Skip to main content
SpringerLink
Log in

h-p finite element vibration analysis of side cracked rectangular nano-plates based on nonlocal elasticity theory

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

Abstract.

The h-p version of the finite element method based on a quadrilateral p-element is applied to free vibration analysis of side cracked nano plates. The h-p version of the finite element method marries both the concepts of the conventional h-version and the p-version. The accuracy of the solution is sought by simultaneously refining the mesh and increasing the polynomial order in each element. The formulation takes into account shear deformation, rotary inertia, and non-local elasticity theory. The proposed model is compared to various analytical, numerical and experimental results to validate it’s accuracy and efficiency, computationally expensive preprocessing tasks are avoided due to hierarchic refining strategy that requires no re-meshing when changing crack parameters. The effects of plate aspect ratio, side-to-thickness ratio, non-local parameter, boundary conditions, crack length and crack angle on the free vibration analysis of side cracked nano plates is discussed and presented for the first time.

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. A.C. Eringen, J. Wegner, Appl. Mech. Rev. 56, B20 (2003)

    Article  Google Scholar 

  2. K.M. Liew, Yang Zhang, L.W. Zhang, J. Model. Mech. Mater., https://doi.org/10.1515/jmmm-2016-0159 (2017)

  3. R. Ansari, S. Sahmani, B. Arash, Phys. Lett. A 375, 53 (2010)

    Article  ADS  Google Scholar 

  4. S.C. Pradhan, A. Kumar, Compos. Struct. 93, 774 (2011)

    Article  Google Scholar 

  5. Parviz Malekzadeh, AliReza Setoodeh, Ali Alibeygi Beni, Compos. Struct. 93, 1631 (2011)

    Article  Google Scholar 

  6. C.Y. Wang, T. Murmu, S. Adhikari, Appl. Phys. Lett. 98, 153101 (2011)

    Article  ADS  Google Scholar 

  7. L.Y. Huang, Q. Han, Y.J. Liang, Nano 07, 1250033 (2012)

    Article  Google Scholar 

  8. Chen Liu, Liao-Liang Ke, Yue-Sheng Wang, Jie Yang, Sritawat Kitipornchai, Compos. Struct. 106, 167 (2013)

    Article  Google Scholar 

  9. Parviz Malekzadeh, Mohammad Shojaee, Compos. Struct. 95, 443 (2013)

    Article  Google Scholar 

  10. Shahrokh Hosseini-Hashemi, Mehdi Kermajani, Reza Nazemnezhad, Eur. J. Mech. - A/Solids 51, 29 (2015)

    Article  MathSciNet  Google Scholar 

  11. S. Chakraverty, Laxmi Behera, Physica E 56, 357 (2014)

    Article  ADS  Google Scholar 

  12. Abdelkrim Necira, Sid Ahmed Belalia, Abdelkrim Boukhalfa, Mech. Adv. Mater. Struct. https://doi.org/10.1080/15376494.2018.1472342 (2018)

  13. R. Ansari, M. Faghih Shojaei, A. Shahabodini, M. Bazdid-Vahdati, Compos. Struct. 131, 753 (2015)

    Article  Google Scholar 

  14. Mohammad Reza Barati, Hossein Shahverdi, J. Vib. Control 24, 4700 (2018)

    Article  MathSciNet  Google Scholar 

  15. Ismahene Belkorissat, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi, E.A. Bedia, S.R. Mahmoud, Steel Compos. Struct. 18, 1063 (2015)

    Article  Google Scholar 

  16. A. Daneshmehr, A. Rajabpoor et al., Int. J. Eng. Sci. 82, 84 (2014)

    Article  Google Scholar 

  17. Mohammad Rahim Nami, Maziar Janghorban, Compos. Struct. 111, 349 (2014)

    Article  Google Scholar 

  18. S. Natarajan, S. Chakraborty, M. Thangavel, Stephane Bordas, Timon Rabczuk, Comput. Mater. Sci. 65, 74 (2012)

    Article  Google Scholar 

  19. B.A. Szabo, A.K. Mehta, Int. J. Numer. Methods Eng. 12, 551 (1978)

    Article  Google Scholar 

  20. Barna Szabó, Ivo Babuška. Introduction to Finite Element Analysis: Formulation, Verification and Validation, Vol. 35 (John Wiley & Sons, 2011)

  21. J.N. Reddy, Theory and Analysis of Elastic Plates and Shells, Second Edition, in Series in Systems and Control (Taylor & Francis, 2006)

  22. Leon Stahl, B. Keer, Int. J. Solids Struct. 8, 69 (1972)

    Article  Google Scholar 

  23. K. Liew, K.C. Hung, M.K. Lim, Eng. Fract. Mech. 48, 393 (1994)

    Article  ADS  Google Scholar 

  24. S. Sumi, T. Fujimoto, Trans. Jpn. Soc. Mech. Eng. Ser. A 53, 1124 (1987)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computational Mechanics, Department of Mechanical Engineering, Faculty of Technology, University of Tlemcen, Tlemcen, Algeria

    B. Zaouagui, S. A. Belalia & A. Boukhalfa

Authors
  1. B. Zaouagui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Belalia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Boukhalfa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Zaouagui.

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

Zaouagui, B., Belalia, S.A. & Boukhalfa, A. h-p finite element vibration analysis of side cracked rectangular nano-plates based on nonlocal elasticity theory. Eur. Phys. J. Plus 134, 336 (2019). https://doi.org/10.1140/epjp/i2019-12724-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2019-12724-9

Search

Navigation