Skip to main content
Log in

Thermoelastic buckling and post-buckling behavior of temperature-dependent nanocomposite pipes reinforced with CNTs

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

This research presents a comprehensive study on the thermal buckling and post-buckling behavior of nanocomposite pipes reinforced by carbon nanotubes (CNTs). The distribution profile of CNTs across the radius of nanocomposite pipe can be non-uniform which results in a functionally graded (FG) media. All the thermo-mechanical properties of the FG-CNT reinforced composite pipe which undergoes the uniform temperature rise loading are temperature-dependent. Different kinds of immovable boundary conditions such as simply supported, clamped-clamped, and clamped-rolling are considered. The principle of virtual displacement in conjunction with the higher-order shear deformation theory is employed to obtain the equilibrium equations of the nanocomposite pipe. The nonlinear governing equations are established with the aid of the von Kármán geometric measure and the uncoupled thermoelasticity theory. Utilizing the two-step perturbation technique, maximum deflection of the pipe in the post-buckling state is obtained by an explicit function of elevated temperature. Results of this paper are compared with the available data in the open literature for a homogeneous isotropic pipe. The influences of boundary conditions, the CNT distribution pattern, geometrical characteristics, and the volume fraction of CNTs upon the critical buckling temperature and thermal post-buckling path of nanocomposite pipes are discussed in detail. The novel numerical results of this research show that the maximum value of critical buckling temperatures belongs to the FG-X case of nanocomposite pipes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Y. Huang, X.F. Li, Buckling of functionally graded circular columns including shear deformation. Mater. Des. 31, 3159–3166 (2010)

    Article  Google Scholar 

  2. P. Zhang, Y. Fu, A higher-order beam model for tubes. Eur. J. Mech. A Solids 38, 12–19 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. J. Zhong, Y. Fu, D. Wan, Y. Li, Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model. Appl. Math. Model. 40, 1–14 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. Chen, Y. Fu, J. Zhong, Y. Li, Nonlinear dynamic responses of functionally graded tubes subjected to moving load based on a refined beam model. Nonlinear Dyn. 88, 1441–1452 (2017)

    Article  Google Scholar 

  5. Y. Tang, T. Yang, Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material. Compos. Struct. 185, 393–400 (2018)

    Article  Google Scholar 

  6. Y. Wang, K. Xie, T. Fu, Vibration analysis of functionally graded porous shear deformable tubes excited by moving distributed load. Acta Astron. 151, 603–613 (2018)

    Article  Google Scholar 

  7. H. Babaei, Y. Kiani, M.R. Eslami, Buckling and post-buckling analysis of geometrically imperfect FGM pin-ended tubes surrounded by nonlinear elastic medium under compressive and thermal loads. Int. J. Struct. Stab. Dyn. 19, 1950089 (2019)

    Article  MathSciNet  Google Scholar 

  8. A.M. Dehrouyeh-Semnani, E. Dehdashti, M.R. Hairi Yazdi, M. Nikkhah-Bahrami, Nonlinear thermo-resonant behavior of fluid-conveying FG pipes. Int. J. Eng. Sci. 144, 103141 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Dai, Y. Liu, H. Liu, C. Miao, G. Tong, A parametric study on thermo-mechanical vibration of axially functionally graded material pipe conveying fluid. Int. J. Mech. Mater. Des. 15, 715–726 (2019)

    Article  Google Scholar 

  10. A. Ebrahimi-Mamaghani, R. Sotudeh-Garebagh, R. Zarghami, N. Mostoufi, Thermo-mechanical stability of axially graded Rayleigh pipes. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2020.1717967

    Article  Google Scholar 

  11. N.D. Duc, Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells (Vietnam National University Press, Hanoi, 2014)

    Google Scholar 

  12. H. Li, F. Pang, Y. Li, C. Gong, Application of first-order shear deformation theory for the vibration analysis of functionally graded doubly-curved shells of revolution. Compos. Struct. 212, 22–42 (2019)

    Article  Google Scholar 

  13. H. Li, F. Pang, Q. Gong, Y. Teng, Free vibration analysis of axisymmetric functionally graded doubly-curved shells with un-uniform thickness distribution based on Ritz method. Compos. Struct. 225, 111145 (2019)

    Article  Google Scholar 

  14. H. Li, F. Pang, Y. Ren, X. Miao, K. Ye, Free vibration characteristics of functionally graded porous spherical shell with general boundary conditions by using first-order shear deformation theory. Thin-Walled Struct. 144, 106331 (2019)

    Article  Google Scholar 

  15. H. Li, F. Pang, H. Chen, Y. Du, Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method. Compos. Part B 164, 249–264 (2019)

    Article  Google Scholar 

  16. H. Li, F. Pang, Y. Du, C. Gao, Free vibration analysis of uniform and stepped functionally graded circular cylindrical shells. Steel Compos. Struct. 33, 163–180 (2019)

    Article  ADS  Google Scholar 

  17. Q. Gong, H. Li, H. Chen, Y. Teng, N. Wang, Application of Ritz method for vibration analysis of stepped functionally graded spherical torus shell with general boundary conditions. Compos. Struct. 243, 112215 (2020)

    Article  Google Scholar 

  18. A.R. Setoodeh, S. Afrahim, Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory. Compos. Struct. 116, 128–135 (2014)

    Article  Google Scholar 

  19. A.M. Dehrouyeh-Semnani, M. Nikkhah-Bahrami, M.R. Hairi Yazdi, On nonlinear vibrations of micropipes conveying fluid. Int. J. Eng. Sci. 117, 20–33 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  20. A.M. Dehrouyeh-Semnani, M. Nikkhah-Bahrami, M.R. Hairi Yazdi, On nonlinear stability of fluid-conveying imperfect micropipes. Int. J. Eng. Sci. 120, 254–271 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. G.L. She, F.G. Yuan, Y.R. Ren, W.S. Xiaoa, On buckling and postbuckling behavior of nanotubes. Int. J. Eng. Sci. 121, 130–142 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Mohammadimehr, M. Mehrabi, Electro-thermo-mechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow. Appl. Math. Model. 60, 255–272 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  23. N. Shafiei, G.L. She, On vibration of functionally graded nanotubes in thermal environment. Int. J. Eng. Sci. 133, 84–98 (2018)

    Article  MATH  Google Scholar 

  24. L. Li, Y. Hu, Torsional statics of two-dimensionally functionally graded microtubes. Mech. Adv. Mater. Struct. 26, 430–442 (2019)

    Article  Google Scholar 

  25. Y. Gao, W.S. Xiao, H. Zhu, Nonlinear vibration of different types of functionally graded nanotubes using nonlocal strain gradient theory. Eur. Phys. J. Plus 134, 345–365 (2019)

    Article  Google Scholar 

  26. B. Karami, M. Janghorban, On the dynamics of porous nanotubes with variable material properties and variable thickness. Int. J. Eng. Sci. 136, 53–66 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  27. H. Liu, Z. Lv, H. Tang, Nonlinear vibration and instability of functionally graded nanopipes with initial imperfection conveying fluid. Appl. Math. Model. 76, 133–150 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  28. G. Tong, Y. Liu, Q. Cengh, J. Dai, Stability analysis of cantilever functionally graded material nanotube under thermo-magnetic coupling effect. Eur. J. Mech. A Solids 80, 103929 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. H. Mohammad Sedighi, H. Ouakad, R. Dimitri, F. Tornabene, Stress-driven nonlocal elasticity for instability analysis of fluid-conveying C-BN hybrid-nanotube in magnetic and thermal environment. Phys. Scr. 95(6), 065204 (2020)

    Article  Google Scholar 

  30. S.K. Jena, S. Chakraverty, M. Malikan, F. Tornabene, Stability analysis of single-walled carbon nanotubes embedded in Winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2019.1698437

    Article  Google Scholar 

  31. N. Mohamed, S.A. Mohamed, M.A. Eltaher, Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model. Eng. Comput. (2020). https://doi.org/10.1007/s00366-020-00976-2

    Article  Google Scholar 

  32. O. Civalek, B. Uzun, M.O. Yaylı, B. Akgöz, Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method. Eur. Phys. J. Plus 135, 381 (2020)

    Article  Google Scholar 

  33. H. Babaei, M.R. Eslami, Limit load analysis and imperfection sensitivity of porous FG micro-tubes surrounded by a nonlinear softening elastic medium. Acta Mech. 231, 4563–4583 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  34. H. Babaei, M.R. Eslami, Thermally induced nonlinear stability and imperfection sensitivity of temperature- and size-dependent FG porous micro-tubes. Int. J. Mech. Mater. Des. 17, 381–401 (2021)

    Article  Google Scholar 

  35. H. Babaei, M.R. Eslami, On nonlinear vibration and snap-through stability of porous FG curved micro-tubes using two-step perturbation technique. Compos. Struct. 247, 112447 (2020)

    Article  Google Scholar 

  36. H. Babaei, M.R. Eslami, Nonlinear analysis of thermal-mechanical coupling bending of clamped FG porous curved micro-tubes. J. Therm. Stress. 44, 409–432 (2021)

    Article  Google Scholar 

  37. L. Lu, G.L. She, X. Guo, Size-dependent post-buckling analysis of graphene reinforced composite microtubes with geometrical imperfection. Int. J. Mech. Sci. 199, 106428 (2021)

    Article  Google Scholar 

  38. H. Babaei, Nonlinear analysis of size-dependent frequencies in porous FG curved nanotubes based on nonlocal strain gradient theory. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01317-7

    Article  Google Scholar 

  39. H. Babaei, Large deflection analysis of FG-CNT reinforced composite pipes under thermal-mechanical coupling loading. Structures 34, 886–900 (2021)

    Article  Google Scholar 

  40. H. Babaei, On frequency response of FG-CNT reinforced composite pipes in thermally pre/post buckled configurations. Compos. Struct. 276, 114467 (2021)

    Article  Google Scholar 

  41. H.S. Shen, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells. Compos. Part B 43, 1030–1038 (2012)

    Article  Google Scholar 

  42. N.D. Duc, P.H. Cong, N.D. Tuan, P. Tran, N.V. Thanh, Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations. Thin-Walled Struct. 115, 300–310 (2017)

    Article  Google Scholar 

  43. N.V. Thanh, N.D. Khoa, N.D. Tuan, P. Tran, N.D. Duc, Nonlinear dynamic response and vibration of functionally graded carbon nanotubes reinforced composite shear deformable plates with temperature dependence properties and surrounded on elastic foundations. J. Therm. Stress. 40, 1254–1274 (2017)

    Article  Google Scholar 

  44. N.D. Duc, T.Q. Quan, N.D. Khoa, New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature. Aerosp. Sci. Technol. 71, 360–372 (2017)

    Article  Google Scholar 

  45. D.Q. Chan, P.D. Nguyen, V.D. Quang, V.T.T. Anh, N.D. Duc, Nonlinear buckling and post-buckling of functionally graded carbon nanotubes reinforced composite truncated conical shells subjected to axial load. Steel Compos. Struct. 31, 243–259 (2019)

    Google Scholar 

  46. N.D. Dat, N.V. Thanh, V.M. Anh, N.D. Duc, Vibration and nonlinear dynamic analysis of sandwich FG-CNTRC plate with porous core layer. Mech. Adv. Mater. Struct. (2020). https://doi.org/10.1080/15376494.2020.1822476

    Article  Google Scholar 

  47. N.D. Dat, T.Q. Quan, V. Mahesh, N.D. Duc, Analytical solutions for nonlinear magneto-electro-elastic vibration of smart sandwich plate with carbon nanotube reinforced nanocomposite core in hygrothermal environment. Int. J. Mech. Sci. 186, 105906 (2020)

    Article  Google Scholar 

  48. D.T. Manh, V.T.T. Anh, P.D. Nguyen, N.D. Duc, Nonlinear post-buckling of CNTs reinforced sandwich-structured composite annular spherical shells. Int. J. Struct. Stab. Dyn. 20, 2050018 (2020)

    Article  MathSciNet  Google Scholar 

  49. A.H. Sofiyev, Z. Mammadov, R. Dimitri, F. Tornabene, Vibration analysis of shear deformable carbon nanotubes-based functionally graded conical shells resting on elastic foundations. Math. Methods Appl. Sci. (2020). https://doi.org/10.1002/mma.6674

    Article  Google Scholar 

  50. H.S. Shen, Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments. Compos. Struct. 91, 9–19 (2009)

    Article  Google Scholar 

  51. R. Moradi-Dastjerdi, M. Foroutan, A. Pourasghari, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Mater. Des. 44, 256–266 (2013)

    Article  Google Scholar 

  52. H.S. Shen, Functionally Graded Materials Nonlinear Analysis of Plates and Shells (CRC Press, Boca Raton, 2009)

    Google Scholar 

  53. H. Babaei, M.R. Eslami, Nonlinear bending analysis of size-dependent FG porous microtubes in thermal environment based on modified couple stress theory. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2020.1784202

    Article  Google Scholar 

  54. M.R. Eslami, Buckling and Postbuckling of Beams, Plates, and Shells (Springer, Cham, 2018)

    Book  MATH  Google Scholar 

  55. J.N. Reddy, Mechanics of Laminated Composite Plates and Shells, Theory and Application (CRC Press, Boca Raton, 2003)

    Book  Google Scholar 

  56. H.S. Shen, A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells (Wiley, Hoboken, 2013)

    Book  MATH  Google Scholar 

  57. H.S. Shen, Y. Xiang, Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments. Eng. Struct. 56, 698–708 (2013)

    Article  Google Scholar 

  58. S. Khosravi, H. Arvin, Y. Kiani, Interactive thermal and inertial buckling of rotating temperature-dependent FG-CNT reinforced composite beams. Compos. Part B 175, 107178 (2019)

    Article  Google Scholar 

  59. Y. Fu, J. Zhong, X. Shao, Y. Chen, Thermal postbuckling analysis of functionally graded tubes based on a refined beam model. Int. J. Mech. Sci. 96, 58–64 (2015)

    Article  Google Scholar 

  60. G.L. She, F.G. Yuan, Y.R. Ren, Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory. Compos. Struct. 165, 74–82 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hadi Babaei.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babaei, H. Thermoelastic buckling and post-buckling behavior of temperature-dependent nanocomposite pipes reinforced with CNTs. Eur. Phys. J. Plus 136, 1093 (2021). https://doi.org/10.1140/epjp/s13360-021-01992-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01992-x

Navigation