Skip to main content
SpringerLink
Log in

Nonlinear bending analysis of carbon nanotube-reinforced composite plates in combined thermal and mechanical loading

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This work, by using numerical methods, analyzes for the first time the nonlinear bending of a composite plate into which carbon nanotubes (CNTs) are functionally embedded through the thickness subjected to thermal or combined thermal and mechanical loading. For this purpose, Bézier extraction-based IGA (isogeometric analysis) implemented in the FEM (finite element method) framework while inheriting the merits of conventional IGA is taken advantage of. The Quasi-3D shear deformable plate theory which is able to account for the through-thickness deformations with only four unknowns for the nonlinear thermo-mechanical analysis of the composite plate having CNT dispersion, is established and utilized to construct the nonlinear equilibrium states. The thermo-mechanical coupling effect is also considered in the formulation. The variant presented IGA method by testing multiple benchmark problems, is shown to predict the nonlinear thermal and thermo-mechanical bending behavior successfully. Further parametric investigations highlight effects of the CNT volume fraction, CNT arrangement pattern, plate geometry, plate constraint condition and thermal load type on the nonlinear bending of the CNT-strengthened composite plate in diverse thermal or combined thermo-mechanical loadings. The obtained new results for the nonlinear thermal and thermo-mechanical bending responses of nanocomposite plates, not yet reported in the open literature, are deemed to be utilized as the future reference.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

References

  1. Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)

    Google Scholar 

  2. Thostenson, E.T., Ren, Z., Chou, T.W.: Advances in the science and technology of carbon nanotubes and their composites: a review. Compos. Sci. Technol. 61, 1899–1912 (2001)

    Google Scholar 

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

    Google Scholar 

  4. Zhu, P., Lei, Z.X., Liew, K.M.: 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 (2012)

    Google Scholar 

  5. Lei, Z.X., Liew, K.M., Yu, J.L.: Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method. Comput. Methods Appl. Mech. Eng. 256, 189–199 (2013)

    MathSciNet  MATH  Google Scholar 

  6. Zhang, L.W., Song, Z.G., Liew, K.M.: Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method. Compos. Struct. 128, 165–175 (2015)

    Google Scholar 

  7. Zhang, L.W., Liew, K.M.: Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach. Compos. Struct. 132, 974–983 (2015)

    Google Scholar 

  8. Zhang, L.W., Liew, K.M.: Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates. Comput. Methods Appl. Mech. Eng. 295, 219–239 (2015)

    MathSciNet  MATH  Google Scholar 

  9. Zhang, L.W., Liu, W.H., Liew, K.M.: Geometrically nonlinear large deformation analysis of triangular CNT-reinforced composite plates. Int. J. Nonlinear Mech. 86, 122–132 (2016)

    Google Scholar 

  10. Do, V.N.V., Lee, C.H.: Bending analyses of FG-CNTRC plates using the modified mesh-free radial point interpolation method based on the higher-order shear deformation theory. Compos. Struct. 168, 485–497 (2017)

    Google Scholar 

  11. Ardestani, M.M., Zhang, L.W., Liew, K.M.: Isogeometric analysis of the effect of CNT orientation on the static and vibration behaviors of CNT-reinforced skew composite plates. Comput. Methods Appl. Mech. Eng. 317, 341–379 (2017)

    MathSciNet  MATH  Google Scholar 

  12. Do, V.N.V., Lee, Y.K., Lee, C.H.: Isogeometric analysis of FG-CNTRC plates in combination with hybrid type higher-order shear deformation theory. Thin Walled Struct. 148, 106565 (2020)

    Google Scholar 

  13. Talebizadehsardari, P., Eyvazian, A., Asmael, M., Karami, B., Shahsavari, D., Roohollah Babaei Mahani, R.B.: Static bending analysis of functionally graded polymer composite curved beams reinforced with carbon nanotubes. Thin Walled Struct. 157, 107139 (2020)

    Google Scholar 

  14. Bendenia, N., Zidour, M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Bedia, E.A.A., Mahmoud, S.R., Tounsi, A.: Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation. Comput. Concr. 26, 213–226 (2020)

    Google Scholar 

  15. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S.R.: Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam. Struct. Eng. Mech. 78, 117–124 (2021)

    Google Scholar 

  16. Ke, L.L., Yang, J., Kitipornchai, S.: Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Compos. Struct. 92, 676–683 (2010)

    Google Scholar 

  17. Lei, Z.X., Zhang, L.W., Liew, K.M., Yu, J.L.: Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method. Compos. Struct. 113, 328–338 (2014)

    Google Scholar 

  18. Lei, Z.X., Zhang, L.W., Liew, K.M.: Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method. Compos. Struct. 127, 245–259 (2015)

    Google Scholar 

  19. Zhang, L.W., Xiao, L.N., Zou, G.L., Liew, L.M.: Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method. Compos. Struct. 148, 144–154 (2016)

    Google Scholar 

  20. Zhang, L.W., Zhang, Y., Zou, G.L., Liew, K.M.: Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method. Compos. Struct. 149, 247–260 (2016)

    Google Scholar 

  21. Zhang, L.W., Song, Z.G., Qiao, P., Liew, K.M.: Modeling of dynamic responses of CNT-reinforced composite cylindrical shells under impact loads. Comput. Methods Appl. Mech. Eng. 313, 889–903 (2017)

    MathSciNet  MATH  Google Scholar 

  22. Zhong, R., Wang, Q., Tang, J., Shuai, C., Qin, B.: Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates. Compos. Struct. 194, 49–67 (2018)

    Google Scholar 

  23. Beni, N.N.: Free vibration analysis of annular sector sandwich plates with FG-CNT reinforced composite face-sheets based on the Carrera’s Unified Formulation. Compos. Struct. 214, 269–292 (2019)

    Google Scholar 

  24. Do, V.N.V., Jeon, J.T.: Lee CH (2020) Dynamic analysis of carbon nanotube reinforced composite plates by using Bézier extraction based isogeometric finite element combined with higher order shear deformation theory. Mech. Mater. 142, 103307 (2020)

    Google Scholar 

  25. Liew, K.M., Alibeigloo, A.: Predicting bucking and vibration behaviors of functionally graded carbon nanotube reinforced composite cylindrical panels with three-dimensional flexibilities. Compos. Struct. 256, 113039 (2021)

    Google Scholar 

  26. Karamanli, A., Aydogdu, M.: Vibration behaviors of two-directional carbon nanotube reinforced functionally graded composite plates. Compos. Struct. 262, 113639 (2021)

    Google Scholar 

  27. Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S., Tounsi, A.: Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory. Eng. Comput. (2021). https://doi.org/10.1007/s00366-021-01382-y

    Article  Google Scholar 

  28. Shen, H.S.: Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments. Part I: Axially-loaded shells. Compos. Struct. 93, 2096–2108 (2011)

    Google Scholar 

  29. Shen, H.S.: Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments. Part II: pressure-loaded shells. Compos. Struct. 93, 2496–2503 (2011)

    Google Scholar 

  30. Shen, H.S., Xiang, Y.: Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment. Compos. Part B 52, 311–322 (2013)

    Google Scholar 

  31. Liew, K.M., Lei, Z.X., Yu, J.L., Zhang, L.W.: Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach. Comput. Methods Appl. Mech. Eng. 268, 1–17 (2014)

    MathSciNet  MATH  Google Scholar 

  32. Zhang, L.W., Lei, Z.X., Liew, K.M.: Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach. Compos. Part B 75, 36–46 (2015)

    MATH  Google Scholar 

  33. Zhang, L.W., Liew, K.M., Reddy, J.N.: Postbuckling analysis of bi-axially compressed laminated nanocomposite plates using the first-order shear deformation theory. Compos. Struct. 152, 418–431 (2016)

    Google Scholar 

  34. Zhang, L.W., Ardestani, M.M., Liew, K.M.: Isogeometric approach for buckling analysis of CNT-reinforced composite skew plates under optimal CNT-orientation. Compos. Struct. 163, 365–384 (2017)

    MATH  Google Scholar 

  35. Salem, T., Xie, X., Jiao, P., Lajnef, N.: Maneuverable postbuckling of extensible mechanical metamaterials using functionally graded materials and carbon nanotubes. Thin-Walled Struct. 159, 107264 (2021)

    Google Scholar 

  36. Heidari, F., Taheri, K., Sheybani, M., Janghorban, M., Tounsi, A.: On the mechanics of nanocomposites reinforced by wavy/defected/aggregated nanotubes. Steel. Compos. Struct. 38, 533–545 (2021)

    Google Scholar 

  37. Huang, Y., Karami, B., Shahsavari, D., Tounsi, A.: Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels. Arch. Civ. Mech. Eng. 21, 139 (2021)

    Google Scholar 

  38. Fazzolari, F.A.: Thermoelastic vibration and stability of temperature-dependent carbon nanotube-reinforced composite plates. Compos. Struct. 196, 199–214 (2018)

    Google Scholar 

  39. Wang, J.F., Cao, S.H., Zhang, W.: Thermal vibration and buckling analysis of functionally graded carbon nanotube reinforced composite quadrilateral plate. Eur. J. Mech A Solid 85, 104105 (2021)

    MathSciNet  MATH  Google Scholar 

  40. Shen, H.S., Zhang, C.L.: Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater. Des. 31, 3403–3411 (2010)

    Google Scholar 

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

    Google Scholar 

  42. Ninh, D.G.: Nonlinear thermal torsional post-buckling of carbon nanotube-reinforced composite cylindrical shell with piezoelectric actuator layers surrounded by elastic medium. Thin-Walled Struct. 123, 528–538 (2018)

    Google Scholar 

  43. Farzam, A., Hassani, B.: Thermal and mechanical buckling analysis of FG carbon nanotube reinforced composite plates using modified couple stress theory and isogeometric approach. Compos. Struct. 206, 774–790 (2018)

    Google Scholar 

  44. Hashemi, R., Mirzaei, M., Adlparvar, M.R.: Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT. Adv. Nano Res. 10, 43–57 (2021)

    Google Scholar 

  45. Chakraborty, S., Dey, T.: Non-linear stability analysis of CNT reinforced composite cylindrical shell panel subjected to thermomechanical loading. Compos. Struct. 255, 112995 (2021)

    Google Scholar 

  46. Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos. Part B Eng. 42, 123–133 (2011)

    Google Scholar 

  47. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)

    MathSciNet  MATH  Google Scholar 

  48. Mehrabadi, S.J., Aragh, B.S., Khoshkhahesh, V., Taherpour, A.: Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes. Compos. Part B 43, 2031–2040 (2012)

    Google Scholar 

  49. Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)

    MATH  Google Scholar 

  50. Arya, H., Shimpi, R.P., Naik, N.K.: A zigzag model for laminated composite beams. Compos. Struct. 56, 21–24 (2002)

    Google Scholar 

  51. Fazzolari, F.A., Carrera, E.: Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions. J. Therm. Stress. 37, 1449–1481 (2014)

    Google Scholar 

  52. Zenkour, A.M., Sobhy, M.: Thermal buckling of various types of FGM sandwich plates. Compos. Struct. 93, 93–102 (2010)

    Google Scholar 

  53. Borden, M.J., Scott, M.A., Evans, J.A., Hughes, T.J.R.: Isogeometric finite element data structures based on Bézier extraction of NURBS. Int. J. Numer. Methods Eng. 87, 15–47 (2011)

    MATH  Google Scholar 

  54. Han, Y., Elliott, J.: Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput. Mater. Sci. 39, 315–323 (2007)

    Google Scholar 

  55. Popov, V.N., Doren, V.E.V., Balkanski, M.: Elastic properties of crystals of single-walled carbon nanotubes. Solid State Commun. 114, 395–399 (2000)

    Google Scholar 

  56. Wu, H., Kitipornchai, S., Yang, J.: Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates. Mater. Des. 132, 430–441 (2017)

    Google Scholar 

  57. Aliaga, J.W., Reddy, J.N.: Nonlinear thermoelastic analysis of functionally graded plates using the third-order shear deformation theory. Int. J. Comput. Eng. Sci. 5, 753–779 (2004)

    Google Scholar 

  58. Brischetto, S., Carrera, E.: Coupled thermo-mechanical analysis of one-layered and multilayered plates. Compos. Struct. 92, 1793–1812 (2010)

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1075346).

Author information

Authors and Affiliations

  1. Applied Computational Civil and Structural Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vuong Nguyen Van Do

  2. Department of Civil and Environmental Engineering, Daelim University College, 29, Imgok-ro, Dongan-ku, Anyang-si, Gyeonggi-do, 13916, Republic of Korea

    Chin-Hyung Lee

Authors
  1. Vuong Nguyen Van Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chin-Hyung Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chin-Hyung Lee.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Van Do, V.N., Lee, CH. Nonlinear bending analysis of carbon nanotube-reinforced composite plates in combined thermal and mechanical loading. Acta Mech 233, 3365–3391 (2022). https://doi.org/10.1007/s00707-022-03268-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-022-03268-6

Search

Navigation