Steel and Composite Structures

  • 제42권1호
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  • Pages.23-32
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  • 2022
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear bending analysis of functionally graded CNT-reinforced composite plates

  • Cho, Jin-Rae (Department of Naval Architecture and Ocean Engineering, Hongik University)
  • 투고 : 2021.03.03
  • 심사 : 2021.11.08
  • 발행 : 2022.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

키워드

과제정보

This work was supported by 2021 Hongik University Research Fund. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924).

참고문헌

  1. Adam, C., Bouabdallah, C., Zarroug, M. and Maitourrnam, H. (2015), "Improved numerical integration for locking treatment in isogemetric structural elements. Part II: Plates and shells", Comput. Meth. Appl. Mech. Engrg., 284, 106-137. https://doi.org /10.1016/j.cma.2014.07.020.
  2. Ajayan, P.M., Stephane, O., Collix, C. and Trauth, D. (1994), "Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite", Science, 256, 1212-1214. https://doi.org/10.1126/science.265.5176.1212.
  3. Alibeigloo, A. and Emtehani A. (2015), "Static and free vibration analyses of carbon nonotube-reinforced composite plate using differential quadrature rule", Meccanica, 50, 61-76. https://doi.org/10.1007/s11012-014-0050-7.
  4. Arani, A., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A. (2011), "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTS using analytical and finite element methods", J. Mech. Sci. Technol., 25, 809-820. https://doi.org/ 10.1007/s12206-011-0127-3.
  5. Barber, A.H., Cohen, S.R. and Wagner, H.D. (2003), "Measurement of canbon nanotube-polymer interfacial strength", Appl. Phys. Lett., 82, 4140-4142. https://doi.org/10.1063/1.1579568.
  6. Borjalilou, V., Taati, E. and Ahmadian, M.T. (2019), "Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: Exact solutions", SN Appl. Sci., 1, 1323. https://doi.org/10.1007/s42452-019-1359-6.
  7. Chavan, S.G. and Lal, A. (2017), "Bending behavior of SWCNT reinforced composite plates", Steel. Compos. Struct., 24(5), 537-548. https://doi.org/10.12989/scs.2017.24.5.537.
  8. Chinesta, F., Cescotto, C., Cueto, E. and Lorong, P. (2013) Natural Element Method for the Simulation of Structures and Processes, Wiley.
  9. Cho, J.R. (2020), "Natural element approximation of hierarchical models of plate-like elastic structures", Finite. Elem. Anal. Des., 180, 103439. https://doi.org/10.1016/j.finel.2020.103439.
  10. Cho, J.R. (2021) "Natural element hierarchical models for the free vibration analyses of laminate composite plates", Compos. Struct., 272, 114247, https://doi.org/10.1016/j.compstruct.2021.114147.
  11. Cho, J.R. and Lee, H.W. (2006), "A Petrov-Galerkin natural element method securing the numerical integration accuracy", J. Mech. Sci. Technol., 20(1), 94-109, https://doi.org/10.1007/BF02916204.
  12. Cho, J.R. and Lee, H.W. (2007), "Polygon-wise constant curvature natural element approximation of Kirchhoff plate model", Int. J. Solids Struct., 44, 4860-4871. https://doi.org/10.1016/j.ijsolstr.2006.12.009.
  13. Cho, J.R. and Oden, J.T. (1996), "A priori modeling error estimates of hierarchical models for elasticity problems for plate- and shell-like structures", Mathl. Comput. Modelling., 23(10), 117-133. https://doi.org/10.1016/0895-7177(96)00058-1.
  14. Cho, J.R. and Oden, J.T. (2000), "Functionally graded material: A parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme", Comput. Meth. Appl. Mech. Engrg., 188, 17-38. https://doi.org/10.1016/S0045-7825(99)00289-3.
  15. Daniel, I.M. and Ishai, O. (1994), Engineering Mechanics of Composite Materials, Oxford University Press, New York.
  16. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28, 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022.
  17. Fidelus, J.D., Wiessel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Composite Part A, 36, 530-540. https://doi.org/10.1016/j.compositesa.2005.02.006.
  18. Fiedler, B., Gojny, F.H., Wichmann, M.H.G., Notle, M.C.M. and Schulte, K. (2006), "Fundamental aspects of nano-reinforced composites", Composite Sci. Technol., 66, 3115-3125. https://doi.org/10.1016/j.compscitech.2005.01.014.
  19. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329, 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020.
  20. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanobute composites", Comput. Mater. Sci., 39, 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011.
  21. Harris, P.J.F. (2001) Carbon Nanotubes and Related Structures: New Materials for the Twenty-first Century, Cambridge University Press.
  22. Heydari, M.M., Bidgoli, A.H., Golshani, H.R., Beygipoor, G. and Davoodi, A. (2014), "Nonlinear bending analysis of functionally graded CNT-reinforced composite Mindlin polymeric temperature-dependent plate resigning on orthotropic elastomeric medium using GDQM", Nonlinear Dyn., 79, 1425-1441. https://doi.org/10.1007/s11071-014-1751-0.
  23. Hu, N., Fugunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", Proc. Royal Soc. A, 461, 1685-1670, https://doi.org /10.1098/rspa.2004.1422.
  24. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Composite Struct., 92, 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024.
  25. Keleshteri, M.M., Asadi, H. and Aghdam, M.M. (2019), "Nonlinear bending analysis of FG-CNTRC annular plates with variable thickness on elastic foundation", Thin-Walled Struct., 135, 453-462. https://doi.org/10.1016/j.tws.2018.11.020.
  26. Kuhlmann, G. and Rolfes, R. (2004), "A hierarchic 3D finite element for laminated composites", Int. J. Numer. Methods Engng., 61, 96-116. https://doi.org/10.1002/nme.1060.
  27. Kumar, P. and Srinivas, J. (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, 158-170. https://doi.org/10.1016/j.compstruct.2017.06.055.
  28. Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method", Comput. Methods Appl. Mech. Engrg., 256, 189-199. https://doi.org/10.1016/j.cma.2012.12.007.
  29. Liew, K.M., Lei, Z.X. and Zhang, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotibe reinforced composite: A review", Composite Struct., 120, 90-97. https://doi.org/10.1016/j.compstruct.2014.09.041.
  30. Mehar, K., Panda, S.K. and Mahapatra, T. (2018), "Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses", Int. Mech. G: J. Aero. Eng., 233(5), 1695-1704. https:// doi.org/10.1177/0954410018761192.
  31. Mirzaei, M. and Kiani, Y. (2017), "Nonlinear free vibration of FG-CNT reinforced composite plates", Struct. Eng. Mech., 64(3), 381-390. https://doi.org/10.12989/sem.2017.64.3.381.
  32. Shen, S.H. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Composite Struct., 19, 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  33. Sukumar, N., Moran, B. and Belytschko, T. (1998), "The natural element method in solid mechanics", Int. J. Numer. Methods Engng., 43(5), 839-887. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R.
  34. Tohidi, H., Hosseini-Hashemi, S., Maghsoudpour, A. and Etemadi, S. (2017), "Strain gradient theory for vibration analysis of embedded cnt-reinforced micro Mindlin cylindrical shells considering agglomeration effects", Struct. Eng. Mech., 62, 551-565. https://doi.org/10.12989/sem.2017.62.5.551.
  35. Van Do, V.N. and Lee, C.H. (2017), "Bending analyses of FG-CNTRC plates using the modified mesh-free radial point interpolation method based on the higher-order shear deformation theory", Composite Struct., 168, 485-497. https://doi.org/10.1016/j.compstruct.2017.02.055.
  36. Wong, M., Paramsothy, M., Xu, X.J., Ren, Y., Li, S. and Liao, K. (2003), "Physical interactions at carbon-nanotube-polymer interface", Polymer, 44, 7757-7764. https://doi.org/10.1016/j.polymer.2003.10.011.
  37. Wu, T.I., Shukla, K.K. and Huang, J.H. (2006), "Nonlinear static and dynamic analysis of functionally graded plates", Int. J. Appl. Mech. Eng., 11:679-698.
  38. Wuite, J. and Adali, S. (2005) "Deflection and stress behavior of nanocomposite reinforced beams using a multiscale amalysis", Compos. Struct., 71, 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011.
  39. Zaghloul, S.A. and Kennedy, J.B. (1975), "Nonlinear behavior of symmetrically laminated plates", J. Appl. Mech. Trans. ASME, 42, 234-236. https://doi.org/10.1115/1.3423532.
  40. Zghal, S., Frikha, A. and Dammak, F. (2018), "Non-linear bending analysis of nanocomposites reinforced by graphene-nanotubes with finite shell element and mabrane enhancement", Eng. Struct., 158, 95-109. https://doi.org/10.1016/j.engstruct. 2017.12.017.
  41. Zhu, P., Lei, Z.X. and 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 Struct., 94, 1450-1460, https://doi.org/10. 1016/j.compstruct.2011.11.010. https://doi.org/10.1016/j.compstruct.2011.11.010
  42. Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971) "Reduced integration technique in general analysis of plates and shells", Int. J. Numer. Methods Engng., 3(2), 275-290. https://doi.org/10.1002 /nme.1620030211. https://doi.org/10.1002/nme.1620030211