Skip to main content
SpringerLink
Log in

A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets

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

Abstract.

In this study, the size effect on the axial buckling behavior of single-layered graphene sheets embedded in elastic foundation is studied. Eringen’s non-local elasticity equations are incorporated into first-order shear deformation, higher-order shear deformation, and classical plate theories. Values of Winkler and Pasternak moduli parameters, side lengths of square SLGSs, non-local parameter and mode numbers are obtained from different non-local plate theories. It is shown that the axial buckling behavior is strongly dependent on non-local parameters and moduli which are different for different numbers and side lengths. Furthermore, we find that non-locality is more influential in first-order shear deformation than other non-local plate theories, especially in certain ranges of non-local parameters. Sensitivity indices are determined based on the Sobol method in their corresponding physical ranges.

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

Similar content being viewed by others

References

  1. S. Kitipornchai, X.Q. He, K.M. Liew, Phys. Rev. B 72, 075443 (2005)

    ADS  Google Scholar 

  2. K.M. Liew, X.Q. He, S. Kitipornchai, Acta Mater. 54, 4229 (2006)

    Google Scholar 

  3. K. Behfar, R. Naghdabadi, Compos. Sci. Technol. 65, 1159 (2005)

    Google Scholar 

  4. Z. Huang, Z. Qin, F. Chu, Compos. Struct. 153, 96 (2016)

    Google Scholar 

  5. Z. Huang, Z. Qin, F. Chu, J. Sandw. Struct. Mater. 18, 531 (2016)

    Google Scholar 

  6. Z. Huang, Z. Qin, F. Chu, J. Vib. Control 22, 1876 (2016)

    MathSciNet  Google Scholar 

  7. J. Peddieson, G.R. Buchanan, R.P. McNitt, Int. J. Eng. Sci. 41, 305 (2003)

    Google Scholar 

  8. S. Sahmani, A.M. Fattahi, Mater. Res. Express 4, 1 (2017)

    Google Scholar 

  9. H.S. Shen, J. Theor. Biol. 264, 386 (2010)

    ADS  Google Scholar 

  10. S. Sahmani, A.M. Fattahi, Comput. Method Appl. Mech. Eng. 322, 187 (2017)

    ADS  Google Scholar 

  11. S. Filiz, M. Aydogdu, Comput. Mater. Sci. 49, 619 (2010)

    Google Scholar 

  12. L. Shen, H.S. Shen, C.L. Zhang, Comput. Mater. Sci. 48, 680 (2010)

    Google Scholar 

  13. B. Safaei, A.M. Fattahi, Mechanics 23, 678 (2017)

    Google Scholar 

  14. J. Yang, L.L. Ke, S. Kitipornchai, Physica E 42, 1727 (2010)

    ADS  Google Scholar 

  15. M.J. Hao, X.M. Guo, Q. Wang, Eur. J. Mech. A/Solids 29, 49 (2010)

    ADS  MathSciNet  Google Scholar 

  16. M. Alizadeh, A.M. Fattahi, Eng. Comput. 35, 215 (2018)

    Google Scholar 

  17. K. Kiani, Int. J. Mech. Sci. 52, 1343 (2010)

    Google Scholar 

  18. A.M. Zenkour, Eur. Phys. J. Plus 133, 193 (2018)

    Google Scholar 

  19. S. Sahmani, A.M. Fattahi, J. Mol. Graph Modell. 75, 20 (2017)

    Google Scholar 

  20. A.M. Fattahi, S. Sahmani, Microsyst. Technol. 23, 5121 (2017)

    Google Scholar 

  21. M.F. Chen, G.Y. Jin, Y.T. Zhang, F.L. Niu, Z.G. Liu, Compos. Struct. 207, 304 (2019)

    Google Scholar 

  22. Y.K. Chen, G.Y. Jin, C.Y. Zhang, T.G. Ye, Y.Q. Xue, Compos. Part B Eng. 153, 376 (2018)

    Google Scholar 

  23. A.M. Fattahi, S. Sahmani, Arab. J. Sci. Eng. 42, 4617 (2017)

    MathSciNet  Google Scholar 

  24. E. Winkler, Theory of Elasticity and Strength (H. Dominicus, Prague, 1867)

  25. P.L. Pasternak, On a new method of analysis of an elastic foundation by means of two foundation constants, in Gosudarstvennoe Izdatelstro Liberaturi po Stroitelstvui Arkhitekture (Moscow, Russia, 1954)

  26. K.M. Liew, X.Q. He, S. Kitipornchai, Acta Mater. 54, 4229 (2006)

    Google Scholar 

  27. S.C. Pradhan, T. Murmu, Physica E 42, 1293 (2010)

    ADS  Google Scholar 

  28. S. Azizi, B. Safaei, A.M. Fattahi, M. Tekere, Adv. Mater. Sci. Eng. 2015, 318539 (2015)

    Google Scholar 

  29. R. Moradi-Dastjerdi, G. Payganeh, M. Tajdari, Polym. Compos. 38, E542 (2017)

    Google Scholar 

  30. R. Moradi-Dastjerdi, G. Payganeh, M. Tajdari, Polym. Compos. 39, 2190 (2018)

    Google Scholar 

  31. Z. Qin, X. Pang, B. Safaei, F. Chu, Compos. Struct. 220, 847 (2019)

    Google Scholar 

  32. R. Moradi-Dastjerdi, H. Malek-Mohammadi, H. Momeni-Khabisi, Z. Angew. Math. Mech. 97, 1418 (2017)

    Google Scholar 

  33. Z. Qin, Z. Yang, J. Zu, F. Chu, Int. J. Mech. Sci. 142-143, 127 (2018)

    Google Scholar 

  34. Z. Qin, F. Chu, Z. Jean, Int. J. Mech. Sci. 133, 91 (2017)

    Google Scholar 

  35. R. Shokri-Oojghaz, R. Moradi-Dastjerdi, H. Mohammadi, K. Behdinan, Polym. Compos. 40, E1918 (2019)

    Google Scholar 

  36. B. Safaei, R. Moradi-Dastjerdi, F. Chu, Compos. Struct. 192, 28 (2018)

    Google Scholar 

  37. B. Safaei, R. Moradi-Dastjerdi, Z. Qin, F. Chu, Compos. Part B Eng. 161, 44 (2019)

    Google Scholar 

  38. B. Safaei, R. Moradi-Dastjerdi, Z. Qin, K. Behdina, F. Chu, J. Sandw. Struct. Mater. (2019) https://doi.org/10.1177/1099636219848282

  39. A. Bouadi, Anis, A.A. Bousahla, M.S.A. Houari, H. Heireche, A. Tounsi, Adv. Nano Res. 6, 147 (2018)

    Google Scholar 

  40. F. Ebrahimi, M.R. Barati, Struct. Eng. Mech. 67, 143 (2018)

    Google Scholar 

  41. T.H. Daouadji, B. Adim, Struct. Eng. Mech. 61, 49 (2017)

    Google Scholar 

  42. M. Malikan, J. Appl. Comput. Mech. 4, 1 (2018)

    Google Scholar 

  43. M. Malikan, Appl. Math. Model. 48, 196 (2017)

    MathSciNet  Google Scholar 

  44. B. Safaei, P. Naseradinmousavi, A. Rahmani, J. Mol. Graph Modell. 65, 43 (2016)

    Google Scholar 

  45. A.M. Fattahi, B. Safaei, Microsyst. Technol. 23, 5079 (2017)

    Google Scholar 

  46. M. Malikan, M. Jabbarzadeh, S. Dastjerdi, Microsyst. Technol. 23, 2973 (2017)

    Google Scholar 

  47. M.E. Golmakani, M. Malikan, M.N. Sadraee Far, H.R. Majidi, Mater. Res. Express 5, 065010 (2018)

    ADS  Google Scholar 

  48. M. Malikan, V.B. Nguyen, F. Tornabene, Eng. Sci. Technol. 21, 778 (2018)

    Google Scholar 

  49. Y.Q. Xue, G.Y. Jin, H. Ding, M.F. Chen, Compos. Struct. 192, 193 (2018)

    Google Scholar 

  50. Q. Wang, D. Shi, Q. Liang, X. Shi, Compos. Part B Eng. 88, 264 (2016)

    Google Scholar 

  51. T. Liu, G. Hu, A. Wang, Q. Wang, Appl. Acoust. 155, 407 (2019)

    Google Scholar 

  52. M. Malikan, J. Appl. Comput. Mech. 5, 103 (2019)

    Google Scholar 

  53. M.E. Golmakani, M.N. Sadraee Far, Microsyst. Technol. 23, 2145 (2017)

    Google Scholar 

  54. B. Safaei, N.A. Ahmed, A.M. Fattahi, Eur. Phys. J. Plus 134, 271 (2019)

    Google Scholar 

  55. B. Safaei, A.M. Fattahi, F. Chu, Microsyst. Technol. 24, 2663 (2018)

    Google Scholar 

  56. S. Azizi, A.M. Fattahi, J.T. Kahnamouei, Comput. Theor. Nanosc. 12, 4179 (2015)

    Google Scholar 

  57. S. Roozpeikar, A.M. Fattahi, SN Appl. Sci. 1, 17 (2018)

    Google Scholar 

  58. B. Safaei, Farzad Hamed Khoda, A.M. Fattahi, Adv. Nano Res. 7, 267 (2019)

    Google Scholar 

  59. B. Safaei, R. Moradi-Dastjerdi, K. Behdinan, F. Chu, Aerospace Sci. Technol. 91, 175 (2019)

    Google Scholar 

  60. A.C. Eringen, Int. J. Eng. Sci. 10, 425 (1972)

    MathSciNet  Google Scholar 

  61. I.M. Sobol, Math. Comput. Simul. 55, 271 (2001)

    Google Scholar 

  62. G. Kirchhoff, Mathematik 40, 51 (1850)

    Google Scholar 

  63. J.N. Reddy, J. Appl. Mech. 51, 745 (1984)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering Science, Faculty of Engineering and Built Environment, University of Johannesburg, 2006, Johannesburg, South Africa

    A. M. Fattahi & N. A. Ahmed

  2. Department of Mechanical Engineering, Tsinghua University, 100084, Beijing, China

    B. Safaei

Authors
  1. A. M. Fattahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Safaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. A. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Fattahi.

Additional information

Publisher’s Note

The EPJ Publishers remain 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

Fattahi, A.M., Safaei, B. & Ahmed, N.A. A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets. Eur. Phys. J. Plus 134, 555 (2019). https://doi.org/10.1140/epjp/i2019-12912-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2019-12912-7

Search

Navigation