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

沈惠申

doi:10.6052/1000-0992-16-007

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

doi: 10.6052/1000-0992-16-007

沈惠申

上海交通大学航天航空学院, 上海 200240

详细信息

通讯作者:
沈惠申,上海交通大学应用力学教授.1970年2月毕业于清华大学工程力学数学系.1986年4月于上海交通大学获博士学位.1991年5月至1992年11月留学英国Wales大学(Cardiff)和Liverpool大学.1992年底回国任教授.1995年至2015年曾多次在英国Cardiff大学、香港理工大学、香港城市大学、新加坡南洋理工大学、日本静冈大学、澳大利亚西悉尼大学和加拿大约克大学作访问教授.主要研究领域为先进复合材料结构非线性分析,纳米力学和细胞生物力学.已出版中英文专著5部,在国内外重要学术期刊上发表研究论文280余篇.研究成果已被280余种国际学术期刊2000余篇论文他引4400余次.总他引6800余次.根据Webof Science,沈惠申的"h-index"为41(截止到2016.4).目前是JSPS Fellow,Composite Structures等7种国际期刊编委.80余种国际学术期刊特邀论文评审专家.

中图分类号: TB332
计量
- 文章访问数: 2178
- HTML全文浏览量: 268
- PDF下载量: 2344
- 被引次数: 0
出版历程
- 收稿日期: 2016-02-22
- 修回日期: 2016-04-21
- 刊出日期: 2016-05-20

Modeling and analysis of functionally graded carbon nanotube reinforced composite structures: A review

SHEN Hui-Sheny

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

More Information

Corresponding author: SHEN Hui-Sheny

摘要

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.
- 功能梯度材料 /
- 碳纳米管增强复合材料 /
- 弯曲 /
- 屈曲 /
- 振动
Abstract: Functionally graded carbon nanotube reinforced composite (FG-CNTRC) 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 FG-CNTRC 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 FG-CNTRC structures. The emphasis are put on the linear and nonlinear bending, buckling and postbuckling, and free and forced vibration of FG-CNTRC 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 FG-CNTRC structures. Some critical aspects for further explorations are highlighted.
- functionally graded materials /
- carbon nanotube reinforced composite /
- bending /
- buckling /
- vibration

HTML全文

参考文献(181)

[1]	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: 615-636 (Fan J H, Chen H B. 2011. Advances in heterogeneous material mechanics: cutting-edge and growing points.
[2]	Advances in Mechanics, 41: 615-636). 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: 53-60 (Shen H S. 2004. Bending, buckling and vibration of functionally graded plates and shells. Advances in Mechanics, 34: 53-60).
[3]	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 Two-Step Perturbation Method in Nonlinear Analysis of Structures. Beijing: Higher Education Press).
[4]	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).
[5]	Ajayan P M, Stephan O, Colliex C, Trauth D. 1994. Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite. Science, 265: 1212-1214.
[6]	Alibeigloo A. 2013a. Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity. Composite Structures, 95: 612-622.
[7]	Alibeigloo A. 2013b. Elasticity solution of functionally graded carbon-nanotube-reinforced composite cylin- drical panel with piezoelectric sensor and actuator layers. Smart Materials & Structures, 22: 075013.
[8]	Alibeigloo A. 2014a. Three-dimensional thermoelasticity solution of functionally graded carbon nanotube reinforced composite plate embedded in piezoelectric sensor and actuator layers. Composite Structures, 118: 482-495.
[9]	Alibeigloo A. 2014b. Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity. European Journal of Mechanics A-Solids, 44: 104-115.
[10]	Alibeigloo A. 2016. Elasticity solution of functionally graded carbon nanotube-reinforced composite cylin- drical panel subjected to thermo mechanical load. Composites Part B, 87: 214-226
[11]	Alibeigloo A, Emtehani A. 2015. Static and free vibration analyses of carbon nanotube-reinforced omposite plate using di®erential quadrature method. Meccanica, 50: 61-76.
[12]	Alibeigloo A, Liew K M. 2013. Thermoelastic analysis of functionally graded carbon nanotube-reinforced composite plate using theory of elasticity. Composite Structures, 106: 873-881.
[13]	Alibeigloo A, Liew K M. 2015. Elasticity Solution of free vibration and bending behavior of function- ally graded carbon nanotube-reinforced composite beam with thin piezoelectric layers using di®erential quadrature method. International Journal of Applied Mechanics, 7: 1550002.
[14]	Ansari R, Hasrati E, Shojaei M F, Gholami R, Shahabodini A. 2015. Forced vibration analysis of functionally graded carbon nanotube-reinforced composite plates using a numerical strategy. Physica E, 69: 294-305.
[15]	Ansari R, Pourashraf T, Gholami R, Shahabodini A. 2016a. Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers. Composites Part B, 90: 267-277.
[16]	Ansari R, Shahabodini A, Faghih Shojaei M. 2016b. Vibrational analysis of carbon nanotube-reinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity. Composite Structures, 139: 167-187.
[17]	Ansari R, Shojaei M F, Mohammadi V, Gholami R, Sadeghi F. 2014. Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams. Composite Structures, 113: 316-327.
[18]	Aragh B S, Barati A H N, Hedayati H. 2012. Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels. Composites Part B, 43: 1943-1954.
[19]	Aragh B S, Farahani E B, Barati A H N. 2013. Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory. Mathematics and Mechanics of Solids, 18: 264-284.
[20]	Ashrafi B, Hubert P, Vengallatore S. 2006. Carbon nanotube-reinforced composites as structural materials for microactuators in microelectromechanical systems. Nanotechnology, 17: 4895-4903.
[21]	Bagchi A, Nomura S. 2006. On the e®ective thermal conductivity of carbon nanotube reinforced polymer composites. Composites Science and Technology, 66: 1703-1712.
[22]	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 nanotube-reinforced composite plates using an e±cient and simple refined theory. Steel and Composite Structures, 14: 335-347.
[23]	Bidgoli M R, Karimi M S, Arani A G. 2016. Nonlinear vibration and instability analysis of functionally graded CNT-reinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium. Mechanics of Advanced Materials and Structures, 23: 819-831.
[24]	Birman V, Byrd L W. 2007. Modeling and Analysis of Functionally Graded Materials and Structures. Applied Mechanics Reviews, 60: 195-216.
[25]	Chatterjee S N, Kulkarni S V. 1979. Shear correction factors for laminated plates. AIAA Journal, 17: 498-499.
[26]	Efraim E, Eisenberger M. 2007. Exact vibration analysis of variable thickness thick annular isotropic and
[27]	FGM plates. Journal of Sound and Vibration, 299: 720-738.
[28]	Fan Y, Wang H. 2015. Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments. Composite Structures, 124: 35-43.
[29]	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: 1-16.
[30]	Fan Y, Wang H. 2016b. Nonlinear dynamics of matrix-cracked hybrid laminated plates containing carbon nanotube-reinforced composite layers resting on elastic foundations. Nonlinear Dynamics, 84: 1181-1199.
[31]	Farahani R D, Dalir H, Le Borgne V, Gautier L A, El Khakani M A, Levesque M, Therriault D. 2012. Direct-write fabrication of freestanding nanocomposite strain sensors. Nanotechnology, 23: 085502.
[32]	Fazelzadeh S A, Pouresmaeeli S, Ghavanloo E. 2015. Aeroelastic characteristics of functionally graded carbon nanotube-reinforced composite plates under a supersonic flow. Computer Methods in Applied Mechanics and Engineering, 285: 714-729.
[33]	Feldman E, Aboudi J. 1997. Buckling analysis of functionally graded plates subjected to uniaxial loading. Composite Structures, 38: 29-36.
[34]	García-Macías E, Castro-Triguero 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: 473-490.
[35]	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: 1524-1531.
[36]	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. CMES-Computer Modeling in Engineering & Sciences, 100: 295-321.
[37]	Griebel M, Hamaekers J. 2004. Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites. Computer Methods in Applied Mechanics and Engineering, 193: 1773-1788.
[38]	Haggenmueller R, Gommans H H, Rinzler A G, Fischer J E, Winey K I. 2000. Aligned single-wall carbon nanotubes in composites by melt processing methods. Chemical Physics Letters, 330: 219-225.
[39]	Han Y, Elliott J. 2007. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Computational Materials Science, 39: 315-323.
[40]	Hedayati H, Aragh B S. 2012. Influence of graded agglomerated CNTs on vibration of CNT-reinforced annular sectorial plates resting on Pasternak foundation. Applied Mathematics and Computation, 218: 8715-8735.
[41]	Heydari M M, Bidgoli A H, Golshani H R, Beygipoor G, Davoodi A. 2015. Nonlinear bending analysis of functionally graded CNT-reinforced composite Mindlin polymeric temperature-dependent plate resting on orthotropic elastomeric medium using GDQM. Nonlinear Dynamics, 79: 1425-1441.
[42]	Heydarpour Y, Aghdam M M, Malekzadeh P. 2014. Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells. Composite Structures, 117: 187-200.
[43]	Hosseini S M. 2013. Application of a hybrid mesh-free method based on generalized finite di®erence (GFD) method for natural frequency analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotubes. CMES-Computer Modeling in Engineering & Sciences, 95: 1-29.
[44]	Iijima S. 1991. Helical microtubules of graphitic carbon. Nature, 354: 56-58.
[45]	Jam J E, Kiani Y. 2015a. Buckling of pressurized functionally graded carbon nanotube reinforced conical shells. Composite Structures, 125: 586-595.
[46]	Jam J E, Kiani Y. 2015b. Low velocity impact response of functionally graded carbon nanotube reinforced composite beams in thermal environment. Composite Structures, 132: 35-43.
[47]	Kaci A, Tounsi A, Bakhti K, Bedia E A. 2012. Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates. Steel and Composite Structures, 12: 491-504.
[48]	Kamarian S, Pourasghar A, Yas M H. 2013. Eshelby-Mori-Tanaka approach for vibrational behavior of functionally graded carbon nanotube-reinforced plate resting on elastic foundation. Journal of Mechanical Science and Technology, 27: 3395-3401.
[49]	Ke L L, Yang J, Kitipornchai S. 2010. Nonlinear free vibration of functionally graded carbon nanotube- reinforced composite beams. Composite Structures, 92: 676-683.
[50]	Ke L L, Yang J, Kitipornchai S. 2013. Dynamic stability of functionally graded carbon nanotube-reinforced composite beams. Mechanics of Advanced Materials and Structures, 20: 28-37.
[51]	Kwon H, Bradbury C R, Leparoux M. 2011. Fabrication of functionally graded carbon nanotube-reinforced aluminum matrix composite. Advanced Engineering Materials, 13: 325-329.
[52]	Lau K T, Hui D. 2002. The revolutionary creation of new advanced materials-carbon nanotube composites. Composites Part B, 33: 263-277.
[53]	Lei Z X, Liew K M, Yu J L. 2013a. Large deflection analysis of functionally graded carbon nanotube- reinforced composite plates by the element-free kp-Ritz method. Computer Methods in Applied Mechanics and Engineering, 256: 189-199.
[54]	Lei Z X, Liew K M, Yu J L. 2013b. Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Composite Structures, 98: 160-168.
[55]	Lei Z X, Liew K M, Yu J L. 2013c. Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Composite Structures, 106: 128-138.
[56]	Lei Z X, Yu J L, Liew K M. 2013d. Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panels. International Journal of Materials Science and Engineering, 1: 36-40.
[57]	Lei Z X, Zhang L W, Liew K M, Yu J L. 2014. Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method. Composite Structures, 113: 328-338.
[58]	Lei Z X, Zhang L W, Liew K M. 2015a. Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method. Composite Structures, 127: 245-259.
[59]	Lei Z X, Zhang L W, Liew K M. 2015b. Vibration analysis of CNT-reinforced functionally graded otating cylindrical panels using the element-free kp-Ritz method. Composites Part B, 77: 291-303.
[60]	Lei Z X, Zhang L W, Liew K M. 2015c. Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates. International Journal of Mechanical Sciences, 99: 208-217.
[61]	Lei Z X, Zhang L W, Liew K M. 2015d. Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach. Applied Mathematics and Computation, 266: 773-791.
[62]	Lei Z X, Zhang L W, Liew K M. 2016a. Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method. Composites Part B, 84: 211-221.
[63]	Lei Z X, Zhang L W, Liew K M. 2016b. Vibration of FG-CNT reinforced composite thick quadrilateral plates resting on Pasternak foundations. Engineering Analysis with Boundary Elements, 64: 1-11.
[64]	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: 251-266.
[65]	Levinson M. 1981. A new rectangular beam theory. Journal of Sound and Vibration, 74: 81-87.
[66]	Liew K M, Lei Z X, Yu J L, Zhang L W. 2014. Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach. Computer Methods in Applied Mechanics and Engineering, 268: 1-17.
[67]	Liew K M, Lei Z X, Zhang L W. 2015. Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review. Composite Structures, 120: 90-97.
[68]	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: 3741-3754.
[69]	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.
[70]	Malekzadeh P, Shojaee M. 2013. Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers. Thin-Walled Structures, 71: 108-118.
[71]	Malekzadeh P, Dehbozorgi M. 2016. Low velocity impact analysis of functionally graded carbon nanotubes reinforced composite skew plates. Composite Structures, 140: 728-748.
[72]	Malekzadeh P, Heydarpour Y. 2015. Mixed Navier-layerwise di®erential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates.
[73]	Meccanica, 50: 143-167.
[74]	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: 37-55.
[75]	Mayandi K, Jeyaraj P. 2015. Bending, buckling and free vibration characteristics of FG-CNT-reinforced polymer composite beam under non-uniform thermal load. Proceedings of the Institution of Mechanical Engineers Part L-Journal of Materials Design and Applications, 229: 13-28.
[76]	Meguid S A, Sun Y. 2004. On the tensile and shear strength of nano-reinforced composite interfaces.
[77]	Materials and Design, 25: 289-296.
[78]	Mehar K, Panda S K. 2016. Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field. Composite Structures, 143: 336-346.
[79]	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.
[80]	Mehrabadi S J, Aragh B S. 2014. Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes. Thin-Walled Structures, 80: 130-141.
[81]	Mehrabadi S J, Aragh B S, Khoshkhahesh V, Taherpour A. 2012. Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes. Composites Part B, 43: 2031-2040.
[82]	Mehrabadi S J, Sobhaniaragh B, Pourdonya V. 2013. Free vibration analysis of nanocomposite plates reinforced by graded carbon nanotubes based on first-order shear deformation plate theory. Advances in
[83]	Applied Mathematics and Mechanics, 5: 90-112.
[84]	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: 75-100.
[85]	Mirzaei M, Kiani Y. 2015a. Snap-through phenomenon in a thermally postbuckled temperature dependent sandwich beam with FG-CNTRC face sheets. Composite Structures, 134: 1004-1013.
[86]	Mirzaei M, Kiani Y. 2015b. Thermal buckling of temperature dependent FG-CNT reinforced composite conical shells. Aerospace Science and Technology, 47: 42-53.
[87]	Mirzaei M, Kiani Y. 2016. Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels. Composite Structures, 142: 45-56.
[88]	Moradi-Dastjerdi R, Foroutan M, Pourasghar A, Sotoudeh-Bahreini R. 2013a. Static analysis of functionally graded carbon nanotube-reinforced composite cylinders by a mesh-free method. Journal of Reinforced Plastics and Composite, 32: 593-601.
[89]	Moradi-Dastjerdi R, Foroutan M, Pourasghar A. 2013b. Dynamic analysis of functionally graded nanocom- posite cylinders reinforced by carbon nanotube by a mesh-free method. Materials & Design, 44: 256-266.
[90]	Moradi-Dastjerdi 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 mesh-free method. Acta Mechanica, 224: 2817-2832.
[91]	NamiMR, Janghorban M. 2015. Free vibration of thick functionally graded carbon nanotube-reinforced rect- angular composite plates based on three-dimensional elasticity theory via di®erential quadrature method. Advanced Composite Materials, 24: 439-450.
[92]	Nan C W, Shi Z, Lin Y. 2003. A simple model for thermal conductivity of carbon nanotube-based composites. Chemical Physics Letters, 375: 666-669.
[93]	Natarajan S, Haboussi M, Manickam G. 2014. Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Composite Structures, 113: 197-207.
[94]	Phung-Van P, Abdel-Wahab M, Liew K M, Bordas S P A, Nguyen-Xuan H. 2015. Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory. Composite Structures, 123: 137-149.
[95]	Popov V N, Doren V E, Balkanski M. 2000. Elastic Properties of crystals of single-walled carbon nanotubes. Solid State Communications, 114: 395-399.
[96]	Pourasghar A, Yas M H, Kamarian S. 2013. Local aggregation e®ect of CNT on the vibrational behavior of four-parameter continuous grading nanotube-reinforced cylindrical panels. Polymer Composites, 34: 707-721.
[97]	Qatu M S, Leissa A W. 1993. Buckling or transverse deformations of unsymmetrically laminated plates subjected to in-plane loads. AIAA Journal, 31: 189-194.
[98]	Qian D, Dickey E C, Andrews R, Rantell T. 2000. Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Applied PhysicsLetters, 76: 2868-2870.
[99]	Rafiee M, He X Q, Liew K M. 2014. Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection. International Journal of Non-Linear Mechanics, 59: 37-51.
[100]	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: 716-725.
[101]	Rafiee M, Yang J, Kitipornchai S. 2013b. Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams. Computers & Mathematics with Applications, 66: 1147-1160.
[102]	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.
[103]	Reddy J N. 1984. A simple higher-order theory for laminated composite plates. Journal of Applied Me- chanics ASME, 51: 745-752.
[104]	Reddy J N. 2003. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (2nd Edition). Boca Raton, FL: CRC Press.
[105]	Reddy J N, Liu C F. 1985. A higher-order shear deformation theory of laminated elastic shells. International Journal of Engineering Science, 23: 319-330.
[106]	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: 187-197.
[107]	Sankar A, Natarajan S, Haboussi M, Ramajeyathilagam K, Ganapathi M. 2014. Panel flutter characteristics of sandwich plates with CNT reinforced facesheets using an accurate higher-order theory. Journal of Fluids and Structures, 50: 376-391.
[108]	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 higher-order structural theory. Composite Structures, 127: 340-355.
[109]	Shahrbabaki E A, Alibeigloo A. 2014. Three-dimensional free vibration of carbon nanotube-reinforced composite plates with various boundary conditions using Ritz method. Composite Structures, 111: 362- 370.
[110]	Shen H S. 1997. Kíarmían-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis. Applied Mathematics and Mechanics, 18: 1137-115242.
[111]	Shen H S. 2002. Postbuckling of axially loaded shear-deformable laminated cylindrical panels. Journal of Strain Analysis for Engineering Design, 37: 413-425.
[112]	Shen H S. 2009a. Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures, 91: 9-19.
[113]	Shen H S. 2009b. Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. Boca Raton, FL:
[114]	CRC Press.
[115]	Shen H S. 2011a. A novel technique for nonlinear analysis of beams on two-parameter elastic foundations. International Journal of Structural Stability and Dynamics, 11: 999-1014.
[116]	Shen H S. 2011b. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Composite Structures, 93: 2096-2108.
[117]	Shen H S. 2011c. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells. Composite Structures, 93: 2496-2503.
[118]	Shen H S. 2012a. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube- reinforced composite cylindrical shells. Composites Part B, 43: 1030-1038.
[119]	Shen H S. 2014a. Torsional postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments. Composite Structures, 116: 477-488.
[120]	Shen H S, He X Q. 2016. Large amplitude free vibration of nanotube-reinforced composite doubly curved pan- els resting on elastic foundations in thermal environments. Journal of Vibration and Control, doi.org/10.1177/1077546315619280.
[121]	Shen H S, Xiang Y. 2012. Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments. Computer Methods in Applied Mechanics and Engineering, 213-216: 196-205.
[122]	Shen H S, Xiang Y. 2013a. Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments. Engineering Structures, 56: 698-708.
[123]	Shen H S, Xiang Y. 2013b. Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment. Composites Part B, 52: 311-322.
[124]	Shen H S, Xiang Y. 2014a. Nonlinear bending of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Engineering Structures, 80: 163-172.
[125]	Shen H S, Xiang Y. 2014b. Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Composite Structures, 111: 291-300.
[126]	Shen H S, Xiang Y. 2014c. Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Composites Part B, 67: 50-61.
[127]	Shen H S, Xiang Y. 2015a. Thermal postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations. Composite Structures, 123: 383-392.
[128]	Shen H S, Xiang Y. 2015b. Nonlinear response of nanotube-reinforced composite cylindrical panels subjected to combined loadings and resting on elastic foundations. Composite Structures, 131: 939-950.
[129]	Shen H S, Xiang Y. 2016. Postbuckling of pressure-loaded nanotube-reinforced composite doubly curved panels resting on elastic foundations in thermal environments. International Journal of Mechanical Sci- ences, 107: 225-234.
[130]	Shen H S, Zhang C L. 2010. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Materials & Design, 31: 3403-3411.
[131]	Shen H S, Zhu Z H. 2010. Buckling and postbuckling behavior of functionally graded nanotube-reinforced composite plates in thermal environments. CMC-Computers Materials & Continua, 18: 155-182.
[132]	Shen H S, Zhu Z H. 2012. Postbuckling of sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations. European Journal of Mechanics A/Solids, 35: 10-21.
[133]	Shi D L, Feng X Q, Huang Y Y, Hwang K C, Gao H. 2004. The e®ect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. Journal of Engineering Materials and Technology ASME, 126: 250-257.
[134]	Song Z G, Zhang L W, Liew K M. 2016a. Aeroelastic analysis of CNT reinforced functionally graded com- posite panels in supersonic airflow using a higher-order shear deformation theory. Composite Structures, 141: 79-90.
[135]	Song Z G, Zhang L W, Liew K M. 2016b. Active vibration control of CNT reinforced functionally graded plates based on a higher-order shear deformation theory. International Journal of Mechanical Sciences, 105: 90-101.
[136]	Spitalsky Z, Tasis D, Papagelis K, Galiotis C. 2010. Carbon nanotube-polymer composites: Chemistry, processing, mechanical and electrical properties. Progress in Polymer Science, 35: 357-401.
[137]	Sun C H, Li F, Cheng H M, Lu G Q. 2005. Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales. Applied Physics Letters, 87: 193101.
[138]	Thomas B, Inamdar P K, Roy T. 2014. Thermal analysis of randomly oriented carbon nanotube reinforced functionally graded Timoshenko beam. Journal of Mechanical Science and Technology, 28: 1779-1788.
[139]	Thomas B, Roy T. 2016. Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures. Acta Mechanica, 227: 581-599.
[140]	Thostenson E T, Ren Z, Chou T W. 2001. Advances in the science and technology of carbon nanotubes and their composites: a review. Composites Science and Technology, 61: 1899-1912.
[141]	Tornabene F, Fantuzzi N, Bacciocchi M, Viola E. 2016. E®ect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly curved shells. Composites Part B, 89: 187-218.
[142]	Wang C Y, Zhang L C. 2008. A critical assessment of the elastic properties and e®ective wall thickness of single-walled carbon nanotubes. Nanotechnology, 19: 075705.
[143]	Wang Z X, Shen H S. 2011. Nonlinear vibration of nanotube-reinforced composite plates in thermal envi- ronments. Computational Materials Science, 50: 2319-2330.
[144]	Wang Z X, Shen H S. 2012a. Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments. Nonlinear Dynamics, 70: 735-754.
[145]	Wang Z X, Shen H S. 2012b. Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets. Composites Part B, 43: 411-421.
[146]	Wang Z X, Xu J, Qiao P. 2014. Nonlinear low-velocity impact analysis of temperature-dependent nanotube- reinforced composite plates. Composite Structures, 108: 423-434.
[147]	Wattanasakulpong N, Chaikittiratana A. 2015. Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation. Applied Mathematical Modelling, 39: 5459-5472.
[148]	Wattanasakulpong N, Ungbhakorn V. 2013. Analytical solutions for bending, buckling and vibration re- sponses of carbon nanotube-reinforced composite beams resting on elastic foundation. Computational Materials Science, 71: 201-208.
[149]	Wu C P, Chang S K. 2014. Stability of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers and under bi-axial compression. Composite Structures, 111: 587-601.
[150]	Wu C P, Jiang R Y. 2014. A state space di®erential reproducing kernel method for the buckling anal- ysis of carbon nanotube-reinforced composite circular hollow cylinders. CMES-Computer Modeling in Engineering & Sciences, 97: 239-279.
[151]	Wu C P, Li H Y. 2016a. Three-dimensional free vibration analysis of functionally graded carbon nanotube- reinforced composite plates with various boundary conditions. Journal of Vibration and Control, 22: 89-107.
[152]	Wu C P, Li W C. 2016b. Quasi-3D stability and vibration analyses of sandwich piezoelectric plates with an embedded CNT-reinforced composite core. International Journal of Structural Stability and Dynamics, 16: 1450097.
[153]	Wu C P, Lin H R. 2015. Three-dimensional dynamic responses of carbon nanotube-reinforced composite plates with surface-bonded piezoelectric layers using Reissner's mixed variational theorem-based finite layer methods. Journal of Intelligent Material Systems and Structures, 26: 260-279.
[154]	Wu H, Kitipornchai S, Yang J. 2015. Free vibration and buckling analysis of sandwich beams with func- tionally graded carbon nanotube-reinforced composite face sheets. International Journal of Structural Stability and Dynamics, 15: 1540011.
[155]	Wu HL, Yang J, Kitipornchai S. 2016. Nonlinear vibration of functionally graded carbon nanotube reinforced composite beams with geometric imperfections. Composites Part B, 90: 86-96.
[156]	Yakobson B I, Brabec C J, Bernholc J. 1996. Nanomechanics of carbon tubes: Instability beyond linear response. Physical Review Letters, 76: 2511-2514.
[157]	Yas M H, Heshmati M. 2012. Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load. Applied Mathematical Modelling, 36: 1371-1394.
[158]	Yas M H, Samadi N. Free vibrations and buckling analysis of carbon nanotube-reinforced composite Tim- oshenko beams on elastic foundation. International Journal of Pressure Vessels and Piping, 2012, 98: 119-128.
[159]	Yas M H, Pourasghar A, Kamarian S, Heshmati M. 2013. Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube. Materials & Design, 49: 583-590.
[160]	Zhang L W, Cui W C, Liew K M. 2015a. Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges. International Journal of Mechanical Sciences, 103: 9-21.
[161]	Zhang L W, Lei Z X, Liew K M, Yu J L. 2014a. Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels. Computer Methods in Applied Mechanics and Engineering, 273: 1-18.
[162]	Zhang L W, Lei Z X, Liew K M, Yu J L. 2014b. Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Composite Structures, 111: 205-212.
[163]	Zhang L W, Lei Z X, Liew K M. 2015b. An element-free IMLS-Ritz framework for buckling analysis of FG-CNT reinforced composite thick plates resting on Winkler foundations. Engineering Analysis with Boundary Elements, 58: 7-17.
[164]	Zhang L W, Lei Z X, Liew K M. 2015c. Computation of vibration solution for functionally graded carbon nanotube-reinforced composite thick plates resting on elastic foundations using the element-free IMLS-Ritz method. Applied Mathematics and Computation, 256: 488-504.
[165]	Zhang L W, Lei Z X, Liew K M. 2015d. Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach. Composites Part B, 75: 36-46.
[166]	Zhang L W, Lei Z X, Liew K M. 2015e. Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates. Composite Structures, 122: 172-183.
[167]	Zhang L W, Lei Z X, Liew K M. 2015f. Free vibration analysis of functionally graded carbon nanotube- reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method. Composite Structures, 120: 189-199.
[168]	Zhang L W, Liew K M. 2015. Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach. Composite Structures, 132: 974-983.
[169]	Zhang L W, Liew K M. 2016. Postbuckling analysis of axially compressed CNT reinforced functionally graded composite plates resting on Pasternak foundations using an element-free approach. Composite
[170]	Structures, 138: 40-51.
[171]	Zhang L W, Liew K M, Jiang Z. 2016a. An element-free analysis of CNT-reinforced composite plates with column supports and elastically restrained edges under large deformation. Composites Part B, 95:18-28.
[172]	Zhang L W, Liew K M, Reddy J N. 2016b. Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression. Com- puter Methods in Applied Mechanics and Engineering, 298: 1-28.
[173]	Zhang L W, Song ZG, Liew K M. 2015g. Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method. Composite Structures, 128: 165-175.
[174]	Zhang L W, Song ZG, Liew K M. 2015h. State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory. Composite Structures, 134: 989-1003.
[175]	Zhang L W, Song ZG, Liew K M. 2016c. Optimal shape control of CNT reinforced functionally graded composite plates using piezoelectric patches. Composites Part B, 85: 140-149.
[176]	Zhang L W, Song Z G, Liew K M. 2016d. Computation of aerothermoelastic properties and active flutter control of CNT reinforced functionally graded composite panels in supersonic airflow. Computer Methods in Applied Mechanics and Engineering, 300: 427-441.
[177]	Zhang L W, Xiao L N, Zou G L, Liew K M. 2016e. Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method. Composite Structures, 148: 144- 154.
[178]	Zhang R, Zhang Y, Zhang Q, Xie H, Qian W, Wei F. 2013. Growth of half-meter long carbon nanotubes based on schulz-flory distribution. ACS Nano, 7: 6156-6161.
[179]	Zhang Y, Matthews F L. 1983. Postbuckling behavior of curved panels of generally layered composite materials. Composite Structures, 2: 115-136.
[180]	Zhu J, Yang J, Kitipornchai S. 2013. Dispersion spectrum in a functionally graded carbon nanotube- reinforced plate based on first-order shear deformation plate theory. Composites Part B, 53: 274-283.
[181]	Zhu P, Lei Z X, Liew K M. 2012. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Composite Structures, 94: 1450-1460.