On buckling characteristics of polymer composite plates reinforced with graphene platelets

Abstract

In the present study, buckling analysis of polymer composite plates reinforced with graphene platelets (GPLs) in thermal environment is investigated based on higher-order shear deformation plate theory. Halpin–Tsai model is used to determine the material properties of multilayer polymer composite plate. In the present study, four patterns of GPL distribution in composite plate are considered. To obtain the Euler–Lagrange equations of composites plate, Hamilton’s principle is employed and utilized Navier’s method for analyzing and solving the problem. The results of this study have been verified by checking them with the previous works. The effects of various parameters such as geometry effect, GPL weight fraction and temperature changes on critical buckling temperature are explored.

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

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

References

  1. 1.

    Zaman I, Kuan H-C, Dai J, Kawashima N, Michelmore A, Sovi A, Dong S, Luong L, Ma J (2012) From carbon nanotubes and silicate layers to graphene platelets for polymer nanocomposites. Nanoscale 4(15):4578–4586

    Article  Google Scholar 

  2. 2.

    Tjong SC (2012) Polymer composites with carbonaceous nanofillers: properties and applications. Wiley, Hoboken

    Google Scholar 

  3. 3.

    Eltaher MA, Almalki TA, Ahmed KIE, Almitani KH (2019) Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach. Adv Nano Res 7(1):39–49

    Google Scholar 

  4. 4.

    Eltaher MA, Almalki TA, Almitani KH, Ahmed KIE, Abdraboh AM (2019) Modal participation of fixed-fixed single-walled carbon nanotube with vacancies. Int J Adv Struct Eng 11:1–13

    Article  Google Scholar 

  5. 5.

    Emam SA, Eltaher MA, Khater ME, Abdalla WS (2018) Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load. Appl Sci 8(11):2238

    Article  Google Scholar 

  6. 6.

    Mohamed N, Eltaher MA, Mohamed SA, Seddek LF (2018) Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations. Int J Non-Linear Mech 101:157–173

    Article  Google Scholar 

  7. 7.

    Soliman AE, Eltaher MA, Attia MA, Alshorbagy AE (2018) Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility. Struct Eng Mech 66(1):85–96

    Google Scholar 

  8. 8.

    Eltaher MA, Agwa M, Kabeel A (2018) Vibration analysis of material size-dependent CNTs using energy equivalent model. J Appl Comput Mech 4(2):75–86

    Google Scholar 

  9. 9.

    Eltaher MA, El-Borgi S, Reddy JN (2016) Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs. Compos Struct 153:902–913

    Article  Google Scholar 

  10. 10.

    Emam S, Eltaher MA (2016) Buckling and postbuckling of composite beams in hygrothermal environment. Compos Struct 152:665–675

    Article  Google Scholar 

  11. 11.

    Ni Z, Hao B, Zou M, Yi H, Bi K, Chen Y (2010) Anisotropic mechanical properties of graphene sheets from molecular dynamics. Physica B 405(5):1301–1306

    Article  Google Scholar 

  12. 12.

    Xu Y, Hong W, Bai H, Li C, Shi G (2009) Strong and ductile poly (vinyl alcohol)/graphene oxide composite films with a layered structure. Carbon 47(15):3538–3543

    Article  Google Scholar 

  13. 13.

    Potts JR, Dreyer DR, Bielawski CW, Ruoff RS (2011) Graphene-based polymer nanocomposites. Polymer 52(1):5–25

    Article  Google Scholar 

  14. 14.

    Zaman I, Phan TT, Kuan H-C, Meng Q, La LTB, Luong L, Youssf O, Ma J (2011) Epoxy/graphene platelets nanocomposites with two levels of interface strength. Polymer 52(7):1603–1611

    Article  Google Scholar 

  15. 15.

    Rafiee MA, Rafiee J, Wang Z, Song H, Zhong-Zhen Yu, Koratkar N (2009) Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3(12):3884–3890

    Article  Google Scholar 

  16. 16.

    Liang J, Huang Y, Zhang L, Wang Y, Ma Y, Guo T, Chen Y (2009) Molecular-level dispersion of graphene into poly (vinyl alcohol) and effective reinforcement of their nanocomposites. Adv Funct Mater 19(14):2297–2302

    Article  Google Scholar 

  17. 17.

    Zhao X, Zhang Q, Chen D, Ping L (2010) Enhanced mechanical properties of graphene-based poly (vinyl alcohol) composites. Macromolecules 43(5):2357–2363

    Article  Google Scholar 

  18. 18.

    Bortz DR, Heras EG, Martin-Gullon I (2011) Impressive fatigue life and fracture toughness improvements in graphene oxide/epoxy composites. Macromolecules 45(1):238–245

    Article  Google Scholar 

  19. 19.

    Rafiee MA, Rafiee J, Yu Z-Z, Koratkar N (2009) Buckling resistant graphene nanocomposites. Appl Phys Lett 95(22):223103

    Article  Google Scholar 

  20. 20.

    Parashar A, Mertiny P (2012) Representative volume element to estimate buckling behavior of graphene/polymer nanocomposite. Nanoscale Res Lett 7(1):515

    Article  Google Scholar 

  21. 21.

    Chandra Y, Chowdhury R, Scarpa F, Adhikari S, Sienz J, Arnold C, Murmu T, Bould D (2012) Vibration frequency of graphene based composites: a multiscale approach. Mater Sci Eng B 177(3):303–310

    Article  Google Scholar 

  22. 22.

    King JA, Klimek DR, Miskioglu I, Odegard GM (2013) Mechanical properties of graphene nanoplatelet/epoxy composites. J Appl Polym Sci 128(6):4217–4223

    Article  Google Scholar 

  23. 23.

    Liu J, Yan H, Jiang K (2013) Mechanical properties of graphene platelet-reinforced alumina ceramic composites. Ceram Int 39(6):6215–6221

    Article  Google Scholar 

  24. 24.

    Wu H, Drzal LT (2014) Effect of graphene nanoplatelets on coefficient of thermal expansion of polyetherimide composite. Mater Chem Phys 146(1–2):26–36

    Article  Google Scholar 

  25. 25.

    Spanos KN, Georgantzinos SK, Anifantis NK (2015) Mechanical properties of graphene nanocomposites: A multiscale finite element prediction. Compos Struct 132:536–544

    Article  Google Scholar 

  26. 26.

    Javvaji B, Budarapu PR, Sutrakar VK, Roy Mahapatra D, Paggi M, Zi G, Rabczuk T (2016) Mechanical properties of graphene: molecular dynamics simulations correlated to continuum based scaling laws. Comput Mater Sci 125:319–327

    Article  Google Scholar 

  27. 27.

    Zarasvand KA, Golestanian H (2017) Investigating the effects of number and distribution of GNP layers on graphene reinforced polymer properties: Physical, numerical and micromechanical methods. Compos Sci Technol 139:117–126

    Article  Google Scholar 

  28. 28.

    Feng C, Wang Yu, Yang J (2018) Effects of reorientation of graphene platelets (GPLs) on Young’s modulus of polymer composites under bi-axial stretching. Nanomaterials 8(1):27

    Article  Google Scholar 

  29. 29.

    Hussein A, Kim B (2018) Graphene/polymer nanocomposites: the active role of the matrix in stiffening mechanics. Compos Struct 202:170–181

    Article  Google Scholar 

  30. 30.

    Gangele A, Pandey AK (2018) Elastic and fracture characteristics of graphene-silicon nanosheet composites using nonlinear finite element method. Int J Mech Sci 142:491–501

    Article  Google Scholar 

  31. 31.

    Song M, Kitipornchai S, Yang J (2017) Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos Struct 159:579–588

    Article  Google Scholar 

  32. 32.

    Feng C, Kitipornchai S, Yang J (2017) Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Eng Struct 140:110–119

    Article  Google Scholar 

  33. 33.

    Feng C, Kitipornchai S, Yang J (2017) Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Compos B Eng 110:132–140

    Article  Google Scholar 

  34. 34.

    Kitipornchai S, Chen D, Yang J (2017) Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des 116:656–665

    Article  Google Scholar 

  35. 35.

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

    MATH  Article  Google Scholar 

  36. 36.

    Sahmani S, Aghdam MM (2017) Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams. Compos Struct 179:77–88

    Article  Google Scholar 

  37. 37.

    Zhao Z, Feng C, Wang Yu, Yang J (2017) Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs). Compos Struct 180:799–808

    Article  Google Scholar 

  38. 38.

    Barati MR, Zenkour AM (2017) Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection. Compos Struct 181:194–202

    Article  Google Scholar 

  39. 39.

    Wang Yu, Feng C, Zhao Z, Yang J (2017) Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL). Compos Struct 202:38–46

    Article  Google Scholar 

  40. 40.

    Sahmani S, Aghdam MM, Rabczuk T (2018) Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory. Compos Struct 186:68–78

    Article  Google Scholar 

  41. 41.

    Gholami R, Ansari R (2018) Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Eng Struct 156:197–209

    Article  Google Scholar 

  42. 42.

    Yas MH, 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

    Article  Google Scholar 

  43. 43.

    Zhao X, Lee YY, Liew KM (2009) Mechanical and thermal buckling analysis of functionally graded plates. Compos Struct 90(2):161–171

    Article  Google Scholar 

  44. 44.

    Yang S-Y, Lin W-N, Huang Y-L, Tien H-W, Wang Jeng-Yu, Ma C-CM, Li S-M, Wang Y-S (2011) Synergetic effects of graphene platelets and carbon nanotubes on the mechanical and thermal properties of epoxy composites. Carbon 49(3):793–803

    Article  Google Scholar 

  45. 45.

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

    Article  Google Scholar 

  46. 46.

    Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745–752

    MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Farzad Ebrahimi or Ali Toghroli.

Additional information

Publisher's Note

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

Appendix

Appendix

$$\begin{aligned} K_{11} & = - m^{2} A_{11} - n^{2} \left( {A_{44} } \right) \\ K_{12} & = - mnA_{12} - mnA_{44} \\ K_{13} & = c_{1} m^{3} \left( {D_{11} } \right) + c_{1} n^{2} m\left( {D_{12} } \right) + 2c_{1} mn^{2} \left( {D_{44} } \right) \\ K_{14} & = - m^{2} \left( {B_{11} } \right) + c_{1} m^{2} \left( {D_{11} } \right) + c_{1} n^{2} \left( {D_{44} } \right) - n^{2} B_{44} \\ K_{15} & = mnc_{1} D_{12} - mnB_{44} + mnc_{1} D_{44} - mnB_{12} \\ K_{21} & = K_{12} \\ K_{22} & = - n^{2} A_{22} - m^{2} A_{44} \\ K_{23} & = c_{1} n^{3} D_{22} + mn^{2} c_{1} D_{12} + 2m^{2} nc_{1} D_{44} \\ K_{24} & = - mnB_{12} + c_{1} mnD_{12} - mnB_{44} c_{1} mnD_{44} \\ K_{25} & = - n^{2} B_{22} + c_{1} n^{2} D_{22} - m^{2} B_{44} + C_{1} m^{2} B_{44} \\ K_{31} & = K_{13} \\ K_{32} & = K_{23} \\ K_{33} & = - m^{4} c_{1}^{2} G_{12} + n^{2} m^{2} \left( { - 2c_{1}^{2} G_{12} - 4c_{1}^{2} G_{44} } \right) - n^{4} c_{1}^{2} G_{22} \\ & \quad - m^{2} \left( {A_{55} - 6c_{1} C_{55} + 9c_{1}^{2} E_{55} } \right) - n^{2} \left( {A_{66} - 6c_{1} C_{66} + 9c_{1}^{2} E_{66} } \right) \\ K_{34} & = c_{1} m^{3} E_{11} - c_{1}^{2} m^{3} G_{11} + mn^{2} \left( {c_{1} E_{12} - c_{1}^{2} G_{12} + 2c_{1} E_{44} - 2c_{1}^{2} G_{44} } \right) \\ & \quad - 3c_{1} mA_{55} C_{55} + 3c_{1} m\left( {C_{55} - 3c_{1} E_{55} } \right) \\ K_{35} & = m^{2} n\left( { - c_{1}^{2} G_{12} + 2c_{1} E_{44} - 2c_{1}^{2} G_{44} + c_{1} E_{12} } \right) - n^{3} c_{1}^{2} G_{22} \\ & \quad - 3c_{1} nA_{66} C_{66} + 3c_{1} n\left( {C_{66} - 3c_{1} E_{66} } \right) + c_{1} n^{3} E_{22} \\ K_{41} & = K_{14} \\ K_{42} & = K_{24} \\ K_{43} & = K_{34} \\ K_{44} & = - m^{2} \left( {C_{11} - 2c_{1} E_{11} + c_{1}^{2} G_{11} } \right) - n^{2} (C_{44} - 2c_{1} E_{44} + c_{1}^{2} G_{44} + 3c_{1} \left( {C_{55} - 3c_{1} E_{55} } \right) - 3c_{1} A_{55} C_{55} \\ K_{45} & = - mn(c_{1} E_{12} + C_{44} - c_{1} E_{44} + c_{1}^{2} G_{12} - c_{1} E_{44} + c_{1}^{2} G_{44} + C_{12} - c_{1} E_{12} \\ K_{51} & = K_{15} \\ K_{52} & = K_{25} \\ K_{53} & = K_{35} \\ K_{54} & = K_{45} \\ K_{55} & = - n^{2} \left( {C_{22} - 2c_{1} E_{22} + c_{1}^{2} G_{22} } \right) - m^{2} \left( {C_{44} - 2c_{1} E_{44} c_{1}^{2} G_{44} } \right) + 3c_{1} C_{66} - A_{66} + 3c_{1} \left( {C_{66} - 3c_{1} E_{66} } \right) \\ \end{aligned}$$

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shariati, A., Qaderi, S., Ebrahimi, F. et al. On buckling characteristics of polymer composite plates reinforced with graphene platelets. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-00992-2

Download citation

Keywords

  • Buckling
  • GPLRC plate
  • Thermal environment
  • Higher-order shear deformation beam theory