An Enhanced Global–Local Higher-Order Model for Thermal Expansion Analysis of Laminated Panels Reinforced by Carbon Nanotubes
Publication: Journal of Aerospace Engineering
Volume 37, Issue 4
Abstract
Carbon nanotubes (CNTs) are added to the matrix according to proper distribution configurations by many researchers to improve the stiffness of laminated composites. However, the distribution configurations of CNTs may induce dramatic changes in displacements and stresses, which significantly affect structural safety. Moreover, such issues have received little attention at present because existing theoretical models encounter difficulties in accurately predicting dramatic changes in stresses of these structures. To accurately analyze the thermal expansion behaviors of laminated panels reinforced by CNTs, an equivalent single-layer higher-order model is proposed in which in-plane displacements are constructed by superimposing the second local displacements onto a smooth cubic varying field. Transverse normal deformation should be considered for the thermal expansion behavior of the laminated plate; therefore, a smooth cubic distribution along the thickness is adopted in the transverse displacement field. The layer-dependent displacement parameters can be expressed using global displacement variables by applying compatible conditions of displacements and stresses. Based on the proposed model, analytical solutions for laminated composites are obtained using Navier’s technique. The capability of the proposed model is verified by comparing the results of the proposed model with the exact solutions and the three-dimensional finite element model. The effect of the distribution configuration and volume fraction of CNTs on the thermomechanical behavior of the composite panels is studied based on the present model. Numerical results show that the distribution configuration and volume fraction of the CNTs significantly influence the distributions and magnitudes of stresses.
Practical Applications
In order to improve the stiffness of aircraft wings, stiffeners are typically used to enforce the skin of the wing. However, the aerodynamic shape of the wing cannot be changed, so that the stiffeners cannot be placed on external surface of the skin. As a result, the panel’s bending stiffness relative to the midplane is not asymmetric, which affected its loading capability. To overcome such problems, previous studies have demonstrated that adding CNTs can improve the stiffness of panels, and it has been found that composite panels reinforced with X-X-distributing CNTs possess the best capability in preventing buckling deformation. However, the effect of the distribution profiles of CNTs on the thermomechanical behavior has been less studied in the existing literature. Therefore, this study proposes a higher-order model to accurately predict the thermomechanical behavior of CNT-reinforced composite panels and investigate the effect of CNT distribution profiles and volume fractions on the thermomechanical responses of composite panels. The present work can provide suggestions for the design of a reinforcing scheme for CNT-reinforced composite panels, so that the stiffness of wings can be enhanced.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The work described in this paper was supported by the National Natural Sciences Foundation of China [No. 12172295].
References
Chakraborty, S., and T. Dey. 2021. “Non-linear stability analysis of CNT reinforced composite cylindrical shell panel subjected to thermomechanical loading.” Compos. Struct. 255 (Jan): 112995. https://doi.org/10.1016/j.compstruct.2020.112995.
Chavan, S. G., and A. Lal. 2017. “Bending analysis of laminated SWCNT reinforced functionally graded plate using FEM.” Curved Layered Struct. 4 (1): 134–145. https://doi.org/10.1515/cls-2017-0010.
Chiker, Y., M. Bachene, S. Bouaziz, M. Guemana, M. B. Amar, and M. Haddar. 2021. “Free vibration analysis of hybrid laminated plates containing multilayer functionally graded carbon nanotube-reinforced composite plies using a layer-wise formulation.” Arch. Appl. Mech. 91 (1): 463–485. https://doi.org/10.1007/s00419-020-01783-3.
Cho, M., and J. Oh. 2004. “Higher order zig-zag theory for fully coupled thermo-electric–mechanical smart composite plates.” Int. J. Solids Struct. 41 (5–6): 1331–1356. https://doi.org/10.1016/j.ijsolstr.2003.10.020.
Di Sciuva, M., and M. Sorrenti. 2019a. “Bending and free vibration analysis of functionally graded sandwich plates: An assessment of the refined zigzag theory.” J. Sandwich Struct. Mater. 23 (3): 760–802. https://doi.org/10.1177/1099636219843970.
Di Sciuva, M., and M. Sorrenti. 2019b. “Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended refined zigzag theory.” Compos. Struct. 227 (Nov): 111324. https://doi.org/10.1016/j.compstruct.2019.111324.
Eghbali, M., and S. A. Hosseini. 2023. “On moving harmonic load and dynamic response of carbon nanotube-reinforced composite beams using higher-order shear deformation theories.” Mech. Adv. Compos. Struct. 10 (2): 257–270. https://doi.org/10.22075/MACS.2022.28205.1431.
Gherlone, M., A. Tessler, and M. D. Sciuva. 2011. “C0 beam elements based on the refined zigzag theory for multilayered composite and sandwich laminates.” Compos. Struct. 93 (11): 2882–2894. https://doi.org/10.1016/j.compstruct.2011.05.015.
Iijima, S. 1991. “Helical microtubules of graphitic carbon.” Nature 354 (6348): 56–58. https://doi.org/10.1038/354056a0.
Iurlaro, L., M. Gherlone, M. Di Sciuva, and A. Tessler. 2013. “Assessment of the refined zigzag theory for bending, vibration, and buckling of sandwich plates: A comparative study of different theories.” Compos. Struct. 106 (Dec): 777–792. https://doi.org/10.1016/j.compstruct.2013.07.019.
Jafari Mehrabadi, S., B. Sobhani Aragh, V. Khoshkhahesh, and A. Taherpour. 2012. “Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes.” Composites, Part B 43 (4): 2031–2040. https://doi.org/10.1016/j.compositesb.2012.01.067.
Jalali, S. K., and M. Heshmati. 2016. “Buckling analysis of circular sandwich plates with tapered cores and functionally graded carbon nanotubes-reinforced composite face sheets.” Thin-Walled Struct. 100 (Mar): 14–24. https://doi.org/10.1016/j.tws.2015.12.001.
Koizumi, M., and M. Niino. 1995. “Overview of FGM research in Japan.” MRS Bull. 20 (1): 19–21. https://doi.org/10.1557/S0883769400048867.
Kumar, P., and J. Srinivas. 2017. “Vibration, buckling and bending behavior of functionally graded multi-walled carbon nanotube reinforced polymer composite plates using the layer-wise formulation.” Compos. Struct. 177 (Oct): 158–170. https://doi.org/10.1016/j.compstruct.2017.06.055.
Li, X. Y., and D. S. Liu. 1997. “Generalized laminate theories based on double superposition hypothesis.” Int. J. Numer. Methods Eng. 40 (7): 1197–1212. https://doi.org/10.1002/(SICI)1097-0207(19970415)40:7%3C;1197::AID-NME109%3E3.0.CO;2-B.
Ly, D. K., T. T. Truong, S. N. Nguyen, and T. Nguyen-Thoi. 2022. “A smoothed finite element formulation using zig-zag theory for hybrid damping vibration control of laminated functionally graded carbon nanotube reinforced composite plates.” Eng. Anal. Bound. Elem. 144 (Nov): 456–474. https://doi.org/10.1016/j.enganabound.2022.08.038.
Ly, D.-K., V. Mahesh, C. Thongchom, and T. Nguyen-Thoi. 2023. “Hybrid control of laminated FG-CNTRC shell structures using an advanced smoothed finite element approach based on zig-zag theory.” Thin-Walled Struct. 184 (Mar): 110463. https://doi.org/10.1016/j.tws.2022.110463.
Matsunaga, H. 2004. “A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings.” Compos. Struct. 64 (2): 161–177. https://doi.org/10.1016/j.compstruct.2003.08.001.
Mehar, K., S. K. Panda, A. Dehengia, and V. R. Kar. 2015. “Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment.” J. Sandwich Struct. Mater. 18 (2): 151–173. https://doi.org/10.1177/1099636215613324.
Moradi-Dastjerdi, R., and H. Momeni-Khabisi. 2017. “Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation.” J. Vib. Control 24 (11): 2327–2343. https://doi.org/10.1177/1077546316686227.
Phung-Van, P., M. Abdel-Wahab, K. M. Liew, S. P. A. Bordas, and H. Nguyen-Xuan. 2015. “Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory.” Compos. Struct. 123 (May): 137–149. https://doi.org/10.1016/j.compstruct.2014.12.021.
Phung-Van, P., T. Nguyen-Thoi, H. Luong-Van, C. Thai-Hoang, and H. Nguyen-Xuan. 2014. “A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation.” Comput. Methods Appl. Mech. Eng. 272 (Apr): 138–159. https://doi.org/10.1016/j.cma.2014.01.009.
Ramezani, M., M. Rezaiee-Pajand, and F. Tornabene. 2022. “Nonlinear thermomechanical analysis of CNTRC cylindrical shells using HSDT enriched by zig-zag and polyconvex strain cover functions.” Thin-Walled Struct. 172 (Mar): 108918. https://doi.org/10.1016/j.tws.2022.108918.
Reddy, J. N. 1984. “A simple higher-order theory for laminated composite plates.” J. Appl. Mech. 51 (4): 745–752. https://doi.org/10.1115/1.3167719.
Sankar, A., S. Natarajan, and M. Ganapathi. 2016. “Dynamic instability analysis of sandwich plates with CNT reinforced facesheets.” Compos. Struct. 146 (Jun): 187–200. https://doi.org/10.1016/j.compstruct.2016.03.026.
Schapery, R. A. 2016. “Thermal expansion coefficients of composite materials based on energy principles.” J. Compos. Mater. 2 (3): 380–404. https://doi.org/10.1177/002199836800200308.
Selim, B. A., L. W. Zhang, and K. M. Liew. 2016. “Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory.” Compos. Struct. 156 (Nov): 276–290. https://doi.org/10.1016/j.compstruct.2015.10.026.
Shen, H.-S. 2009. “Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments.” Compos. Struct. 91 (1): 9–19. https://doi.org/10.1016/j.compstruct.2009.04.026.
Shen, H.-S. 2012. “Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells.” Composites, Part B 43 (3): 1030–1038. https://doi.org/10.1016/j.compositesb.2011.10.004.
Soni, S. K., B. Thomas, A. Swain, and T. Roy. 2022. “Functionally graded carbon nanotubes reinforced composite structures: An extensive review.” Compos. Struct. 299 (Nov): 116075. https://doi.org/10.1016/j.compstruct.2022.116075.
Spitalsky, Z., D. Tasis, K. Papagelis, and C. Galiotis. 2010. “Carbon nanotube–polymer composites: Chemistry, processing, mechanical and electrical properties.” Prog. Polym. Sci. 35 (3): 357–401. https://doi.org/10.1016/j.progpolymsci.2009.09.003.
Tessler, A., M. Di Sciuva, and M. Gherlone. 2010. “A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics.” J. Mech. Mater. Struct. 5 (2): 341–367. https://doi.org/10.2140/jomms.2010.5.341.
Thakur, B. R., S. Verma, B. N. Singh, and D. K. Maiti. 2021. “Dynamic analysis of flat and folded laminated composite plates under hygrothermal environment using a nonpolynomial shear deformation theory.” Compos. Struct. 274 (Oct): 114327. https://doi.org/10.1016/j.compstruct.2021.114327.
Wang, A., H. Chen, Y. Hao, and W. Zhang. 2018. “Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets.” Results Phys. 9 (Jun): 550–559. https://doi.org/10.1016/j.rinp.2018.02.062.
Zhang, L. W., Z. X. Lei, and K. M. Liew. 2015. “Computation of vibration solution for functionally graded carbon nanotube-reinforced composite thick plates resting on elastic foundations using the element-free IMLS-Ritz method.” Appl. Math. Comput. 256 (Apr): 488–504. https://doi.org/10.1016/j.amc.2015.01.066.
Zhang, L. W., Z. X. Lei, K. M. Liew, and J. L. Yu. 2014. “Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels.” Compos. Struct. 111 (May): 205–212. https://doi.org/10.1016/j.compstruct.2013.12.035.
Zhen, W., and C. Wanji. 2006. “An efficient higher-order theory and finite element for laminated plates subjected to thermal loading.” Compos. Struct. 73 (1): 99–109. https://doi.org/10.1016/j.compstruct.2005.01.034.
Zhen, W., and C. Wanji. 2007. “A quadrilateral element based on refined global-local higher-order theory for coupling bending and extension thermo-elastic multilayered plates.” Int. J. Solids Struct. 44 (10): 3187–3217. https://doi.org/10.1016/j.ijsolstr.2006.09.015.
Zhu, P., Z. X. Lei, and K. M. Liew. 2012. “Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory.” Compos. Struct. 94 (4): 1450–1460. https://doi.org/10.1016/j.compstruct.2011.11.010.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 37 • Issue 4 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jul 10, 2023
Accepted: Dec 14, 2023
Published online: Mar 27, 2024
Published in print: Jul 1, 2024
Discussion open until: Aug 27, 2024
ASCE Technical Topics:
- Composite materials
- Continuum mechanics
- Displacement (mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Fiber reinforced composites
- Laminated materials
- Materials engineering
- Model accuracy
- Models (by type)
- Panels (structural)
- Solid mechanics
- Structural engineering
- Structural mechanics
- Structural members
- Structural systems
- Thermal analysis
- Thermal properties
- Thermodynamics
- Three-dimensional models
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.