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Geometrically nonlinear bending of functionally graded nanocomposite trapezoidal plates reinforced with graphene platelets (GPLs)

  • Zhan Zhao
  • Chuang Feng
  • Youheng Dong
  • Yu Wang
  • Jie YangEmail author
Article
  • 28 Downloads

Abstract

This paper investigates the nonlinear bending behaviours of functionally graded trapezoidal nanocomposite plates reinforced with graphene platelets (GPLs) under thermo-mechanical loading by employing finite element method. The modified Halpin–Tsai model and rule of mixtures are adopted to determine the Young’s modulus, Poisson’s ratio and the thermal expansion coefficient of the nanocomposites. The influences of a number of factors, including the distribution pattern, concentration and size of GPLs, plate geometry and temperature, on the nonlinear bending of the nanocomposite plates are comprehensively investigated. Numerical results demonstrate that dispersing a small amount of GPLs into nanocomposites can significantly enhance the nonlinear bending performance of the trapezoidal plates. The trapezoidal plates with more GPLs dispersing close to the top and bottom surfaces has the minimum bending deflection and are less sensitive to the temperature increases. GPLs with fewer layers and larger surface area are better reinforcing fillers than their counterparts. Moreover, the plates with bigger bottom angles are found to have better bending performances. However, when the bottom angles are greater than 75°, the variation of the bottom angles will have limited effects on the bending behaviours of the trapezoidal plates.

Keywords

Nonlinear bending Trapezoidal plate Functionally graded nanocomposite Graphene platelets Thermo-mechanical loading 

Notes

Acknowledgements

The work described in the present paper is fully funded by research Grants from the Australian Research Council under Discovery Project scheme (DP160101978) and Linkage Project scheme (LP140100747). The authors are grateful for the financial support.

References

  1. Alzebdeh, K.: Evaluation of the in-plane effective elastic moduli of single-layered graphene sheet. Int. J. Mech. Mater. Des. 8(3), 269–278 (2012)CrossRefGoogle Scholar
  2. Chen, D., Yang, J., Kitipornchai, S.: Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams. Compos. Sci. Technol. 142(Supplement C), 235–245 (2017)CrossRefGoogle Scholar
  3. Feng, C., Kitipornchai, S., Yang, J.: Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Compos. B Eng. 110(Supplement C), 132–140 (2017a)CrossRefGoogle Scholar
  4. Feng, C., Kitipornchai, S., Yang, J.: Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Eng. Struct. 140(Supplement C), 110–119 (2017b)Google Scholar
  5. Feng, C., Wang, Y., Kitipornchai, S., Yang, J.: Effects of reorientation of graphene platelets (GPLs) on Young’s modulus of polymer nanocomposites under uni-axial stretching. Polymers 9(10), 532 (2017c)CrossRefGoogle Scholar
  6. Feng, C., Wang, Y., Yang, J.: Effects of reorientation of graphene platelets (GPLs) on Young’s modulus of polymer composites under bi-axial stretching. Nanomaterials 8(1), 27 (2018)CrossRefGoogle Scholar
  7. Gholami, R., Ansari, R.: Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates. Compos. Struct. 180, 760–771 (2017)CrossRefGoogle Scholar
  8. Han, W., Petyt, M.: Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method—I: the fundamental mode of isotropic plates. Comput. Struct. 63(2), 295–308 (1997).  https://doi.org/10.1016/s0045-7949(96)00345-8 CrossRefzbMATHGoogle Scholar
  9. Ji, X.-Y., Cao, Y.-P., Feng, X.-Q.: Micromechanics prediction of the effective elastic moduli of graphene sheet-reinforced polymer nanocomposites. Model. Simul. Mater. Sci. Eng. 18(4), 045005 (2010)CrossRefGoogle Scholar
  10. Jiang, G.Q., Li, F.M., Li, X.W.: Nonlinear vibration analysis of composite laminated trapezoidal plates. Steel Compos Struct 21(2), 395–409 (2016).  https://doi.org/10.12989/scs.2016.21.2.395 MathSciNetCrossRefGoogle Scholar
  11. Kiani, Y., Mirzaei, M.: Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements. Compos. Struct. 186, 114–122 (2018)CrossRefGoogle Scholar
  12. Kumar, A., Singha, M., Tiwari, V.: Nonlinear bending and vibration analyses of quadrilateral composite plates. Thin Walled Struct. 113, 170–180 (2017)CrossRefGoogle Scholar
  13. Kundalwal, S., Shingare, K., Rathi, A.: Effect of flexoelectricity on the electromechanical response of graphene nanocomposite beam. Int. J. Mech. Mater. Des. 1–24 (2018)Google Scholar
  14. Le, M.-Q.: Prediction of Young’s modulus of hexagonal monolayer sheets based on molecular mechanics. Int. J. Mech. Mater. Des. 11(1), 15–24 (2015)CrossRefGoogle Scholar
  15. Leung, A.Y.T., Zhu, B.: Geometric nonlinear vibration of clamped Mindlin plates by analytically integrated trapezoidal p-element. Thin Walled Struct. 42(7), 931–945 (2004).  https://doi.org/10.1016/j.twas.2004.03.010 CrossRefGoogle Scholar
  16. Park, Y.T., Qian, Y.Q., Chan, C., Suh, T., Nejhad, M.G., Macosko, C.W., Stein, A.: Epoxy toughening with low graphene loading. Adv. Funct. Mater. 25(4), 575–585 (2015).  https://doi.org/10.1002/adfm.201402553 CrossRefGoogle Scholar
  17. Potts, J.R., Dreyer, D.R., Bielawski, C.W., Ruoff, R.S.: Graphene-based polymer nanocomposites. Polymer 52(1), 5–25 (2011).  https://doi.org/10.1016/j.polymer.2010.11.042 CrossRefGoogle Scholar
  18. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z., Koratkar, N.: Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3(12), 3884–3890 (2009a).  https://doi.org/10.1021/nn9010472 CrossRefGoogle Scholar
  19. Rafiee, M.A., Rafiee, J., Yu, Z.Z., Koratkar, N.: Buckling resistant graphene nanocomposites. Appl. Phys. Lett. 95(22), 223103 (2009b).  https://doi.org/10.1063/1.3269637 CrossRefGoogle Scholar
  20. Rahman, R., Haque, A.: Molecular modeling of crosslinked graphene–epoxy nanocomposites for characterization of elastic constants and interfacial properties. Compos. B Eng. 54, 353–364 (2013)CrossRefGoogle Scholar
  21. Reimanis, I.E.: Functionally graded materials. Handbook of advanced materials, pp. 465–486 (2004)Google Scholar
  22. Sahmani, S., Aghdam, M.: Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams. Compos. Struct. 179, 77–88 (2017)CrossRefGoogle Scholar
  23. 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 (2017a)CrossRefGoogle Scholar
  24. Shen, H.-S., Xiang, Y., Lin, F.: Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments. Comput. Methods Appl. Mech. Eng. 319, 175–193 (2017b)MathSciNetCrossRefGoogle Scholar
  25. Shen, H.-S., Xiang, Y., Lin, F., Hui, D.: Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments. Compos. B Eng. 119, 67–78 (2017c)CrossRefGoogle Scholar
  26. Shufrin, I., Rabinovitch, O., Eisenberger, M.: A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates. Int. J. Mech. Sci. 52(12), 1588–1596 (2010)CrossRefGoogle Scholar
  27. Singha, M., Daripa, R.: Nonlinear vibration of symmetrically laminated composite skew plates by finite element method. Int. J. Non-Linear Mech. 42(9), 1144–1152 (2007)CrossRefzbMATHGoogle Scholar
  28. Song, M., Kitipornchai, S., Yang, J.: Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos. Struct. 159, 579–588 (2017a)CrossRefGoogle Scholar
  29. Song, M., Yang, J., Kitipornchai, S.: Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos. Part B: Eng. 13, 106–113 (2017b)Google Scholar
  30. Spanos, K., Georgantzinos, S., Anifantis, N.: Mechanical properties of graphene nanocomposites: a multiscale finite element prediction. Compos. Struct. 132, 536–544 (2015)CrossRefGoogle Scholar
  31. Sun, R., Li, L., Feng, C., Kitipornchai, S., Yang, J.: Tensile behavior of polymer nanocomposite reinforced with graphene containing defects. Eur. Polym. J. 98, 475–482 (2018)CrossRefGoogle Scholar
  32. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M., Carrera, E.: Stress, vibration and buckling analyses of FGM plates: a state-of-the-art review. Compos. Struct. 120, 10–31 (2015).  https://doi.org/10.1016/j.compstruct.2014.09.070 CrossRefGoogle Scholar
  33. Watts, G., Pradyumna, S., Singha, M.K.: Nonlinear analysis of quadrilateral composite plates using moving kriging based element free Galerkin method. Compos. Struct. 159, 719–727 (2017).  https://doi.org/10.1016/j.compstruct.2016.09.100 CrossRefGoogle Scholar
  34. Wu, H., Yang, J., Kitipornchai, S.: Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment. Compos. Struct. 162(Supplement C), 244–254 (2017)CrossRefGoogle Scholar
  35. Yang, B., Yang, J., Kitipornchai, S.: Thermoelastic analysis of functionally graded graphene reinforced rectangular plates based on 3D elasticity. Meccanica 52(10), 2275–2292 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  36. Yang, J., Wu, H., Kitipornchai, S.: Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Compos. Struct. 161(Supplement C), 111–118 (2017)CrossRefGoogle Scholar
  37. Zhao, X., Zhang, Q.H., Chen, D.J., Lu, P.: Enhanced mechanical properties of graphene-based poly(vinyl alcohol) composites. Macromolecules 43(5), 2357–2363 (2010).  https://doi.org/10.1021/ma902862u CrossRefGoogle Scholar
  38. Zhao, Z., Feng, C., Wang, Y., Yang, J.: Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs). Compos. Struct. 180(Supplement C), 799–808 (2017)CrossRefGoogle Scholar
  39. Zheng, C., Zhou, X., Cao, H., Wang, G., Liu, Z.: Synthesis of porous graphene/activated carbon composite with high packing density and large specific surface area for supercapacitor electrode material. J. Power Sources 258, 290–296 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of EngineeringRMIT UniversityBundooraAustralia
  2. 2.School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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