DOI QR코드

DOI QR Code

Nonlinear FG-CNT effect on the critical buckling load of nanocomposite beams with different boundary conditions

  • Youcef Tlidji (Materials and Structures Laboratory, Civil Engineering Department, University of Tiaret) ;
  • Mohamed Zidour (Laboratory of Geomatics and Sustainable Development, University of Tiaret) ;
  • Rachid Zerrouki (Laboratory of Geomatics and Sustainable Development, University of Tiaret) ;
  • Abdelillah Benahmed (Laboratory of Geomatics and Sustainable Development, University of Tiaret) ;
  • Boumediene Serbah (Water and Works in Their Environment Laboratory (EOLE), University of Tlemcen) ;
  • Kada Draiche (Civil Engineering Department, University of Tiaret) ;
  • Khaled Bouakkaz (Materials and Structures Laboratory, Civil Engineering Department, University of Tiaret)
  • Received : 2024.05.10
  • Accepted : 2024.09.19
  • Published : 2024.10.25

Abstract

This paper deals with the effect of non-linear volume fraction distribution of carbon nanotube in the FG-CNTRC beams on the critical buckling via a hyperbolic shear deformation theory. Here, different boundary condition was considered including hinged hinged, clamped clamped and clamped-free. Single-walled carbon nanotubes are aligned and distributed in the polymer matrix in different ways to reinforce it and the material properties of (CNTRC) beams are assumed to vary gradually along the thickness direction, following a new exponential power law distribution of (CNT). The effective material properties of nanocomposite beams are estimated using the rule of mixture. The governing equations of the mathematical models are obtained by applying Hamilton's principle. The results provided of mathematical models in this work are compared and validated with similar ones in the literature. The critical buckling loads of nanocomposite beams with different boundary conditions of linear and non-linear distribution of CNT volume fraction were obtained. The effects of several parameters, including the type of beam, the volume fraction of carbon nanotubes (CNTs), the exponent degree (n), and the aspect ratio, were investigated. The distribution non-linearity of CNT volume fraction in the beam has a significant impact on the mechanical properties, particularly in buckling behavior with different boundary conditions.

Keywords

Acknowledgement

The authors would like to acknowledge the support provided by the Directorate General for Scientific Research and Technological Development (DGRSDT).

References

  1. Alhaifi, K., Khorshidvand, A.R., Al-Masoudy, M.M., Arshid, E. and Madani, S.H. (2023), "A shooting method for buckling and post-buckling analyses of FGSP circular plates considering various patterns of Pores' placement", Struct. Eng. Mech., 85(3), 419-432. https://doi.org/10.12989/sem.2023.85.3.419
  2. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with Carbonnanotubes", Comput. Concr., 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  3. Belarbi, M.O., Salami, S.J., Garg, A., Daikh, A.A., Houari, M.S. A., Dimitri, R. and Tornabene, F. (2023), "Mechanical behavior analysis of FG-CNT-reinforced polymer composite beams via a hyperbolic shear deformation theory", Continuum Mech. Thermodyn., 35, 497-520. https://doi.org/10.1007/s00161-023-01191-2
  4. Chang, G., Huang, H. and Li, Z. (2024). "Systematic failure mechanism of an FGMs polyhedral arched liner under a fire disaster environment", Eng. Struct., 305, 117655. https://doi.org/10.1016/j.engstruct.2024.117655
  5. Chang, G. and Li, Z. (2024). "Systematic schemes for buckling analyses of a subsea bio-inspired non-circular FGM polyhedral liner with an arch invert", Ocean Eng., 300, 117484. https://doi.org/10.1016/j.oceaneng.2024.117484
  6. Ebrahimi, F. and Habibi, S. (2017). "Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment", Adv. Nano Res., 5(2), 69. https://doi.org/10.12989/anr.2017.5.2.069
  7. Dresselhaus, M.S. and Avouris, P. (2001), Introduction to Carbon Materials Research, In Carbon Nanotubes, Topics Appl. Phys., 80, 1-9, Springer, Berlin, Heidelberg.
  8. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39-49, http://doi.org/10.12989/anr.2019.7.1.039
  9. Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res, 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405
  10. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  11. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  12. Jiang B., Liu C., Zhang C., Liang R. and Wang B. (2009), "Maximum nanotube volume fraction and its effect on overall elastic properties of nanotube-reinforced composites", Compos. Part B, 40, 212-217. https://doi.org/10.1016/j.compositesb.2008.11.003
  13. Jin, Y. and Yuan, F.G. (2003), "Simulation of elastic properties of single-walled carbon nanotubes", Compos. Sci. Technol., 63(11), 1507-1515. https://doi.org/10.1016/S0266-3538(03)00074-5
  14. Kiani, Y. (2017), "Buckling of FG-CNT-reinforced composite plates subjected to parabolic loading", Acta Mechanica, 228(4), 1303-1319, https://doi.org/10.1007/s00707-016-1781-4.
  15. Kiani, Y., Bagherizadeh, E. and Eslami, M.R. (2011), "Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation (Three approximate analytical solutions)", Zeitschr. Angwe. Math. Mech, 91(7), 581-593. https://doi.org/10.1002/zamm.201000184.
  16. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2020). "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezo-elasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., 22(1), 3-27. https://doi.org/10.1177/1099636217731071
  17. Li, Z., Zhang, Q., Shen, H., Xiao, X., Kuai, H. and Zheng, J. (2023). "Buckling performance of the encased functionally graded porous composite liner with polyhedral shapes reinforced by graphene platelets under external pressure", Thin Wall. Struct., 183, 110370. https://doi.org/10.1016/j.tws.2022.110370
  18. Mallek, H., Jrad, H., Wali, M., Kessentini, A., Gamaoun, F. and Dammak, F. (2020), "Dynamic analysis of functionally graded carbon nanotube-reinforced shell structures with piezoelectric layers under dynamic loads", J. Vib. Control, 26(13-14), 1157-1172. https://doi.org/10.1177/1077546319892753.
  19. Heidari, F., Afsari, A. and Janghorban, M. (2020), "Several models for bending and buckling behaviors of FG-CNTRCs with piezoelectric layers including size effects", Adv. Nano Res., 9(3), 193-210. https://doi.org/10.12989/anr.2020.9.3.193
  20. Mayandi, K. and Jeyaraj, P. (2015), "Bending, buckling and free vibration characteristics of FG-CNT polymer composite beam under non-uniform thermal load", J. Mater. Des. Appl., 229, 13-28. https://doi.org/10.1177/1464420713493720
  21. Mehar, K. and Panda, S.K. (2018), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39, 2751-2764. https://doi.org/10.1002/pc.24266
  22. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2020), "Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method", Comput. Math. Appl., 79(11), 3160-3187,. https://doi.org/10.1016/j.camwa.2020.01.015.
  23. Mirzaei, M. and Kiani, Y. (2016), "Thermal buckling of temperature dependent FG-CNT reinforced composite plates", Meccanica, 51, 2185-2201. https://doi.org/10.1007/s11012-015-0348-0
  24. Mohammadimehr, M., Shahedi, S. and Rousta Navi, B. (2017), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 231(20), 3866-3885. https://doi.org/10.1177/0954406216653622
  25. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology" Int. J. Eng. Sci., 41(3-5), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  26. Phung-Van, P., Thanh, C.L., Nguyen-Xuan, H. and Abdel-Wahab, M. (2018), "Nonlinear transient isogeometric analysis of FG-CNTRC nanoplates in thermal environments", Compos. Struct., 201, 882-892. https://doi.org/10.1016/j.compstruct.2018.06.087.
  27. Ru, C.Q. (2000), "Elastic buckling of single-walled carbon nanotube ropes under high pressure", Phys. Rev. B, 62(15), 10405. https://doi.org/10.1103/PhysRevB.62.10405.
  28. She, G.L., Yuan, F.G., Ren, Y.R. and Xiao, W.S. (2017), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005
  29. 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.
  30. Simsek M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng. Des., 240, 697-705. http://doi.org/10.1016/j.nucengdes.2009.12.013
  31. Tagrara, S.H., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  32. 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. https://doi.org/10.12989/anr.2022.13.5.453
  33. Vodenitcharova, T. and Zhang, L.C. (2006), "Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube", J. Sol. Struct., 43(10), 3006-3024. https://doi.org/10.1016/j.ijsolstr.2005.05.014
  34. Wang, Q., Varadan, V. K. and Quek, S. T. (2006), "Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models", Phys. Lett. A, 357(2), 130-135. https://doi.org/10.1016/j.physleta.2006.04.026.
  35. Weon, J.I. (2009), "Mechanical and thermal behavior of polyamide-6/clay nanocomposite using continuumbased micro-mechanical modeling", Macromol. Res., 17(10), 797-806. https://doi.org/10.1007/BF03218617.
  36. Wu, H., Kitipornchai, S. and Yang, J. (2015), "Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets", J. Struct. Stab. Dyn., 15(7), 1540011. https://doi.org/10.1142/S0219455415400118
  37. Yang, J., Ke, L.L. and Feng, C. (2015), "Dynamic buckling of thermo-electro-mechanically loaded FGCNTRC beams", J. Struct. Stab. Dyn., 15(8), 1540017. https://doi.org/10.1142/S0219455415400179
  38. 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. Vessels Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  39. Zenkour, A.M. (2018), "Modified couple stress theory for micro-machined beam resonators with linearly varying thickness and various boundary conditions", Arch. Mech. Eng., 65(1), 43-64. https://doi.org/10.24425/119409.
  40. Zerrouki, R., Karas, A. and Zidour, M. (2020), "Critical buckling analyses of nonlinear FG-CNT reinforced nano-composite beam", Adv. Nano Res., 9(3), 211-220. https://doi.org/10.12989/anr.2020.9.3.211
  41. Zghal, S., Ataoui, D. and Dammak, F (2020), "Static bending analysis of beams made of functionally graded porous materials", Mech. Based Des. Struct., 50(3),1-18. https://doi.org/10.1080/15397734.2020.1748053.
  42. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015), "Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach", Compos. Part B Eng., 75, 36-46. https://doi.org/10.1016/j.compositesb.2015.01.033.
  43. Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016), "Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression", Comput. Meth. Appl. Mech. Eng., 298, 1-28. https://doi.org/10.1016/j.cma.2015.09.016.
  44. Zhang, S., Bu, R., Zhang, Z., Gao, L. and Li, Z. (2024). "A systematic model for the mechanical behavior of thin-walled composite FGM pipelines subjected to strike-slip faults in geohazard area", Thin Wall. Struct., 112135. https://doi.org/10.1016/j.tws.2024.112135
  45. 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", Compos. Struct., 94, 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010
  46. Xiao, X., Bu, G., Ou, Z. and Li, Z. (2022), "Nonlinear in-plane instability of the confined FGP arches with nanocomposites reinforcement under radially-directed uniform pressure", Eng. Struct., 252, 113670. https://doi.org/10.1016/j.engstruct.2021.113670
  47. Xiao, X., Zhang, Q., Chang, G., Liu, Y. and Li, Z. (2024), "Structural optimization model of confined polyhedral composite subsea pipelines under pressure and thermal fields", Marine Struct., 94, 103548. https://doi.org/10.1016/j.marstruc.2023.103548
  48. Xiao, X., Zhang, Q., Zheng, J. and Li, Z. (2023), "Analytical model for the nonlinear buckling responses of the confined polyhedral FGP-GPLs lining subjected to crown point loading", Eng. Struct., 282, 115780. https://doi.org/10.1016/j.engstruct.2023.115780