, A.S., “Piezoelectric hollow cylinder with thermal gradient”, Journal of Mechanical Science and Technology, Vol. 23, pp. 4553, 2009. ##[3] Galic, D. and Horgan, C.O., “The stress response of radially polarized rotating piezoelectric cylinders”, Journal of Appllied Mechanics, Vol. 66, pp. 257272, 2002. ##[4] Chen, Y., Shi, Z.F., “Analysis of a functionally graded piezothermoelatic hollow cylinder”, Journal of Zhejiang University SCIENCE A, Vol. 6, pp. 956–61, 2005. ##[5] Babaei, M.H. and Chen, Z.T. “Analytical solution for the electromechanical behaviour of a rotating functionally graded piezoelectric hollow shaft”, Archive of Appllied Mechanics, Vol. 78, pp. 489–500, 2008. ##[6] Khoshgoftar, M.J., Ghorbanpour Arani, A. and Arefi, M. “Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material”, Smart Materials and Structures, Vol. 18, pp. 115007 (8pp), 2009. ##[7] Ray, M.C. and Reddy,J.N. “Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites”, Composite Science and Technology, Vol. 65, pp. 1226–1236, 2005. ##[8] Bohm, H.j. and Nogales, S. “Mori–Tanaka models for the thermal conductivity of composites with interfacial resistance and particle size distributions”, Composite Science and Technology, Vol. 68, pp. 1181–1187, 2008. ##[9] Tan, P. and Tong, L. “Microelectromechanics models for piezoelectricfiberreinforced composite materials”, Composite Science and Technology, Vol. 61, pp. 759–769, 2001. ##[10] Loghman, A. and Cheraghbak, A. “Agglomeration effects on electromagnetothermo elastic behavior of nanocomposite piezoelectric cylinder”, Polymer Composites, 2016, DOI: 10.1002/pc.24104. ##[11] Mori, T. and Tanaka, K., “Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions”, Acta Metallurgica et Materialia, Vol. 21, pp. 571 574, 1973. ##[12] Shi, D.L. and Feng, X.Qو. T“he Effect ofNanotube Waviness and Agglomeration on the elastic Property of Carbon NanotubeReinforced Composties”, Journal of Engineering Materials and Technology ASME, Vol. 126, pp. 250270, 2004. ##[13] Ghorbanpour Arani, A., Kolahchi, R. and Mosallaie Barzoki, A.A. “Effect of material inhomogeneity on electromechanical behaviors of functionally graded piezoelectric rotating shaft”, Applied Mathematical Modelling, Vol. 135, pp. 2771–2789, 2011. ##[14] Ghorbanpour Arani, A., Loghman, A., Abdollahitaheri, M. and Atabakhshian, V. “Electrothermomechanical behaviour of a radially polarized functionally graded piezoelectric cylinder”, Journal of Mechanics of Materials and Structures, Vol. 6, pp. 869–882, 2011. ##[15] Dai, H.L., Hong, H., Fu, Y. and Xiao, M. “Analytical solution for electromagneto thermoelastic behaviours of a Functionally Graded Piezoelectric Hollow Cylinder”, Applied Mathematical Modeling, Vol. 34, pp. 343357, 2010. ##[16] Ghorbanpour Arani, A., Mosallaie Barzoki, A.A., Kolahchi, R., Mozdianfard, M.R. and Loghman, A. “Semianalytical solution of timedependent electrothermomechanical creep for radially polarized piezoelectric cylinder”, Computers and Structures, Vol. 89, pp. 1494–1502, 2011.##]
Uniaxial Buckling Analysis Comparison of Nanoplate and Nanocomposite Plate with Central Square Cut out Using Domain Decomposition Method
2
2
A comparison of the buckling analysis of the nanoplate and nanocomposite plate with a central square hole embedded in the Winkler foundation is presented in this article. In order to enhance the mechanical properties of the nanoplate with a central cutout, the uniformly distributed carbon nanotubes (CNTs) are applied through the thickness direction. In order to define the shape function of the plate with a square cutout, the domain decomposition method and the orthogonal polynomials are used. At last, to obtain the critical buckling load of the system, the RayleighRitz energy method is provided. The impacts of the length and width of the plate, the dimension of the square cutout, and the elastic medium on the nanoplate and nanocomposite plate are presented in this study.
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230
242


Majid
Jamali
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran, eng.mjamali@gmail.com
School of Mechanical Engineering, Iran University
Iran
eng.mjamali@gmail.com


Taghi
Shojaee
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran,
School of Mechanical Engineering, Iran University
Iran
ta_shojaee@cmps2.iust.ac.ir


Bijan
Mohammadi
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran,
School of Mechanical Engineering, Iran University
Iran
bijan_mohammadi@iust.ac.ir
Analytical buckling
Nanocomposite plate
Central square hole
Winkler foundation
Domain decomposition method
RayleighRitz energy method
[[1] Murmu, T., and Pradhan, S. C., "Buckling of biaxially compressed orthotropic plates at small scales," Mechanics Research Communications, Vol. 36, pp. 933938, 2009. ##[2] Pradhan, S. C., "Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory," Physics Letters A, Vol. 373, pp. 41824188, 2009. ##[3] Aksencer, T., and Aydogdu, M., "Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory," Physica E: Lowdimensional Systems and Nanostructures, Vol. 43, pp. 954959, 2011. ##[4] Hashemi, S. H., and Samaei, A. T., "Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory," Physica E: Lowdimensional Systems and Nanostructures, Vol. 43, pp. 14001404, 2011. ##[5] Samaei, A. T., Abbasion, S., and Mirsayar, M. M., "Buckling analysis of a singlelayer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory," Mechanics Research Communications, Vol. 38, pp. 481485, 2011. ##[6] Farajpour, A., Danesh, M., and M. Mohammadi, "Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics," Physica E: Lowdimensional Systems and Nanostructures, Vol. 44, pp. 719727, 2011. ##[7] Farajpour, A., Shahidi, A. R., Mohammadi, M., and Mahzoon, M., "Buckling of orthotropic micro/nanoscale plates under linearly varying inplane load via nonlocal continuum mechanics," Composite Structures, Vol. 94, pp. 16051615, 2012. ##[8] Murmu, T., Sienz, J., Adhikari, S., and Arnold, C., "Nonlocal buckling of doublenanoplatesystems under biaxial compression," Composites Part B: Engineering, Vol. 44, pp. 8494, 2013. ##[9] Radić, N., Jeremić, D., Trifković, S., and Milutinović, M., "Buckling analysis of doubleorthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory," Composites Part B: Engineering, Vol. 61, pp. 162171, 2014. ##[10] Golmakani, M. E., and Rezatalab, J., "Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory," Composite Structures, Vol. 119, pp. 238250, 2015. ##[11] Arani, A. G., Maghamikia, S., Mohammadimehr, M., and Arefmanesh, A., "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods," Journal of Mechanical Science and Technology, Vol. 25, pp. 809820, 2011. ##[12] Jam, J. E., and Maghamikia, S., "Elastic buckling of composite plate reinforced with carbon nano tubes," International Journal of Engineering Science and Technology, Vol. 3, pp. 40904101, 2011. ##[13] Mohammadimehr, M., Mohandes, M., and Moradi, M., "Size dependent effect on the buckling and vibration analysis of doublebonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory," Journal of Vibration and Control, 2014. ##[14] Asadi, E., and Jam, J. E., "Analytical and Numerical Buckling Analysis of Carbon Nanotube Reinforced Annular Composite Plates," Int J Advanced Design and Manufacturing Technology, Vol. 7, pp. 3544, 2014. ##[15] Mohammadimehr, M., RoustaNavi, B., and GhorbanpourArani, A., "Biaxial Buckling and Bending of Smart Nanocomposite Plate Reinforced by CNTs using Extended Mixture Rule Approach," Mechanics of Advanced Composite Structures, Vol. 1, pp. 1726, 2014. ##[16] Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M., and Kolahchi, R., "Wave propagation in FGCNTreinforced piezoelectric composite micro plates using viscoelastic quasi3D sinusoidal shear deformation theory," Composites Part B: Engineering, Vol. 95, pp. 209224, 2016. ##[17] Ghorbanpour Arani, A., Jamali, M., GhorbanpourArani, A., Kolahchi, R., and Mosayyebi, M., "Electromagneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016. ##[18] Wattanasakulpong, N., and Chaikittiratana, A., "Exact solutions for static and dynamic analyses of carbon nanotubereinforced composite plates with Pasternak elastic foundation," Applied Mathematical Modelling, Vol. 39, pp. 54595472, 2015. ##[19] Ashoori Movassagh, A., and Mahmoodi, M. J., "A microscale modeling of Kirchhoff plate based on modified straingradient elasticity theory," European Journal of Mechanics  A/Solids, Vol. 40, pp. 5059, 2013. ##[20] Ghorbanpour Arani, A., and Shokravi, M., "Vibration response of viscoelastically coupled doublelayered viscoelastic graphene sheet systems subjected to magnetic field via strain gradient theory considering surface stress effects," Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 2014. ##[21] Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M., and Kolahchi, R., "Analytical modeling of wave propagation in viscoelastic functionally graded carbon nanotubes reinforced piezoelectric microplate under electromagnetic field," Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 2015. ##[22] Pan, Z., Cheng, Y., and Liu, J., "A semianalytical analysis of the elastic buckling of cracked thin plates under axial compression using actual nonuniform stress distribution," ThinWalled Structures, Vol. 73, pp. 229241, 2013. ##[23] Ghorbanpour Arani, A., Kolahchi, R., Mosayyebi, M., and Jamali, M., "Pulsating fluid induced dynamic instability of viscodoublewalled carbon nanotubes based on sinusoidal strain gradient theory using DQM and Bolotin method," International Journal of Mechanics and Materials in Design, pp. 122, 2014. ##[24] Reddy, J. N., "Mechanics of Laminated Composite Plates and Shells: Theory and Analysis," second edition ed: CRC Press, 2003. ##[25] Ghorbanpour Arani, A., Kolahchi, R., and Vossough, H., "Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory," Physica B: Condensed Matter, Vol. 407, pp. 44584465, 2012. ##[26] Lam, K. Y., Hung, K. C., and Chow, S. T., "Vibration analysis of plates with cutouts by the modified RayleighRitz method," Applied Acoustics, Vol. 28, pp. 4960, 1989. ##[27] Lam K. Y., and Hung, K. C., "Orthogonal polynomials and subsectioning method for vibration of plates," Computers & Structures, Vol. 34, pp. 827834, 1990. ##[28] Liew, K. M., Hung, K. C., and Lim, M. K., "Method of domain decomposition in vibrations of mixed edge anisotropic plates," International Journal of Solids and Structures, Vol. 30, pp. 32813301, 1993. ##[29] Liew, K. M., Hung, K. C., and Sum, Y. K., "Flexural vibration of polygonal plates: treatments of sharp reentrant corners," Journal of Sound and Vibration, Vol. 183, pp. 221238, 1995. ##[30] Liew, K. M., Kitipornchai, S., Leung, A. Y. T., and Lim, C. W., "Analysis of the free vibration of rectangular plates with central cutouts using the discrete Ritz method," International Journal of Mechanical Sciences, Vol. 45, pp. 941959, 2003. ##[31] Bhat, R. B., " Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleighritz method," Journal of Sound and Vibration, Vol. 102, pp. 493499, 1985. ##[32] Lam, K. Y., and Hung, K. C., "Vibration study on plates with stiffened openings using orthogonal polynomials and partitioning method," Computers & Structures, Vol. 37, pp. 295301, 1990. ##[33] Liew, K. M., Ng, T. Y., and Kitipornchai, S., "A semianalytical solution for vibration of rectangular plates with abrupt thickness variation," International Journal of Solids and Structures, Vol. 38, pp. 49374954, 2001. ##[34] Shams, S., and Soltani, B., "Buckling of Laminated Carbon NanotubeReinforced Composite Plates on Elastic Foundations Using a Meshfree Method," Arabian Journal for Science and Engineering, Vol. 41, pp. 19811993, 2016. ##[35] Pradhan, S. C., and Murmu, T., "Small scale effect on the buckling of singlelayered graphene sheets under biaxial compression via nonlocal continuum mechanics," Computational Materials Science, Vol. 47, pp. 268274, 2009.##]
Optimum Design of FGXCNTReinforced Reddy Pipes Conveying Fluid Subjected to Moving Load
2
2
The harmony search algorithm is applied to the optimum designs of functionally graded (FG)carbon nanotubes (CNTs)reinforced pipes conveying fluid which are subjected to a moving load. The structure is modeled by the Reddy cylindrical shell theory, and the motion equations are derived by Hamilton's principle. The dynamic displacement of the system is derived based on the differential quadrature method (DQM). Moreover, the length, thickness, diameter, velocity, and acceleration of the load, the temperature and velocity of the fluid, and the volume fraction of CNT are considered for the design variables. The results illustrate that the optimum diameter of the pipe is decreased by increasing the volume percentage of CNTs. In addition, by increasing the moving load velocity and acceleration, the FS is decreased.
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243
253


Farid
Vakili Tahami
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Faculty of Mechanical Engineering, University
Iran


Hasan
Biglari
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Faculty of Mechanical Engineering, University
Iran


Morteza
Raminnea
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Faculty of Mechanical Engineering, University
Iran
m.raminnia@tabrizu.ac.ir
Optimization
Pipe
Moving load
Conveying fluid
DQM
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Dynamic Buckling of Embedded Laminated Nanocomposite Plates Based on Sinusoidal Shear Deformation Theory
2
2
In this study, the dynamic buckling of the embedded laminated nanocomposite plates is investigated. The plates are reinforced with the singlewalled carbon nanotubes (SWCNTs), and the MoriTanaka model is applied to obtain the equivalent material properties of them. Based on the sinusoidal shear deformation theory (SSDT), the motion equations are derived using the energy method and Hamilton's principle. The Navier’s method is used in conjunction with the Bolotin's method for obtaining the dynamic instability region (DIR) of the structure. The effects of different parameters such as the volume percentage of SWCNTs, the number and orientation angle of the layers, the elastic medium, and the geometrical parameters of the plates are shown on DIR of the structure. Results indicate that by increasing the volume percentage of SWCNTs the resonance frequency increases, and DIR shifts to right. Moreover, it is found that the present results are in good agreement with the previous researches.
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Mohammd
Sharif Zarei
Faculty of Engineering, Ayatollah Boroujerdi University, Boroujerd, Iran
Faculty of Engineering, Ayatollah Boroujerdi
Iran


Mohammad Hadi
Hajmohammad
Department of mechanical engineering, Imam hossein University, Tehran, Iran
Department of mechanical engineering, Imam
Iran
hadi.hajmohammad@gmail.com


Ali
Nouri
Department of mechanical engineering, Imam hossein University, Tehran, Iran
Department of mechanical engineering, Imam
Iran
Dynamic buckling
Nanocomposite laminated plates
elastic medium
SSDT
Bolotin method
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