Skip to main content
Log in

Stability of functionally graded graphene-reinforced composite laminated thick plates in thermal environment

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

Abstract

Considering the excellent physical properties, graphene can be regarded as an ideal reinforcing material for composite structures today. Nevertheless, the existing higher-order models neglecting the continuity conditions of interlaminar stresses may lose capability to analyze precisely the stability of functionally graded graphene-reinforced composite (FG-GRC) laminated thick plates. For FG-GRC laminated structures, the compatibility conditions of interlaminar stresses will directly affect the accuracy of critical loads. As a result, an appealing plate theory with only seven unknowns is suggested for buckling analysis of FG-GRC laminated thick plates. The compatibility requirements of interlaminar shear stresses between adjacent layers are satisfied in the proposed model. Improved transverse shear stresses are obtained using a preprocessing approach based on the three-dimensional (3D) equilibrium equation and Reissner's mixed variational theorem (RMVT). The performance of the suggested model is assessed by using the 3D elasticity solutions and the results obtained from some existing models. Numerical results indicate that the proposed model can reliably predict critical loads of laminated and sandwich plates. Additionally, the impact of the graphene distribution pattern, staking sequence, volume fraction, boundary conditions, thermal environment, and geometric parameters of the plate on the buckling behavior of FG-GRC laminated plates is explored.

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

Similar content being viewed by others

References

  1. Wu, H.L., Yang, J., Kitipornchai, S.: Dynamic instability of functionally graded multilayer graphene nano-composite beams in thermal environment. Compos. Struct. 162, 244–254 (2017)

    Article  Google Scholar 

  2. Moghadam, A.D., Omrani, E., Menezes, P.L., Rohatgi, P.K.: Mechanical and tribological properties of self-lubricating metal matrix nanocomposites reinforced by carbon nanotubes (CNTs) and graphene—a review. Compos. Part B-Eng. 77, 402–420 (2015)

    Article  Google Scholar 

  3. Affdl, J.C.H., Kardos, J.L.: The Halpin-Tsai equations: a review. Polym. Eng. Sci. 16, 344–352 (1976)

    Article  Google Scholar 

  4. Li, Q., Wu, D., Chen, X., Liu, L., Yu, Y., Gao, W.: Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation. Int. J. Mech. Sci. 148, 596–610 (2018)

    Article  Google Scholar 

  5. Anamagh, M.R., Bediz, B.: Free vibration and buckling behavior of functionally graded porous plates reinforced by graphene platelets using spectral Chebyshev approach. Compos. Struct. 253, 112765 (2020)

    Article  Google Scholar 

  6. Zhao, S., Yang, Z., Kitipornchai, S., Yang, J.: Dynamic instability of functionally graded porous arches reinforced by graphene platelets. Thin Walled Struct. 147, 106491 (2020)

    Article  Google Scholar 

  7. Yang, Z., Huang, Y., Liu, A., Fu, J., Di, W.: Nonlinear in-plane buckling of fixed shallow functionally graded graphene reinforced composite arches subjected to mechanical and thermal loading. Appl. Math. Model. 70, 315–327 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  8. Song, M.T., Yang, J., Kitipornchai, S.: Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos. Part B-Eng. 134, 106–113 (2018)

    Article  Google Scholar 

  9. Feng, C., Kitipornchai, S., Yang, J.: Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Eng. Struct. 140, 110119 (2017)

    Article  Google Scholar 

  10. Song, M.T., Li, X.Q., Kitipornchai, S., Bi, Q.S., Yang, J.: Low-velocity impact response of geometrically nonlinear functionally graded graphene platelet-reinforced nanocomposite plates. Nonlinear Dyn. 95, 2333–2352 (2019)

    Article  Google Scholar 

  11. Song, M.T., Yang, J., Kitipornchai, S., Zhu, W.D.: Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatele treinforced polymer composite plates. Int. J. Mech. Sci. 131–132, 345–355 (2017)

    Article  Google Scholar 

  12. Yang, J., Wu, H.L., Kitipornchai, S.: Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Compos. Struct. 161, 111–118 (2017)

    Article  Google Scholar 

  13. Wu, H.L., Yang, J., Kitipornchai, S.: Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates. Int. J. Mech. Sci. 135, 431–440 (2018)

    Article  Google Scholar 

  14. Tam, M., Yang, Z., Zhao, S., Yang, J.: Vibration and buckling characteristics of functionally graded graphene nanoplatelets reinforced composite beams with open edge cracks. Materials 12, 1412 (2019)

    Article  Google Scholar 

  15. Wang, Y., Xie, K., Fu, T.: Vibration analysis of functionally graded graphene oxide-reinforced composite beams using a new Ritz-solution shape function. J. Braz. Soc. Mech. Sci. 42, 1–14 (2020)

    Google Scholar 

  16. Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B., Xuan, H.N.: A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets. Compos. Struct. 245, 112321 (2020)

    Article  Google Scholar 

  17. Lu, L., Wang, S., Li, M., Guo, X.: Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets. Compos. Struct. 272, 114231 (2021)

    Article  Google Scholar 

  18. Thai, C.H., Ferreira, A.J.M., Tran, T.D., Phung-Van, P.: Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation. Compos. Struct. 220, 749–759 (2019)

    Article  Google Scholar 

  19. Anirudh, B., Ganapathi, M., Anant, C., Polit, O.: A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling. Compos. Struct. 222, 110899 (2019)

    Article  Google Scholar 

  20. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M.: Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory. Comput. Concr. 26, 439–450 (2021)

    Google Scholar 

  21. Al-Furjan, M.S.H., Habibi, M., Ghabussi, A., Safarpour, H., Safarpour, M., Tounsi, A.: Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory. Eng. Struct. 228, 111496 (2021)

    Article  Google Scholar 

  22. Arefi, M., Bidgoli, E.M., Rabczuk, T.: Effect of various characteristics of graphene nanoplatelets on thermal buckling behavior of FGRC micro plate based on MCST. Eur. J. Mech. A-Solids 77, 103802 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  23. Lei, Z., Su, Q., Zeng, H., Zhang, Y., Yu, C.: Parametric studies on buckling behavior of functionally graded graphene-reinforced composites laminated plates in thermal environment. Compos. Struct. 202, 695–709 (2018)

    Article  Google Scholar 

  24. Mao, J.J., Zhang, W., Lu, H.M.: Static and dynamic analyses of graphene-reinforced aluminium-based composite plate in thermal environment. Aerosp. Sci. Technol. 107, 106354 (2020)

    Article  Google Scholar 

  25. Ebrahimi, F., Nouraei, M., Dabbagh, A.: Modeling vibration behavior of embedded graphene-oxide powder-reinforced nanocomposite plates in thermal environment. Mech. Based Des. Struct. 48, 217–240 (2020)

    Article  Google Scholar 

  26. Zheng, J., Zhang, C., Musharavati, F., Khan, A., Sebaey, T.A., Eyvazian, A.: Forced vibration characteristics of embedded graphene oxide powder reinforced metal foam nanocomposite plate in thermal environment. Case. Studies Therm. Eng. 27, 101167 (2021)

    Article  Google Scholar 

  27. Yang, Z.C., Lu, H.W., Sahmani, S., Safaei, B.: Isogeometric couple stress continuum-based linear and nonlinear flexural responses of functionally graded composite microplates with variable thickness. Arch. Civ. Mech. Eng. 21, 114 (2021)

    Article  Google Scholar 

  28. Yang, Z.C., Feng, C., Yang, J., Wang, Y., Lv, J.G., Liu, A.R.: Geometrically nonlinear buckling of graphene platelets reinforced dielectric composite (GPLRDC) arches with rotational end restraints. Aerosp. Sci. Technol. 107, 106326 (2020)

    Article  Google Scholar 

  29. Yang, Z.C., Safaei, B., Sahmani, S., Zhang, Y.J.: A couple-stress-based moving Kriging meshfree shell model for axial postbuckling analysis of random checkerboard composite cylindrical microshells. Thin Walled Struct. 170, 108631 (2022)

    Article  Google Scholar 

  30. Yang, Z.C., Liu, A.R., Lai, S.K., Safaei, B., Lv, J.G., Huang, Y.H., Fu, J.Y.: Thermally induced instability on asymmetric buckling analysis of pinned-fixed FG-GPLRC arches. Eng. Struct. 250, 113243 (2022)

    Article  Google Scholar 

  31. Yang, Z.C., Wu, D., Lai, S.K., Lv, J.G., Liu, A.R., Fu, J.Y.: Dynamic buckling of rotationally restrained FG porous arches reinforced with graphene nanoplatelets under a uniform step load. Thin Walled Struct. 166, 108103 (2021)

    Article  Google Scholar 

  32. Shen, H.S., Xiang, Y., Lin, F.: Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments. Comput. Method Appl. Mech. 319, 175–193 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. Kiania, Y., Mirzaei, M.: Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements. Compos. Struct. 186, 114–122 (2018)

    Article  Google Scholar 

  34. Mirzaei, M., Kiania, Y.: Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation. Compos. Struct. 180, 606–616 (2017)

    Article  Google Scholar 

  35. Kiania, Y.: Buckling of functionally graded graphene reinforced conical shells under external pressure in thermal environment. Compos. Part B-Eng. 156, 128–137 (2019)

    Article  Google Scholar 

  36. Kiani, Y.: NURBS-Based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates. J. Therm. Stress 43, 90–108 (2019)

    Article  Google Scholar 

  37. Singha, T.D., Rout, M., Bandyopadhyay, T., Karmakar, A.: Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT. Compos. Struct. 257, 113144 (2020)

    Article  Google Scholar 

  38. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–752 (1984)

    Article  MATH  Google Scholar 

  39. Shen, H.S., Xiang, Y., Lin, F.: Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments. Compos. Struct. 170, 80–90 (2017)

    Article  Google Scholar 

  40. Shen, H.S., Xiang, Y.: Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical shells subjected to external pressure in thermal environments. Thin-Walled Struct. 124, 151–160 (2018)

    Article  Google Scholar 

  41. Shen, H.S., Xiang, Y., Lin, F.: Thermal buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations. Thin-Walled Struct. 118, 229–237 (2017)

    Article  Google Scholar 

  42. Shen, H.S., Xiang, Y., Fan, Y., Hui, D.: Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments. Compos. Part B-Eng. 136, 177–186 (2018)

    Article  Google Scholar 

  43. Wang, Z.X., Shen, H.S.: Nonlinear vibration of sandwich plates with FG-GRC face sheets in thermal environments. Compos. Struct. 192, 642–653 (2018)

    Article  Google Scholar 

  44. Zhang, D.J., Zheng, X.T., Wang, C.Z., Wu, Z.: Experiments and analysis on stability of the sandwich structures with soft core. Int. J. Struct. Stab. Dyn. 19, 1950159 (2019)

    Article  MathSciNet  Google Scholar 

  45. Robbins, D.H., Reddy, J.N.: Modelling of thick composites using a layer wise laminate theory. Int. J. Numer. Methods Eng. 36, 665–677 (1993)

    Article  Google Scholar 

  46. Zhen, W., Chen, W.: An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams. Compos. Struct. 84, 337–349 (2008)

    Article  Google Scholar 

  47. Reissner, E.: On a certain mixed variational theorem and a proposed application. Int. J. Numer. Methods Eng. 20, 1366–1368 (1984)

    Article  MATH  Google Scholar 

  48. Reissner, E.: On a mixed variational theorem and on a shear deformable plate theory. Int. J. Numer. Methods Eng. 23, 193–198 (1986)

    Article  MATH  Google Scholar 

  49. Kant, T., Swaminathan, K.: Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos. Struct. 56, 329–344 (2002)

    Article  Google Scholar 

  50. Noor, A.K.: Stability of multilayered composite plates. Fibre Sci. Technol. 8, 81–89 (1975)

    Article  Google Scholar 

  51. Dafedar, J.B., Desai, Y.M., Mufti, A.A.: Stability of sandwich plates by mixed, higher-order analytical formulation. Int. J. Solids Struct. 40, 4501–4517 (2003)

    Article  MATH  Google Scholar 

  52. Matsunaga, H.: Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos. Struct. 48, 231–244 (2000)

    Article  Google Scholar 

  53. Shi, P., Dong, C.Y., Sun, F., Liu, W., Hu, Q.: A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis. Compos. Struct. 204, 342–358 (2018)

    Article  Google Scholar 

  54. Mantari, J.L., Oktem, A.S., Soares, C.G.: A new higher order shear deformation theory for sandwich and compo-site laminated plates. Compos. Part B-Eng. 43, 1489–1499 (2012)

    Article  Google Scholar 

  55. Shukla, A., Vishwakarma, P.C., Singh, J., Singh, J.: Vibration analysis of angle-ply laminated plates with RBF based meshless approach. Mater. Today Proc. 18, 4605–4612 (2019)

    Article  Google Scholar 

  56. Lin, F., Xiang, Y., Shen, H.S.: Temperature dependent mechanical properties of graphene reinforced polymer nanocomposites—a molecular dynamics simulation. Compos. Part B-Eng. 111, 261–269 (2017)

    Article  Google Scholar 

  57. Shen, H.S., Xiang, Y., Lin, F., Hui, D.: Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments. Compos. Part B-Eng. 119, 67–78 (2017)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Rui Ma or Qilin Jin.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, R., Jin, Q. Stability of functionally graded graphene-reinforced composite laminated thick plates in thermal environment. Acta Mech 233, 3977–3996 (2022). https://doi.org/10.1007/s00707-022-03300-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-022-03300-9

Navigation