Nonlinear modeling and simulation of piezoelectric integrated carbon nanotube reinforced functionally graded structures
WANG Xiong1, GAO Yingshan2, ZHANG Shunqi2, XUE Ting3, CHEN Min4
1.School of Energy Engineering, Yulin University, Yulin 719000,China;
2.School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444,China;
3.School of Mechanical Engineering, Northwestern Polytechincal University, Xi’an 720071,China;
4.Department of Electronic and Electric Engineering, Xi’an Jiaotong-Liverpool University, Suzhou 215123,China
Abstract：The distribution of carbon nanotube (CNT) reinforcements in fundamental material may form functionally graded CNT structures (FG-CNT).To simulate the FG-CNT structures at large deformation, four typical CNT distribution patterns were considered, i.e., uniform, V-shaped, O-shaped and X-shaped.A geometrically nonlinear model was built based on the plate and shell theory of Reissner-Mindlin hypothesis.The nonlinear model includes not only the fully geometrically nonlinear strain-displacement relations, but also the large rotations of the shell structure in normal direction.The proposed approach was first validated through the comparison with the literature results.Then, it was applied to solve the large deformations of FG-CNT reinforced composite structures, aiming at the study of the impact of CNT on the stiffness design of composite plates.The results illustrate that the CNT distributions and reinforcement orientations have a remarkable influence on the mechanical properties of FG-CNT composite plates.
［1］贺丹, 乔瑞, 杨子豪.碳纳米管增强型功能梯度板的屈曲预测［J］.复合材料学报, 2018, 35(10): 2804-2812.
HE Dan, QIAO Rui, YANG Zihao.Buckling prediction of carbon nanotubes reinforced functionally gradient plates［J］.Journal of Composite Materials,2018,35(10):2804-2812.
［2］BHAVAR V, KATTIRE P, THAKARE S, et al.A review on functionally gradient materials (FGMs) and their applications［J］.IOP Conference Series (Materials Science and Engineering), 2017, 229(1):012021.
［3］唐一科,郑富中,周兆英,等.基于单壁碳纳米管阵列的力敏传感器［J］.机械工程学报, 2010, 46(18): 13-17.
TANG Yike, ZHENG Fuzhong, ZHOU Zhaoying, et al.Force sensor based on single wall carbon nanotube array［J］.Journal of Mechanical Engineering, 2010, 46(18): 13-17.
［4］IIJIMA S.Helical microtubules of graphitic carbon［J］.Nature,1991,354(6348): 56.
［5］SHEN H S.Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments［J］.Composite Structures, 2009, 91(1): 9-19.
［6］HAN Y, ELLIOTT J.Molecular dynamics simulations of the elastic properties of polymer_carbon nanotube composites［J］.Computational Materials Science, 2007,39(2): 315-323.
［7］YAS M H, HESHMATI M.Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load［J］.Applied Mathematical Modelling, 2012, 36(4): 1371-1394.
［8］LEI Z X, LIEW K M, YU J L.Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method［J］.Composite Structures, 2013,98:160-168.
［9］贺丹, 门亮.碳纳米管增强型复合材料功能梯度板的自由振动模型与尺度效应［J］.计算力学学报, 2018, 35(3):326-330.
HE Dan, MEN Liang.Free vibration model and scale effect of carbon nanotube reinforced functionally gradient composite plates［J］.Journal of Computational Mechanics, 2018, 35(3):326-330.
［10］姚小虎,韩强,辛浩.单壁碳纳米管非线性力学行为的数值模拟［J］.物理学报,2008(1):329-338.
YAO Xiaohu, HAN Qiang, XIN Hao.Numerical simulation of nonlinear mechanical behavior of single wall carbon nanotubes ［J］.Acta Physica Sinica,2008(1):329-338.
［11］SHEN H S.Postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations subjected to lateral pressure in thermal environments［J］.Engineering Structures, 2016, 122(1): 174-183.
［12］KE L L, YANG J, KITIPORNCHAI S.Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams［J］.Composite Structures, 2010, 92(3): 676-683.
［13］ZHANG L W, SONG Z G, LIEW K M.Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method［J］.Composite Structures, 2015, 128: 165-175.
［14］KELESHTERI M M, ASADI H, WANG Q.Large amplitude vibration of FG-CNT reinforced composite annular plates with integrated piezoelectric layers on elastic foundation［J］.Thin-Walled Structures, 2017, 120:203-214.
［15］KELESHTERI M M, ASADI H, WANG Q.Postbuckling analysis of smart FG-CNTRC annular sector plates with surface-bonded piezoelectric layers using generalized differential quadrature method［J］.Computer Methods in Applied Mechanics and Engineering, 2017, 325: 689-710.
［16］SETOODEH A R, SHOJAEE M, MALEKZADEH P.Application of transformed differential quadrature to free vibration analysis of FG-CNTRC quadrilateral spherical panel with piezoelectric layers［J］.Computer Methods in Applied Mechanics and Engineering, 2018, 335:510-537.
［17］ZHANG S Q, SCHMIDT R.Static and dynamic FE analysis of piezoelectric integrated thin-walled composite structures with large rotations［J］.Composite Structures,2014, 112(1): 345-357.［18］ZHANG S Q, WANG Z X, QIN X S,et al.Geometrically nonlinear analysis of composite laminated structures with multiple macro-fiber composite (MFC) actuators［J］.Composite Structures, 2016, 150: 62-72.
［19］LIEW K M, LEI Z X, ZHANG L W, Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review［J］.Composite Structures,2015,120: 90-97.
［20］沈惠申.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［J］.力学进展,2016,46(1):478-505.
SHEN Huishen.Progress in structural modeling and analysis of functionally graded carbon nanotube reinforced composites ［J］.Progress in Mechanics, 2016,46(1):478-505.
［21］ARDESTANI M M, ZHANG L W, LIEW K M.Isogeometric analysis of the effect of CNT orientation on the static and vibration behaviors of CNT-reinforced skew composite plates［J］.Computer Methods in Applied Mechanics and Engineering, 2017,317:341-379.
