Static Buckling and Free Vibration Analysis of Aligned CNTs Reinforced Composite Plates
Main Article Content
Abstract
This work introduces an analysis of the nonlinear buckling and free vibration behavior of polymer plates reinforced with aligned carbon nanotubes using Reddy's third-order shear deformation plate theory and incorporating Theodore von Kármán's geometric nonlinearity. The polymer plates were enhanced with single-walled carbon nanotubes assumed to exhibit either uniform distribution or functionally graded distribution across the thickness. The equations of motion were established through Hamilton’s principle and then solved by the Galerkin method and Airy’s stress function for the composite plates with fully simply supported edges. The investigation focused on assessing the effects of carbon nanotube distribution, volume fraction, and geometrical parameters on the buckling load and fundamental frequency parameters of composite plates through numerical results.
Keywords:
Analytical Approach, Free Vibration, Aligned carbon nanotubes, Composite plates, Static Buckling.
References
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[2] F. D. Borbón, D. Ambrosini, Dynamic Response of Composites Sandwich Plates with Carbon Nanotubes Subjected to Blast Loading, Compos. B. Eng., Vol. 45, 2013, pp. 466-73, https://doi.org/10.1016/j.compositesb.2012.07.035.
[3] G. J. Wang, Y. P. Cai, Y. J. Ma, S. C. Tang, J. A. Syed, Z. H. Cao, X. K. Meng, Ultrastrong and Stiff Carbon Nanotube/Aluminum-Copper Nanocomposite via Enhancing Friction between Carbon Nanotubes, Nano Lett.,
Vol. 19, 2019, pp. 6255-62, https://doi.org/10.1021/acs.nanolett.9b02332.
[4] S. Pal, P. N. B. Babu, B. S. K. Gargeya, C. S. Becquart, Molecular Dynamics Simulation-Based Investigation of Possible Enhancement in Strength and Ductility of Nanocrystalline Aluminum by CNT Reinforcement, Mater. Chem. Phys., Vol. 243, 2020, pp. 122593, https://doi.org/10.1016/j.matchemphys.2019.122593.
[5] H. S. Shen, Nonlinear Bending of Functionally Graded Carbon Nanotube-Reinforced Composite Plates in Thermal Environments, Compos. Struct., Vol. 91, 2009, pp. 9-19, https://doi.org/10.1016/j.compstruct.2009.04.026.
[6] H. S. Shen, H. Z. Zheng, Buckling and Postbuckling Behavior of Functionally Graded Nanotube-Reinforced Composite Plates in Thermal Environments, Comput. Mater. Contin, Vol. 18, 2010, pp. 155-182, https://doi.org/10.3970/cmc.2010.018.155.
[7] P. Kumar, J. Srinivas, Vibration, Buckling and Bending Behavior of Functionally Graded Multiwalled Carbon Nanotube Reinforced Polymer Composite Plates using the Layer-Wise Formulation, Compos. Struct., Vol. 177, 2017, pp. 158-170, https://doi.org/10.1016/j.compstruct.2017.06.055.
[8] R. Gholami, R. Ansari, Y. Gholami, Numerical Study on the Nonlinear Resonant Dynamics of Carbon Nanotube/Fiber/Polymer Multiscale Laminated Composite Rectangular Plates with Various Boundary Conditions, Aerosp. Sci. Technol., Vol. 78, 2018, pp. 118-129, https://doi.org/10.1016/j.ast.2018.03.043.
[9] D. L. Shi, X. Q. Feng, Y. Y. Huang, K. C. Hwang, H. J. Gao, The Effect of Nanotube Waviness and Agglomeration on the Elastic Property of Carbon Nanotube-Reinforced Composites, Compos. Struct., Vol. 63, 2004, pp. 305-313, https://doi.org/10.1115/1.1751182.
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[11] L. W. Zhang, Z. X. Lei, K. M. Liew, Buckling Analysis of FG-CNT Reinforced Composite Thick Skew Plates Using An Element-Free Approach, Compos. Part B: Eng., Vol. 75, 2015, pp. 36-46, https://doi.org/10.1016/j.compositesb.2015.01.033.
[12] L. W. Zhang, K. M. Liew, Postbuckling Analysis of Axially Compressed CNT Reinforced Functionally Graded Composite Plates Resting on Pasternak Foundations using An Element-Free Approach, Compos. Struct.,
Vol. 138, 2016, pp. 40-51, https://doi.org/10.1016/j.compstruct.2015.11.031.
[13] J. Torabi, R. Ansari, R. Hassani, Numerical Study on the Thermal Buckling Analysis of CNT-Reinforced Composite Plates with Different Shapes Based on the Higher-Order Shear Deformation Theory, Eur. J. Mech. A Solids, Vol. 73, 2019, pp. 144-160, https://doi.org/10.1016/j.euromechsol.2018.07.009.
[14] J. Peng, C. Zhiping, M. He, Z. Delin, G. Peng, Buckling Analysis of Thin Rectangular FG-CNTRC Plate Subjected to Arbitrarily Distributed Partial Edge Compression Loads Based on Differential Quadrature Method, Thin-Walled Struct., Vol. 145, 2019, pp. 106417, https://doi.org/10.1016/j.tws.2019.106417.
[15] O. Civaleka, M. H. Jalaei, Shear Buckling Analysis of Functionally Graded (FG) Carbon Nanotube Reinforced Skew Plates with Different Boundary Conditions, Aerosp. Sci. Technol., Vol. 99, 2020, pp. 105753, https://doi.org/10.1016/j.ast.2020.105753.
[16] M. Mirzaei, Y. Kiani, Thermal Buckling of Temperature Dependent FG-CNT Reinforced Composite Plates, Meccanica., Vol. 47, 2015, pp. 1-17, https://doi.org/10.1007/s11012-015-0348-0.
[17] Y. Kiani, Shear Buckling of FG-CNT Reinforced Composite Plates Using Chebyshev-Ritz Method, Compos Part B: Eng., Vol. 105, 2016, pp. 176-187, https://doi.org/10.1016/j.compositesb.2016.09.001.
[18] Y. Kiani, Thermal Post-Buckling of FG-CNT Reinforced Composite Plates, Compos. Struct., Vol. 159, 2017,
pp. 299-306, https://doi.org/10.1016/j.compstruct.2016.09.084.
[19] Y. Kiani, M. Mirzaei, Rectangular and Skew Shear Buckling of FG-CNT Reinforced Composite Skew Plates using Ritz Method, Aerosp. Sci. Technol., Vol. 77, 2018, pp. 388-398, https://doi.org/10.1016/j.ast.2018.03.022.
[20] A. Hussain, Buckling Analysis of Functionally Graded Carbon Nanotubes Reinforced Composite (Fg-Cntrc) Plate. Thesis, National Institute of Technology Rourkela, India, 2014.
[21] P. P. Van, M. A. Wahab, K. M. Liew, S. P. A. Bordas, H. N. Xuan, Isogeometric Analysis of Functionally Graded Carbon Nanotube-Reinforced Compositeoflates using Higher-Order Shear Deformation Theory, Compos. Struct., Vol. 123, 2015, pp. 137-149, https://doi.org/10.1016/j.compstruct.2014.12.021.
[22] A. K. Singh, A. Bhar, Isogeometric FE Analysis of CNT‑Reinforced Composite Plates: Free Vibration, SN Applied Sciences, Vol. 1, 2019, pp. 1010, https://doi.org/10.1007/s42452-019-1027-x.
[23] E. G. Macías, R. C. Triguero, E. I. S. Flores, M. I. Friswell, R. Gallego, Static and Free Vibration Analysis of Functionally Graded Carbon Nanotube Reinforced Skew Plates, Compos. Struct., Vol. 140, 2016, pp. 473-490, https://doi.org/10.1016/j.compstruct.2015.12.044.
[24] Z. X. Lei, K. M. Liew, J. L. Yu, Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Plates using the Element-Free Kp-Ritz Method in Thermal Environment, Compos. Struct., Vol. 106, 2013, pp. 128-138, https://doi.org/10.1016/j.compstruct.2013.06.003.
[25] L. W. Zhang, W. C. Cui, K. M. Liew, Vibration Analysis of Functionally Graded Carbon Nanotube Reinforced Composite Thick Plates with Elastically Restrained Edges, Int. J. Mech. Sci., Vol. 103, 2015, pp. 9-21, https://doi.org/10.1016/j.ijmecsci.2015.08.021.
[26] L.W. Zhang, Z. X. Lei, K. M. Liew, Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Triangular Plates using the FSDT and Element-Free Imls-Ritz Method, Compos. Struct., Vol. 120, 2015, pp. 189-199, https://doi.org/10.1016/j.compstruct.2014.10.009.
[27] N. Fantuzzi, F. Tornabene, M. Bacciocchi, R. Dimitri, Free Vibration Analysis of Arbitrarily Shaped Functionally Graded Carbon Nanotube-Reinforced Plates, Compos. Part B: Eng., Vol. 115, 2017, pp. 384-408, https://doi.org/10.1016/j.compositesb.2016.09.021.
[28] E. G. Macías, R. C. Triguero, M. I. Friswell, S. Adhikari, A. Sáez, Metamodel-Based Approach for Stochastic Free Vibration Analysis of Functionally Graded Carbon Nanotube Reinforced Plates, Compos. Struct., Vol. 152, 2016, pp. 183-198, https://doi.org/10.1016/j.compstruct.2016.05.019.
[29] E. G. Macías, L. R. Tembleque, A. Sáez, Bending and Free Vibration Analysis of Functionally Graded Graphene vs Carbon Nanotube Reinforced Composite Plates, Compos. Struct., Vol. 186, 2018, pp. 123-138, https://doi.org/10.1016/j.compstruct.2017.11.076.
[30] A. Karamanli, M. Aydogdu, Vibration Behaviors of Two-Directional Carbon Nanotube Reinforced Functionally Graded Composite Plates, Compos. Struct., Vol. 262, 2021, pp. 113639, https://doi.org/10.1016/j.compstruct.2021.113639.
[31] J. N. Reddy, Mechanics of Laminated Composite Plates and Shells, CRC Press, 2004.
[32] N. D. Duc, Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi, 2014.