Coupled systems mechanics

  • 제13권5호
  • /
  • Pages.375-393
  • /
  • 2024
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A nonlocal strain gradient model for buckling analysis of advanced FG CNT-reinforced composite nanobeams

  • Djillali Mokhefi (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Aicha Bessaim (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohammed Sid Ahmed Houari (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Zakaria Deffane (Aerospace Engineering Division, Universitat Politecnica de Catalunya) ;
  • Hakima Houari-Belkadi (Dental Technology and Biomaterials Research Laboratory, Department of Dentistry-Oran's, Faculty of Medicine, University of Oran) ;
  • Belhocine Ali (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Ahmed Amine Daikh (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Habib Hebali (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Hadj Youzera (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Tarek Merzouki (LISV, University of Versailles Saint-Quentin)
  • 투고 : 2024.05.02
  • 심사 : 2024.08.07
  • 발행 : 2024.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

The main objective of this paper is to investigate the buckling behavior of symmetric and non-symmetric carbon nanotube-reinforced composite (CNTRC) nanobeams with nonlocal strain gradient effects. For this purpose, a novel trigonometric shear deformation beam theory is employed, and the Galerkin method is used for analysis. The carbon nanotube-reinforced composite beam consists of a polymeric matrix reinforced with aligned and distributed single-walled carbon nanotubes (SWCNTs) having various reinforcement patterns. The material properties of the carbon nanotube-reinforced composite beams are estimated using the rule of mixture.The governing equations of the problem are derived based on the principle of total potential energy. The proposed theory accurately represents the parabolic distribution of transverse shear stress across the beam thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces without requiring shear correction factors. The mathematical models presented in this work are validated numerically by comparing them with existing literature to assess their accuracy and reliability. The buckling analyses of the carbon nanotube-reinforced composite nanobeams are conducted, considering various factors such as beam types, nonlocal length-scale parameter, strain gradient microstructure-scale parameter, geometry, carbon nanotube volume fraction, and boundary conditions. Additionally, new results are reported in this study, which can serve as a benchmark for future research.

키워드

참고문헌

  1. Alazwari, M.A., Daikh, A.A. and Eltaher, M.A. (2022a), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano Res., 12(2), 117. https://doi.org/10.12989/anr.2022.12.2.117.
  2. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40(3), 389-404. http://doi.org/10.12989/scs.2021.40.3.389.
  3. Alazwari, M.A., Esen, I., Abdelrahman, A.A., Abdraboh, A.M. and Eltaher, M.A. (2022b), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load", Adv. Nano Res., 12, 231-251. https://doi.org/10.12989/anr.2022.12.3.231.
  4. Alibeigloo, A. (2014), "Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity", Eur. J. Mech.-A/Solid., 44, 104-115. https://doi.org/10.1016/j.euromechsol.2013.10.002.
  5. Bachiri, A., Daikh, A.A. and Tounsi, A. (2022), "On the thermo-elastic response of FG-CNTRC cross-ply laminated plates under temperature loading using a new HSDT", J. Appl. Comput. Mech., 8(4), 1370-1386. https://doi.org/10.22055/JACM.2022.40148.3529.
  6. Belarbi, M.O., Houari, M.S.A., Hirane, H., Daikh, A.A. and Bordas, S.P.A. (2022), "On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory", Compos. Struct., 279, 114715. https://doi.org/10.1016/j.compstruct.2021.114715.
  7. Bouafia, H., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A., ... & Hussain, M. (2021), "Natural frequencies of FGM nanoplates embedded in an elastic medium", Adv. Nano Res., 11(3), 239-249. https://doi.org/10.12989/anr.2021.11.3.239.
  8. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H. and Luo, J. (2021), "Nonlinear vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying tube in thermal environment", Steel Compos. Struct., 45(5), 641. https://doi.org/10.12989/scs.2022.45.5.641.
  9. Daikh, A.A., Bensaid, I., Bachiri, A., Houari, M.S.A., Tounsi, A. and Merzouki, T. (2020a), "On static bending of multilayered carbon nanotube-reinforced composite plates", Comput. Concrete, 26(2), 137-150. http://doi.org/10.12989/cac.2020.26.2.137.
  10. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher, M.A. (2020b), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36(6), 643-656. https://doi.org/10.12989/scs.2020.36.6.643.
  11. Daikh, A.A., Houari, M.S.A., Belarbi, M.O., Mohamed, S.A. and Eltaher, M.A. (2022), "Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory", Def. Technol., 18(10), 1778-1809. https://doi.org/10.1016/j.dt.2021.09.011.
  12. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11(7), 3250. https://doi.org/10.3390/app11073250.
  13. De Borbon, F., Ambrosini, D. and Curadelli, O. (2014), "Damping response of composites beams with carbon nanotubes", Compos. Part B: Eng., 60, 106-110. https://doi.org/10.1016/j.compositesb.2013.12.041.
  14. Dobrilla, S., Matthies, H.G. and Ibrahimbegovic, A. (2023), "Considerations on the identifiability of fracture and bond properties of reinforced concrete", Int. J. Numer. Meth. Eng., 124(17), 3662-3686. https://doi.org/10.1002/nme.7289.
  15. Drai, A., Daikh, A.A., Belarbi, M.O., Houari, M.S.A., Aour, B., Hamdi, A. and Eltaher, M.A. (2023), "Bending of axially functionally graded carbon nanotubes reinforced composite nanobeams", Adv. Nano Res., 14(3), 211-224. https://doi.org/10.12989/anr.2023.14.3.211
  16. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  17. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  18. Esmaeilzadeh, M., Esmaeil Golmakani, M., Kadkhodayan, M., Amoozgar, M. and Bodaghi, M. (2021), "Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates", Adv. Nano Res., 10(2), 151-163. https://doi.org/10.12989/anr.2021.10.2.151.
  19. Eyvazian, A., Zhang, C., Musharavati, F., Khan, A. and Mohamed, A.M. (2021), "Elastic wave phenomenon of nanobeams including thickness stretching effect", Adv. Nano Res., 10(3), 271. https://doi.org/10.12989/anr.2021.10.3.271.
  20. Ghandourah, E.E., Ahmed, H.M., Eltaher, M.A., Attia, M.A. and Abdraboh, A.M. (2021), "Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model", Adv. Nano Res., 11(4), 405. https://doi.org/10.12989/anr.2021.11.4.405.
  21. Gholami, M., Azandariani, M.G., Ahmed, A.N. and Abdolmaleki, H. (2023), "Proposing a dynamic stiffness method for the free vibration of bi-directional functionally-graded Timoshenko nanobeams", Adv. Nano Res., 14(2), 127-139. https://doi.org/10.12989/.2023.14.2.127.
  22. Gia Phi, B., Van Hieu, D., Sedighi, H.M. and Sofiyev, A.H. (2022), "Size-dependent nonlinear vibration of functionally graded composite micro-beams reinforced by carbon nanotubes with piezoelectric layers in thermal environments", Acta Mechanica, 233(6), 2249-2270. https://doi.org/10.1007/s00707-022-03224-4.
  23. Hajdo, E., Mejia-Nava, R.A., Imamovic, I. and Ibrahimbegovic, A. (2021), "Linearized instability analysis of frame structures under nonconservative loads: Static and dynamic approach", Couple. Syst. Mech., 10(1), 79-102. https://doi.org/10.12989/csm.2021.10.1.079.
  24. Ibrahimbegovic, A. and Nava, R.A.M. (2021), "Heterogeneities and material-scales providing physically-based damping to replace Rayleigh damping for any structure size", Couple. Syst. Mech., 10(3), 201-216. https://doi.org/10.12989/csm.2021.10.3.201.
  25. Ibrahimbegovic, A., Matthies, H.G., Dobrilla, S., Karavelic, E., Nava, R.A.M., Nguyen, C.U., ... & Vondrejc, J. (2022), "Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects", SN Appl. Sci., 4, 191. https://doi.org/10.1007/s42452-022-04935-y.
  26. Ibrahimbegovic, A., Mejia-Nava, R.A., Hajdo, E. and Limnios, N. (2022), "Instability of (Heterogeneous) Euler beam: Deterministic vs. stochastic reduced model approach", Couple. Syst. Mech., 11(2), 167-198. https://doi.org/10.12989/csm.2022.11.2.167.
  27. Ibrahimbegovic, A., Rukavina, I. and Suljevic, S. (2022), "Multiscale model with embedded discontinuity discrete approximation capable of representing full set of 3D failure modes for heterogeneous materials with no scale separation", Int. J. Multisc. Comput. Eng., 20(1), 1-32. https://doi.org/10.1615/IntJMultCompEng.2021038378.
  28. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  29. Jin, Q., Yuan, F.G. and Ren, Y. (2022), "Resonance interaction of flow-conveying nanotubes under forced vibration", Acta Mechanica, 1-21. https://doi.org/10.1007/s00707-022-03425-x.
  30. Ke, L.L., Yang, J. and Kitipornchai, S. (2013), "Dynamic stability of functionally graded carbon nanotube-reinforced composite beams", Mech. Adv. Mater. Struct., 20(1), 28-37. https://doi.org/10.1080/15376494.2011.581412.
  31. Khadir, A. I., Daikh, A.A. and Eltaher, M.A. (2021), "Novel four-unknowns quasi 3D theory for bending, buckling and free vibration of functionally graded carbon nanotubes reinforced composite laminated nanoplates", Adv. Nano Res., 11(6), 621-640. https://doi.org/10.12989/anr.2021.11.6.621.
  32. King, J.A., Via, M.D., Mills, O.P., Alpers, D.S., Sutherland, J.W. and Bogucki, G.R. (2012), "Effects of multiple carbon fillers on the electrical and thermal conductivity and tensile and flexural modulus of polycarbonate-based resins", J. Compos. Mater., 46(3), 331-350. https://doi.org/10.1177/0021998311422750.
  33. Lim, C.W., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  34. Lin, F. and Xiang, Y. (2014), "Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories", Appl. Math. Model., 38(15-16), 3741-3754. https://doi.org/10.1016/j.apm.2014.02.008.
  35. Lu, L., Guo, X. and Zhao, J. (2017), "A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms", Int. J. Eng. Sci., 119, 265-277. https://doi.org/10.1016/j.ijengsci.2017.06.024.
  36. Moreno-Navarro, P., Ibrahimbegovic, A. and Damjanovic, D. (2021), "Multi-scale model for coupled piezoelectric-inelastic behavior", Couple. Syst. Mech., 10(6), 521-544. https://doi.org/10.12989/csm.2021.10.6.521.
  37. Nguyen, C.U., Hoang, T.V., Hadzalic, E., Dobrilla, S., Matthies, H.G. and Ibrahimbegovic, A. (2022), "Viscoplasticity model stochastic parameter identification: Multi-scale approach and Bayesian inference", Couple. Syst. Mech., 11(5), 411-438. https://doi.org/10.12989/csm.2022.11.5.411
  38. Okamoto, M. (2006), "Recent advances in polymer/layered silicate nanocomposites: An overview from science to technology", Mater. Sci. Technol., 22(7), 756-779. https://doi.org/10.1179/174328406X101319.
  39. Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers", Compos. Struct., 96, 716-725. https://doi.org/10.1016/j.compstruct.2012.10.005.
  40. Sagar, S., Iqbal, N., Maqsood, A., Shahid, M., Shah, N.A., Jamil, T. and Bassyouni, M.I. (2015), "Fabrication and thermal characteristics of functionalized carbon nanotubes impregnated polydimethylsiloxane nanocomposites", J. Compos. Mater., 49(8), 995-1006. https://doi.org/10.1177/0021998314528733.
  41. Salem, K.S., Lubna, M.M., Rahman, A.M., NurNabi, M., Islam, R. and Khan, M.A. (2015), "The effect of multiwall carbon nanotube additions on the thermo-mechanical, electrical, and morphological properties of gelatin-polyvinyl alcohol blend nanocomposite", J. Compos. Mater., 49(11), 1379-1391. https://doi.org/10.1177/0021998314534704.
  42. 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.
  43. Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Meth. Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.
  44. Shen, H.S. and Xiang, Y. (2013), "Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments", Eng. Struct., 56, 698-708. https://doi.org/10.1016/j.engstruct.2013.06.002.
  45. Suljevic, S., Ibrahimbegovic, A., Karavelic, E. and Dolarevic, S. (2022), "Meso-scale based parameter identification for 3D concrete plasticity model", Couple. Syst. Mech., 11(1), 55-78. https://doi.org/10.12989/csm.2022.11.1.055.
  46. Tlidji, Y., Benferhat, R., Daouadji, T.H., Tounsi, A. and Trinh, L.C. (2022), "Free vibration analysis of FGP nanobeams with classical and non-classical boundary conditions using State-space approach", Adv. Nano Res., 13(5), 453-463. https://doi.org/10.12989/anr.2022.13.5.453.
  47. Tojaga, V., Gasser, T.C., Kulachenko, A., O stlund, S. and Ibrahimbegovic, A. (2023), "Geometrically exact beam theory with embedded strong discontinuities for the modeling of failure in structures. Part I: Formulation and finite element implementation", Comput. Meth. Appl. Mech. Eng., 410, 116013. https://doi.org/10.1016/j.cma.2023.116013.
  48. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028.
  49. Witvrouw, A. and Mehta, A. (2005), "The use of functionally graded poly-SiGe layers for MEMS applications", Mater. Sci. Forum, 492, 255-260. https://doi.org/10.4028/www.scientific.net/MSF.492-493.255.
  50. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite beams", Appl. Math. Model., 42, 735-752. https://doi.org/10.1016/j.apm.2016.10.045.
  51. Yamamoto, N., de Villoria, R.G. and Wardle, B.L. (2012), "Electrical and thermal property enhancement of fiber-reinforced polymer laminate composites through controlled implementation of multi-walled carbon nanotubes", Compos. Sci. Technol., 72(16), 2009-2015. https://doi.org/10.1016/j.compscitech.2012.09.006.
  52. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Ves. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  53. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., ... & Luo, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.