功能梯度碳纳米管增强复合材料结构建模与分析研究进展  
英文篇名  Modeling and analysis of functionally graded carbon nanotube reinforced composite structures: A review  期刊名称  力学进展  作者  沈惠申  摘要  功能梯度碳纳米管增强复合材料是一种新一代的先进复合材料.在这种材料中,碳纳米管作为增强体在空间位置上梯度排布.功能梯度碳纳米管增强复合材料的力学行为已成为近年来材料科学与工程科学的研究热点.本文对功能梯度碳纳米管增强复合材料结构的建模与分析的研究进展进行评述,集中讨论功能梯度碳纳米管增强复合材料梁、板、壳在各种载荷条件下,边界条件下和环境条件下的线性和非线性弯曲、屈曲和后屈曲、振动和动力响应.文中所列成果可以看作是进一步研究的基石.最后,提出需要进一步研究的方向.  英文摘要  Functionally graded carbon nanotube reinforced composite (FGCNTRC) is a new generation of advanced composite materials, where carbon nanotubes (CNTs) are used as the reinforcements in a functionally graded pattern. The mechanical behavior of FGCNTRC has emerged as one of the recent hot research topics in materials science and engineering. This paper presents a review of the developments in the modeling and analysis of FGCNTRC structures. The emphasis are put on the linear and nonlinear bending, buckling and postbuckling, and free and forced vibration of FGCNTRC beams, plates, shells and shell panels under various loading, boundary and environmental conditions. The presented progresses lay foundation for future studies in the area of FGCNTRC structures. Some critical aspects for further explorations are highlighted.  关键词  功能梯度材料; 碳纳米管增强复合材料; 弯曲; 屈曲; 振动  英文关键词  functionally graded materials; carbon nanotube reinforced composite; bending; buckling; vibration  参考文献  范镜泓, 陈海波. 2011. 非均质材料力学研究进展: 热点、焦点和生长点. 力学进展, 41: 615636 (Fan J H, Chen H B. 2011. Advances in heterogeneous material mechanics: cuttingedge and growing points. Advances in Mechanics, 41: 615636). 沈惠申. 2004. 功能梯度复合材料板壳结构的弯曲、屈曲和振动. 力学进展,34: 5360 (Shen H S. 2004. Bending, buckling and vibration of functionally graded plates and shells. Advances in Mechanics, 34: 5360). 沈惠申. 2012b. 结构非线性分析的二次摄动法. 北京: 高等教育出版社(Shen H S. 2012b. A TwoStep Perturbation Method in Nonlinear Analysis of Structures. Beijing: Higher Education Press). 沈惠申. 2014b. 板壳后屈曲行为(第二版). 上海: 上海科学技术出版社(Shen H S. 2014b. Postbuckling Behavior of Plates and Shells (2nd Edition). Shanghai: Shanghai Science & Technological Press). Ajayan P M, Stephan O, Colliex C, Trauth D. 1994. Aligned carbon nanotube arrays formed by cutting a polymer resinnanotube composite. Science, 265: 12121214. Alibeigloo A. 2013a. Static analysis of functionally graded carbon nanotubereinforced composite plate embedded in piezoelectric layers by using theory of elasticity. Composite Structures, 95: 612622. Alibeigloo A. 2013b. Elasticity solution of functionally graded carbonnanotubereinforced composite cylin drical panel with piezoelectric sensor and actuator layers. Smart Materials & Structures, 22: 075013. Alibeigloo A. 2014a. Threedimensional thermoelasticity solution of functionally graded carbon nanotube reinforced composite plate embedded in piezoelectric sensor and actuator layers. Composite Structures, 118: 482495. Alibeigloo A. 2014b. Free vibration analysis of functionally graded carbon nanotubereinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity. European Journal of Mechanics ASolids, 44: 104115. Alibeigloo A. 2016. Elasticity solution of functionally graded carbon nanotubereinforced composite cylin drical panel subjected to thermo mechanical load. Composites Part B, 87: 214226 Alibeigloo A, Emtehani A. 2015. Static and free vibration analyses of carbon nanotubereinforced omposite plate using di®erential quadrature method. Meccanica, 50: 6176. Alibeigloo A, Liew K M. 2013. Thermoelastic analysis of functionally graded carbon nanotubereinforced composite plate using theory of elasticity. Composite Structures, 106: 873881. Alibeigloo A, Liew K M. 2015. Elasticity Solution of free vibration and bending behavior of function ally graded carbon nanotubereinforced composite beam with thin piezoelectric layers using di®erential quadrature method. International Journal of Applied Mechanics, 7: 1550002. Ansari R, Hasrati E, Shojaei M F, Gholami R, Shahabodini A. 2015. Forced vibration analysis of functionally graded carbon nanotubereinforced composite plates using a numerical strategy. Physica E, 69: 294305. Ansari R, Pourashraf T, Gholami R, Shahabodini A. 2016a. Analytical solution for nonlinear postbuckling of functionally graded carbon nanotubereinforced composite shells with piezoelectric layers. Composites Part B, 90: 267277. Ansari R, Shahabodini A, Faghih Shojaei M. 2016b. Vibrational analysis of carbon nanotubereinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity. Composite Structures, 139: 167187. Ansari R, Shojaei M F, Mohammadi V, Gholami R, Sadeghi F. 2014. Nonlinear forced vibration analysis of functionally graded carbon nanotubereinforced composite Timoshenko beams. Composite Structures, 113: 316327. Aragh B S, Barati A H N, Hedayati H. 2012. EshelbyMoriTanaka approach for vibrational behavior of continuously graded carbon nanotubereinforced cylindrical panels. Composites Part B, 43: 19431954. Aragh B S, Farahani E B, Barati A H N. 2013. Natural frequency analysis of continuously graded carbon nanotubereinforced cylindrical shells based on thirdorder shear deformation theory. Mathematics and Mechanics of Solids, 18: 264284. Ashrafi B, Hubert P, Vengallatore S. 2006. Carbon nanotubereinforced composites as structural materials for microactuators in microelectromechanical systems. Nanotechnology, 17: 48954903. Bagchi A, Nomura S. 2006. On the e®ective thermal conductivity of carbon nanotube reinforced polymer composites. Composites Science and Technology, 66: 17031712. Bakhti K, Kaci A, Bousahla A A, Houari M S A, Tounsi A, Bedia E A A. 2013. Large deformation analysis for functionally graded carbon nanotubereinforced composite plates using an e±cient and simple refined theory. Steel and Composite Structures, 14: 335347. Bidgoli M R, Karimi M S, Arani A G. 2016. Nonlinear vibration and instability analysis of functionally graded CNTreinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium. Mechanics of Advanced Materials and Structures, 23: 819831. Birman V, Byrd L W. 2007. Modeling and Analysis of Functionally Graded Materials and Structures. Applied Mechanics Reviews, 60: 195216. Chatterjee S N, Kulkarni S V. 1979. Shear correction factors for laminated plates. AIAA Journal, 17: 498499. Efraim E, Eisenberger M. 2007. Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. Journal of Sound and Vibration, 299: 720738. Fan Y, Wang H. 2015. Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments. Composite Structures, 124: 3543. Fan Y, Wang H. 2016a. Nonlinear bending and postbuckling analysis of matrix cracked hybrid laminated plates containing carbon nanotube reinforced composite layers in thermal environments. Composites Part B, 86: 116. Fan Y, Wang H. 2016b. Nonlinear dynamics of matrixcracked hybrid laminated plates containing carbon nanotubereinforced composite layers resting on elastic foundations. Nonlinear Dynamics, 84: 11811199. Farahani R D, Dalir H, Le Borgne V, Gautier L A, El Khakani M A, Levesque M, Therriault D. 2012. Directwrite fabrication of freestanding nanocomposite strain sensors. Nanotechnology, 23: 085502. Fazelzadeh S A, Pouresmaeeli S, Ghavanloo E. 2015. Aeroelastic characteristics of functionally graded carbon nanotubereinforced composite plates under a supersonic flow. Computer Methods in Applied Mechanics and Engineering, 285: 714729. Feldman E, Aboudi J. 1997. Buckling analysis of functionally graded plates subjected to uniaxial loading. Composite Structures, 38: 2936. GarcíaMacías E, CastroTriguero R, Saavedra Flores E I, Friswell M I, Gallego R. 2016. Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates. Composite Structures, 140: 473490. Ghayoumizadeh H, Shahabian F, Hosseini S M. 2013. Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs). En gineering Analysis with Boundary Elements, 37: 15241531. Ghouhestani S, Shahabian F, Hosseini S M. 2014. Dynamic analysis of a layered cylinder reinforced by functionally graded carbon nanotubes distributions subjected to shock loading using MLPG method. CMESComputer Modeling in Engineering & Sciences, 100: 295321. Griebel M, Hamaekers J. 2004. Molecular dynamics simulations of the elastic moduli of polymercarbon nanotube composites. Computer Methods in Applied Mechanics and Engineering, 193: 17731788. Haggenmueller R, Gommans H H, Rinzler A G, Fischer J E, Winey K I. 2000. Aligned singlewall carbon nanotubes in composites by melt processing methods. Chemical Physics Letters, 330: 219225. Han Y, Elliott J. 2007. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Computational Materials Science, 39: 315323. Hedayati H, Aragh B S. 2012. Influence of graded agglomerated CNTs on vibration of CNTreinforced annular sectorial plates resting on Pasternak foundation. Applied Mathematics and Computation, 218: 87158735. Heydari M M, Bidgoli A H, Golshani H R, Beygipoor G, Davoodi A. 2015. Nonlinear bending analysis of functionally graded CNTreinforced composite Mindlin polymeric temperaturedependent plate resting on orthotropic elastomeric medium using GDQM. Nonlinear Dynamics, 79: 14251441. Heydarpour Y, Aghdam M M, Malekzadeh P. 2014. Free vibration analysis of rotating functionally graded carbon nanotubereinforced composite truncated conical shells. Composite Structures, 117: 187200. Hosseini S M. 2013. Application of a hybrid meshfree method based on generalized finite di®erence (GFD) method for natural frequency analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotubes. CMESComputer Modeling in Engineering & Sciences, 95: 129. Iijima S. 1991. Helical microtubules of graphitic carbon. Nature, 354: 5658. Jam J E, Kiani Y. 2015a. Buckling of pressurized functionally graded carbon nanotube reinforced conical shells. Composite Structures, 125: 586595. Jam J E, Kiani Y. 2015b. Low velocity impact response of functionally graded carbon nanotube reinforced composite beams in thermal environment. Composite Structures, 132: 3543. Kaci A, Tounsi A, Bakhti K, Bedia E A. 2012. Nonlinear cylindrical bending of functionally graded carbon nanotubereinforced composite plates. Steel and Composite Structures, 12: 491504. Kamarian S, Pourasghar A, Yas M H. 2013. EshelbyMoriTanaka approach for vibrational behavior of functionally graded carbon nanotubereinforced plate resting on elastic foundation. Journal of Mechanical Science and Technology, 27: 33953401. Ke L L, Yang J, Kitipornchai S. 2010. Nonlinear free vibration of functionally graded carbon nanotube reinforced composite beams. Composite Structures, 92: 676683. Ke L L, Yang J, Kitipornchai S. 2013. Dynamic stability of functionally graded carbon nanotubereinforced composite beams. Mechanics of Advanced Materials and Structures, 20: 2837. Kwon H, Bradbury C R, Leparoux M. 2011. Fabrication of functionally graded carbon nanotubereinforced aluminum matrix composite. Advanced Engineering Materials, 13: 325329. Lau K T, Hui D. 2002. The revolutionary creation of new advanced materialscarbon nanotube composites. Composites Part B, 33: 263277. Lei Z X, Liew K M, Yu J L. 2013a. Large deflection analysis of functionally graded carbon nanotube reinforced composite plates by the elementfree kpRitz method. Computer Methods in Applied Mechanics and Engineering, 256: 189199. Lei Z X, Liew K M, Yu J L. 2013b. Buckling analysis of functionally graded carbon nanotubereinforced composite plates using the elementfree kpRitz method. Composite Structures, 98: 160168. Lei Z X, Liew K M, Yu J L. 2013c. Free vibration analysis of functionally graded carbon nanotubereinforced composite plates using the elementfree kpRitz method in thermal environment. Composite Structures, 106: 128138. Lei Z X, Yu J L, Liew K M. 2013d. Free vibration analysis of functionally graded carbon nanotubereinforced composite cylindrical panels. International Journal of Materials Science and Engineering, 1: 3640. Lei Z X, Zhang L W, Liew K M, Yu J L. 2014. Dynamic stability analysis of carbon nanotubereinforced functionally graded cylindrical panels using the elementfree kpRitz method. Composite Structures, 113: 328338. Lei Z X, Zhang L W, Liew K M. 2015a. Free vibration analysis of laminated FGCNT reinforced composite rectangular plates using the kpRitz method. Composite Structures, 127: 245259. Lei Z X, Zhang L W, Liew K M. 2015b. Vibration analysis of CNTreinforced functionally graded otating cylindrical panels using the elementfree kpRitz method. Composites Part B, 77: 291303. Lei Z X, Zhang L W, Liew K M. 2015c. Elastodynamic analysis of carbon nanotubereinforced functionally graded plates. International Journal of Mechanical Sciences, 99: 208217. Lei Z X, Zhang L W, Liew K M. 2015d. Buckling of FGCNT reinforced composite thick skew plates resting on Pasternak foundations based on an elementfree approach. Applied Mathematics and Computation, 266: 773791. Lei Z X, Zhang L W, Liew K M. 2016a. Analysis of laminated CNT reinforced functionally graded plates using the elementfree kpRitz method. Composites Part B, 84: 211221. Lei Z X, Zhang L W, Liew K M. 2016b. Vibration of FGCNT reinforced composite thick quadrilateral plates resting on Pasternak foundations. Engineering Analysis with Boundary Elements, 64: 111. Lei Z X, Zhang L W, Liew K M. 2016c. Parametric analysis of frequency of rotating laminated CNT reinforced functionally graded cylindrical panels. Composites Part B, 90: 251266. Levinson M. 1981. A new rectangular beam theory. Journal of Sound and Vibration, 74: 8187. Liew K M, Lei Z X, Yu J L, Zhang L W. 2014. Postbuckling of carbon nanotubereinforced functionally graded cylindrical panels under axial compression using a meshless approach. Computer Methods in Applied Mechanics and Engineering, 268: 117. Liew K M, Lei Z X, Zhang L W. 2015. Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review. Composite Structures, 120: 9097. Lin F, Xiang Y. 2014a. Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories. Applied Mathematical Modelling, 38: 37413754. Lin F, Xiang Y. 2014b. Numerical analysis on nonlinear free vibration of carbon nanotube reinforced composite beams. International Journal of Structural Stability and Dynamics, 14: 1350056. Malekzadeh P, Shojaee M. 2013. Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers. ThinWalled Structures, 71: 108118. Malekzadeh P, Dehbozorgi M. 2016. Low velocity impact analysis of functionally graded carbon nanotubes reinforced composite skew plates. Composite Structures, 140: 728748. Malekzadeh P, Heydarpour Y. 2015. Mixed Navierlayerwise di®erential quadrature threedimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates. Meccanica, 50: 143167. Malekzadeh P, Dehbozorgi M, Monajjemzadeh S M. 2015. Vibration of functionally graded carbon nanotube reinforced composite plates under a moving load. Science and Engineering of Composite Materials, 22: 3755. Mayandi K, Jeyaraj P. 2015. Bending, buckling and free vibration characteristics of FGCNTreinforced polymer composite beam under nonuniform thermal load. Proceedings of the Institution of Mechanical Engineers Part LJournal of Materials Design and Applications, 229: 1328. Meguid S A, Sun Y. 2004. On the tensile and shear strength of nanoreinforced composite interfaces. Materials and Design, 25: 289296. Mehar K, Panda S K. 2016. Geometrical nonlinear free vibration analysis of FGCNT reinforced composite flat panel under uniform thermal field. Composite Structures, 143: 336346. Mehar K, Panda S K, Dehengia A, Kar V R. 2016. Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment. Journal of Sandwich Structures & Materials, 18: 151 173. Mehrabadi S J, Aragh B S. 2014. Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes. ThinWalled Structures, 80: 130141. Mehrabadi S J, Aragh B S, Khoshkhahesh V, Taherpour A. 2012. Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight singlewalled carbon nanotubes. Composites Part B, 43: 20312040. Mehrabadi S J, Sobhaniaragh B, Pourdonya V. 2013. Free vibration analysis of nanocomposite plates reinforced by graded carbon nanotubes based on firstorder shear deformation plate theory. Advances in Applied Mathematics and Mechanics, 5: 90112. Mehri M, Asadi H, Wang Q. 2016. Buckling and vibration analysis of a pressurized CNT reinforced function ally graded truncated conical shell under an axial compression using HDQ method. Computer Methods in Applied Mechanics and Engineering, 303: 75100. Mirzaei M, Kiani Y. 2015a. Snapthrough phenomenon in a thermally postbuckled temperature dependent sandwich beam with FGCNTRC face sheets. Composite Structures, 134: 10041013. Mirzaei M, Kiani Y. 2015b. Thermal buckling of temperature dependent FGCNT reinforced composite conical shells. Aerospace Science and Technology, 47: 4253. Mirzaei M, Kiani Y. 2016. Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels. Composite Structures, 142: 4556. MoradiDastjerdi R, Foroutan M, Pourasghar A, SotoudehBahreini R. 2013a. Static analysis of functionally graded carbon nanotubereinforced composite cylinders by a meshfree method. Journal of Reinforced Plastics and Composite, 32: 593601. MoradiDastjerdi R, Foroutan M, Pourasghar A. 2013b. Dynamic analysis of functionally graded nanocom posite cylinders reinforced by carbon nanotube by a meshfree method. Materials & Design, 44: 256266. MoradiDastjerdi R, Pourasghar A, Foroutan M. 2013c. The e®ects of carbon nanotube orientation and ag gregation on vibrational behavior of functionally graded nanocomposite cylinders by a meshfree method. Acta Mechanica, 224: 28172832. NamiMR, Janghorban M. 2015. Free vibration of thick functionally graded carbon nanotubereinforced rect angular composite plates based on threedimensional elasticity theory via di®erential quadrature method. Advanced Composite Materials, 24: 439450. Nan C W, Shi Z, Lin Y. 2003. A simple model for thermal conductivity of carbon nanotubebased composites. Chemical Physics Letters, 375: 666669. Natarajan S, Haboussi M, Manickam G. 2014. Application of higherorder structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Composite Structures, 113: 197207. PhungVan P, AbdelWahab M, Liew K M, Bordas S P A, NguyenXuan H. 2015. Isogeometric analysis of functionally graded carbon nanotubereinforced composite plates using higherorder shear deformation theory. Composite Structures, 123: 137149. Popov V N, Doren V E, Balkanski M. 2000. Elastic Properties of crystals of singlewalled carbon nanotubes. Solid State Communications, 114: 395399. Pourasghar A, Yas M H, Kamarian S. 2013. Local aggregation e®ect of CNT on the vibrational behavior of fourparameter continuous grading nanotubereinforced cylindrical panels. Polymer Composites, 34: 707721. Qatu M S, Leissa A W. 1993. Buckling or transverse deformations of unsymmetrically laminated plates subjected to inplane loads. AIAA Journal, 31: 189194. Qian D, Dickey E C, Andrews R, Rantell T. 2000. Load transfer and deformation mechanisms in carbon nanotubepolystyrene composites. Applied PhysicsLetters, 76: 28682870. Rafiee M, He X Q, Liew K M. 2014. Nonlinear dynamic stability of piezoelectric functionally graded carbon nanotubereinforced composite plates with initial geometric imperfection. International Journal of NonLinear Mechanics, 59: 3751. Rafiee M, Yang J, Kitipornchai S. 2013a. Large amplitude vibration of carbon nanotube reinforced func tionally graded composite beams with piezoelectric layers. Composite Structures, 96: 716725. Rafiee M, Yang J, Kitipornchai S. 2013b. Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams. Computers & Mathematics with Applications, 66: 11471160. Rashidifar M A, Ahmadi D. 2015. Vibration analysis of randomly oriented carbon nanotube based on FGM beam using Timoshenko theory. Advances in Mechanical Engineering, 7: 653950. Reddy J N. 1984. A simple higherorder theory for laminated composite plates. Journal of Applied Me chanics ASME, 51: 745752. Reddy J N. 2003. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (2nd Edition). Boca Raton, FL: CRC Press. Reddy J N, Liu C F. 1985. A higherorder shear deformation theory of laminated elastic shells. International Journal of Engineering Science, 23: 319330. Salami S J. 2016. Extended high order sandwich panel theory for bending analysis of sandwich beams with carbon nanotube reinforced face sheets. Physica E, 76: 187197. Sankar A, Natarajan S, Haboussi M, Ramajeyathilagam K, Ganapathi M. 2014. Panel flutter characteristics of sandwich plates with CNT reinforced facesheets using an accurate higherorder theory. Journal of Fluids and Structures, 50: 376391. Sankar A, Natarajan S, Ben Zineb T, Ganapathi M. 2015. Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higherorder structural theory. Composite Structures, 127: 340355. Shahrbabaki E A, Alibeigloo A. 2014. Threedimensional free vibration of carbon nanotubereinforced composite plates with various boundary conditions using Ritz method. Composite Structures, 111: 362 370. Shen H S. 1997. Kíarmíantype equations for a higherorder shear deformation plate theory and its use in the thermal postbuckling analysis. Applied Mathematics and Mechanics, 18: 1137115242. Shen H S. 2002. Postbuckling of axially loaded sheardeformable laminated cylindrical panels. Journal of Strain Analysis for Engineering Design, 37: 413425.  年  2016  卷  46  期  1  开始页码  478  结束页码  505  DOI  10.6052/1000099216007  点击率  885  作者地址  上海交通大学航天航空学院, 上海 200240  英文作者  SHEN HuiSheny  英文作者地址  School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China 
