CNT纤维增强功能梯度复合板非线性建模与仿真
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摘要
基于一阶剪切变形假设和哈密顿原理建立了碳纳米管(Carbonnanotube,CNT)增强功能梯度板大变形非线性有限元模型,实现了CNT纤维增强功能梯度复合板在发生大变形时的准确计算。该非线性模型不但包含几何全非线性应变—位移关系,还考虑薄板结构法向发生大转角的情形。通过与已有数据对比验证了所建模型的准确性。利用所建模型对四种典型的CNT分布形式,即均匀分布、O型分布、V型分布和X型分布的CNT纤维增强功能梯度复合板进行几何大变形非线性计算和分析,讨论CNT体积分数、CNT分布方式、结构宽厚比和载荷对CNT纤维增强功能梯度复合板的影响。研究表明:随着CNT体积分数的增加,该功能梯度复合板的刚度随之增加;相同体积分数下,X型分布复合板的刚度最大,均匀分布和V型分布次之,O型分布复合板的刚度最小。为CNT纤维增强功能梯度复合板的工程应用提供参考。
To achieve an accurate calcultation of carbon nanotube(CNT) fiber reinforced functionally graded composite plates in the case of large deformation, a large rotation nonlinear finite element model is developed for the CNT composite plates based on the first order shear deformation(FOSD) hypothesis and the Hamilton priciple, which not only includes the fully geometrically nonlinear strian – displacement relations, but also considers the large rotation of the shell director of plates. The model is first verified by the data in the reference. The geometrically nonlinear model are then applied to calculate and analyze four different CNT distributions,uniform, O-shaped, V-shaped and X-shapeddistributions. The effects of the CNT volume fraction, the CNT distribution, width to thickness ratio and loading of CNT fiber reinforced functional gradient composite plates. The investigations show that the larger of the volume fraction of CNT the higher of the stiffness of the composite plate; for the same volume fraction, the stiffness of X-shaped CNT plate is the largest, followed by uniform and V-shaped, and O-shaped CNT plate is the weaknest. Finally, the model provides a reference for the engineering application of CNT fiber reinforced funtionally graded composite plates.
To achieve an accurate calcultation of carbon nanotube(CNT) fiber reinforced functionally graded composite plates in the case of large deformation, a large rotation nonlinear finite element model is developed for the CNT composite plates based on the first order shear deformation(FOSD) hypothesis and the Hamilton priciple, which not only includes the fully geometrically nonlinear strian – displacement relations, but also considers the large rotation of the shell director of plates. The model is first verified by the data in the reference. The geometrically nonlinear model are then applied to calculate and analyze four different CNT distributions,uniform, O-shaped, V-shaped and X-shapeddistributions. The effects of the CNT volume fraction, the CNT distribution, width to thickness ratio and loading of CNT fiber reinforced functional gradient composite plates. The investigations show that the larger of the volume fraction of CNT the higher of the stiffness of the composite plate; for the same volume fraction, the stiffness of X-shaped CNT plate is the largest, followed by uniform and V-shaped, and O-shaped CNT plate is the weaknest. Finally, the model provides a reference for the engineering application of CNT fiber reinforced funtionally graded composite plates.
引文
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[2]SINGH R,BHAVAR V,KATTIRE P,et al.A review on functionally gradient materials(fgms)and their applications[J].Materials Science and Engineering,2017,229(1):012021.
[3]徐娜,李晨希,李荣德,等.功能梯度材料的制备、应用及发展趋势[J].材料保护,2008(5):54-57,93.XU Na,LI Xichen,LI Rongde,et al.Preparation,application and development trend of functional gradient materials[J].Materials protection,2008(5):54-57,93.
[4]IIJIMA S.Helical microtubules of graphitic carbon[J].Nature,1991,354(6348):56.
[5]FIDELUS J D,WIESEL E,GOJNY F H,et al.Thermo-mechanical properties of randomly oriented carbon_epoxy nanocomposites[J].Applied Science and Manufacturing,2005,36(11):1555-1561.
[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]HESHMATI M,YAS M H.Vibrations of non-uniform functionally graded MWCNT spolystyrene nanocomposite beams under action of moving load[J].Materials and Design,2013,46:206-218.
[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 composite functionally gradient plate[J].Journal of Computational Mechanics,2018,35(3):326-330.
[10]ZHONG J,LIANG T,ISAYEV A I.Linear and nonlinear behavior on PPCNT composites prepared by continuous ultrasonic twin-screw extrusion[C]//Annual Technical Conference and Exhibition of the Society of Plastics Engineers,2017:225-232.
[11]GARCíA-MACíAS E,CASTRO-TRIGUERO R,SAAVEDRA F E I,et al.Static and free vibration analysis of functionally graded carbon nanotube[J].Composite Structures,2016,140:473-490.
[12]张宇.碳纳米管增强复合材料屈曲及自由振动行为的数值研究[D].上海:上海海洋大学,2017.ZHANG Yu.Numerical study on buckling and free vibration behavior of carbon nanotubes reinforced composites materials[D].Shanghai:Shanghai Ocean University,2017.
[13]SHEN H S,XIANG Y.Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments[J].Computer Methods in Applied Mechanics and Engineering,2012,213-216:196-205.
[14]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.
[15]KOLAHCHI R,SAFARI M,ESMAILPOUR M.Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium[J].Composite Structures,2014,150:255-265.
[16]ZHANGL W,SONGZ G,LIEWK 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.
[17]ZHANG S Q,SCHMIDT R.Large rotation theory for static analysis of composite and piezoelectric laminated thin-walled structures[J].Thin-Walled Structures,2014,78:16-25.
[18]ZHANG S Q,SCHMIDT R.Large rotation FE transient analysis of piezolaminated thin-walled smart structures[J].Smart Materials and Structures,2013,22(10):105025.
[19]ZHANG S Q,SCHMIDT R.Static and dynamic FEanalysis of piezoelectric integrated thin-walled composite structures with large rotations[J].Composite Structures,2014,112(1):345-357.
[20]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.
[21]MEMAR A 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.