Skip to main content
Log in

On the buckling of meta-graphene-origami-enabled magnetostrictive nanoplates under temperature gradient

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

Abstract

The main goal of this study is to examine the buckling properties of a composite material that combines graphene-origami-enabled features with magnetostrictive facesheets. The nonlocal theory, as developed by Eringen, has been used for the purpose of quantifying the small-scale parameter. However, the system being presented is based on the theoretical framework established by Winkler and Pasternak, which incorporates the analysis of a deformable medium. The use of a theoretical framework referred to as higher-order sinusoidal shear deformation theory has been utilized to formulate the governing equation. The governing equation is then solved via the Galerkin solution approach, while considering various boundary conditions. In order to assess the precision and effectiveness of the present inquiry, the findings are juxtaposed with the prevailing scholarly publications in the academic literature. Furthermore, this study aims to examine the impact of several factors, including as the weight fraction, hydrogen atom coverage, aspect ratio, and temperature, on the critical buckling load. The findings of the present investigation indicate that an increase in the weight fraction of graphene-origami-enabled material leads to an increase in the buckling load. The main aim of this study is to improve the understanding and predictive capability of engineers and designers about the phenomenon of buckling response. The aforementioned data have the potential to provide advantages in the advancement of nanoscale systems, including highly sought-after technologies such as sensors and actuators.

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

Similar content being viewed by others

References

  1. Ebrahimi, F., Ahari, M.F.: Dynamic analysis of meta-material plates with magnetostrictive face sheets. Int. J. Struct. Stab. Dyn. (2023). https://doi.org/10.1142/S0219455424501748

    Article  Google Scholar 

  2. Ebrahimi, F., Ahari, M.F.: Thermomechanical active vibration control of auxetic plates with magnetostrictive layers. J. Braz. Soc. Mech. Sci. Eng. 46, 19 (2024)

    Google Scholar 

  3. Liu, G., Chen, X., Reddy, J.: Buckling of symmetrically laminated composite plates using the element-free Galerkin method. Int. J. Struct. Stab. Dyn. 2, 281–294 (2002)

    Google Scholar 

  4. Liew, K., Peng, L., Kitipornchai, S.: Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory. Comput. Mech. 38, 61–75 (2006)

    Google Scholar 

  5. Kim, S.-E., Thai, H.-T., Lee, J.: Buckling analysis of plates using the two variable refined plate theory. Thin Walled Struct. 47(4), 455–462 (2009)

    Google Scholar 

  6. Lei, Z., Liew, K., Yu, J.: Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Compos. Struct. 98, 160–168 (2013)

    Google Scholar 

  7. Karimi, M., Shahidi, A.R.: Buckling analysis of skew magneto-electro-thermo-elastic nanoplates considering surface energy layers and utilizing the Galerkin method. Appl. Phys. A 124, 1–15 (2018)

    Google Scholar 

  8. Karami, B., Janghorban, M., Tounsi, A.: Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Eng. Comput. 35(4), 1297–1316 (2019)

    Google Scholar 

  9. Zenkour, A., Radwan, A.: Hygrothermo-mechanical buckling of FGM plates resting on elastic foundations using a quasi-3D model. Int. J. Comput. Methods Eng. Sci. Mech. 20(2), 85–98 (2019)

    MathSciNet  Google Scholar 

  10. Zenkour, A., Radwan, A.: Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment. Arch. Civ. Mech. Eng. 20(4), 112 (2020)

    Google Scholar 

  11. Rouabhia, A., et al.: Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory. In: ICREATA’21, vol. 37, p. 180 (2020)

  12. Xia, L., et al.: The finite element method for dynamics of FG porous truncated conical panels reinforced with graphene platelets based on the 3-D elasticity. Adv. Nano Res. 14(4), 375 (2023)

    Google Scholar 

  13. Huang, Y., et al.: Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels. Arch. Civ. Mech. Eng. 21(4), 139 (2021)

    Google Scholar 

  14. Kumar, Y., Gupta, A., Tounsi, A.: Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model. Adv. Nano Res. 11(1), 001 (2021)

    Google Scholar 

  15. Van Vinh, P., Tounsi, A.: The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates. Eng. Comput. 38(Suppl 5), 4301–4319 (2022)

    Google Scholar 

  16. Garg, A., et al.: Predicting elemental stiffness matrix of FG nanoplates using Gaussian Process Regression based surrogate model in framework of layerwise model. Eng. Anal. Bound. Elem. 143, 779–795 (2022)

    MathSciNet  Google Scholar 

  17. Cuong-Le, T., et al.: Nonlinear bending analysis of porous sigmoid FGM nanoplate via IGA and nonlocal strain gradient theory. Adv Nano Res. 12(5), 441 (2022)

    Google Scholar 

  18. Van Vinh, P., Tounsi, A.: Free vibration analysis of functionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters. Thin Walled Struct. 174, 109084 (2022)

    Google Scholar 

  19. Liu, G., et al.: Dynamics of imperfect inhomogeneous nanoplate with exponentially-varying properties resting on viscoelastic foundation. Eur. J. Mech. A. Solids 95, 104649 (2022)

    MathSciNet  Google Scholar 

  20. Ebrahimi, F., Ahari, M.F. Active vibration control of the multilayered smart nanobeams: velocity feedback gain effects on the system’s behavior. Acta Mech. 1–18 (2023)

  21. Ebrahimi, F., Barati, M.R.: Hygrothermal buckling analysis of magnetically actuated embedded higher order functionally graded nanoscale beams considering the neutral surface position. J. Therm. Stress. 39(10), 1210–1229 (2016)

    Google Scholar 

  22. Shafiei, H., Setoodeh, A.R.: Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation. Steel Compos. Struct. 24(1), 65–77 (2017)

    Google Scholar 

  23. Malikan, M., Dastjerdi, S.: Analytical buckling of FG nanobeams on the basis of a new one variable first-order shear deformation beam theory. Int. J. Eng. Appl. Sci. 10(1), 21–34 (2018)

    Google Scholar 

  24. Taati, E.: On buckling and post-buckling behavior of functionally graded micro-beams in thermal environment. Int. J. Eng. Sci. 128, 63–78 (2018)

    MathSciNet  Google Scholar 

  25. Wang, T.-M., Laskey, A., Ahmad, M.: Natural frequencies for out-of-plane vibrations of continuous curved beams considering shear and rotary inertia. Int. J. Solids Struct. 20(3), 257–265 (1984)

    Google Scholar 

  26. Khosravi, S., Arvin, H., Kiani, Y.: Interactive thermal and inertial buckling of rotating temperature-dependent FG-CNT reinforced composite beams. Compos. B Eng. 175, 107178 (2019)

    Google Scholar 

  27. Abo-Bakr, R., et al.: Optimal weight for buckling of FG beam under variable axial load using Pareto optimality. Compos. Struct. 258, 113193 (2021)

    Google Scholar 

  28. Carrera, E., Demirbas, M.D.: Evaluation of bending and post-buckling behavior of thin-walled FG beams in geometrical nonlinear regime with CUF. Compos. Struct. 275, 114408 (2021)

    Google Scholar 

  29. Bellifa, H., et al.: Influence of porosity on thermal buckling behavior of functionally graded beams. Smart Struct. Syst. 27(4), 719–728 (2021)

    Google Scholar 

  30. Tounsi, A., et al.: Thermodynamical bending analysis of P-FG sandwich plates resting on nonlinear visco-Pasternak’s elastic foundations. Steel Compos. Struct. 49(3), 307–323 (2023)

    Google Scholar 

  31. Khorasani, M., Lampani, L., Tounsi, A.: A refined vibrational analysis of the FGM porous type beams resting on the silica aerogel substrate. Steel Compos. Struct. 47(5), 633–644 (2023)

    Google Scholar 

  32. Tounsi, A., et al.: Influences of different boundary conditions and hygro-thermal environment on the free vibration responses of FGM sandwich plates resting on viscoelastic foundation. Int. J. Struct. Stab. Dyn. (2023). https://doi.org/10.1142/S0219455424501177

    Article  Google Scholar 

  33. Zaitoun, M.W., et al.: Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment. Thin Walled Struct. 170, 108549 (2022)

    Google Scholar 

  34. Mudhaffar, I.M., et al.: Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermo-mechanical loads. Struct. Eng. Mech. 86(2), 167–180 (2023)

    Google Scholar 

  35. Merazka, B., et al.: Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations. Steel Compos. Struct. Int. J. 39(5), 631–643 (2021)

    Google Scholar 

  36. Tounsi, A., et al.: Free vibration investigation of functionally graded plates with temperaturedependent properties resting on a viscoelastic foundation. Struct. Eng. Mech. 86(1), 1 (2023)

    Google Scholar 

  37. Zaitoun, M.W., et al.: An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects. Eng. Comput. 39(2), 1127–1141 (2023)

    Google Scholar 

  38. Tahir, S.I., et al.: The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT. Steel Compos. Struct. 42(4), 501 (2022)

    Google Scholar 

  39. Bouafia, K., et al.: Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model. Steel Compos. Struct. Int. J. 41(4), 487–503 (2021)

    Google Scholar 

  40. Ren, H., Li, Z., Shu, X.: The numerical simulation of magnetoelastic buckling based on magnetostrictive material model. J. Taiyuan Univ. Technol. 36(5), 561 (2005)

    Google Scholar 

  41. Ghorbanpour Arani, A., Abdollahian, M., Rahmati, A.H.: Nonlocal piezomagnetoelasticity theory for buckling analysis of piezoelectric/magnetostrictive nanobeams including surface effects. J. Solid Mech. 9(4), 707–729 (2017)

    Google Scholar 

  42. Tabbakh, M., Nasihatgozar, M.: Buckling analysis of nanocomposite plates coated by magnetostrictive layer. Smart Struct. Syst. Int. J. 22(6), 743–751 (2018)

    Google Scholar 

  43. Yuan, Y., et al.: Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation. Thin Walled Struct. 159, 107249 (2021)

    Google Scholar 

  44. Fan, L., Sahmani, S., Safaei, B.: Couple stress-based dynamic stability analysis of functionally graded composite truncated conical microshells with magnetostrictive facesheets embedded within nonlinear viscoelastic foundations. Eng. Comput. 37, 1635–1655 (2021)

    Google Scholar 

  45. Touratier, M.: An efficient standard plate theory. Int. J. Eng. Sci. 29(8), 901–916 (1991)

    Google Scholar 

  46. Ebrahimi, F., Ahari, M.F.: Mechanics of Magnetostrictive Materials and Structures. CRC Press (2023)

    Google Scholar 

  47. Ahari, M.F., Ghadiri, M.: Resonator vibration of a magneto-electro-elastic nano-plate integrated with FGM layer subjected to the nano mass-Spring-damper system and a moving load. Waves Random Complex Media (2022). https://doi.org/10.1007/s00707-023-03746-5

    Article  Google Scholar 

  48. Ebrahimi, F. and M.F. Ahari, Magnetostriction-assisted active control of the multi-layered nanoplates: effect of the porous functionally graded facesheets on the system’s behavior. Engineering with Computers, 2021: p. 1–15.

  49. Ebrahimi, F., A. Mollazeinal, and M.F. Ahari, Nonlinear vibration analysis of smart truncated conical porous composite shells reinforced with Terfenol-D particles. Acta Mechanica, 2023: p. 1–44.

  50. Ebrahimi, F., Ahari, M.F.: Dynamic analysis of sandwich magnetostrictive nanoplates with a mass-spring-damper stimulator. Int. J. Struct. Stab. Dyn. (2023). https://doi.org/10.1142/S0219455424501360

    Article  Google Scholar 

  51. Shariati, A., et al.: On buckling characteristics of polymer composite plates reinforced with graphene platelets. Eng. Comput. (2022). https://doi.org/10.1007/s00366-020-00992-2

    Article  Google Scholar 

  52. Ebrahimi, F., et al.: Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates. Adv. Nano Res. 7(3), 157 (2019)

    Google Scholar 

  53. Ebrahimi, F., Mollazeinal, A., Ahari, M.F.: Active vibration control of truncated conical porous smart composite shells. Int. J. Struct. Stab. Dyn. 200, 300 (2023). https://doi.org/10.1142/S0219455424501323

    Article  Google Scholar 

  54. Ebrahimi, F., Sepahvand, M.: Wave propagation analysis of cylindrical sandwich shell with auxetic core utilizing first-order shear deformable theory (FSDT). Mech. Based Des. Struct. Mach. 1–25 (2022)

  55. Rao, S.S.: Vibration of Continuous Systems. John Wiley & Sons (2019)

    Google Scholar 

  56. Ebrahimi, F., Dabbagh, A.: Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization model. Compos. B Eng. 173, 106955 (2019)

    Google Scholar 

  57. Ebrahimi, F., Shafiei, M.S., Ahari, M.F.: Vibration analysis of single and multi-walled circular graphene sheets in thermal environment using GDQM. Waves Random Complex Media 1–40 (2022)

  58. Ebrahimi, F., Shafiee, M.-S., Ahari, M.F.: Buckling analysis of single and double-layer annular graphene sheets in thermal environment. Eng. Comput. 39(1), 625–639 (2023)

    Google Scholar 

  59. Ebrahimi, F., Barati, M.R.: Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory. Int. J. Smart Nano Mater. 7(3), 119–143 (2016)

    Google Scholar 

  60. Rahimi, Y., et al.: Temperature-dependent vibrational behavior of bilayer doubly curved micro-nano liposome shell: simulation of drug delivery mechanism. J. Therm. Stress. 1–28 (2023)

  61. Mizuji, Z.K., et al.: Numerical modeling of a body vessel for dynamic study of a nano cylindrical shell carrying fluid and a moving nanoparticle. Eng. Anal. Bound. Elem. 152, 362–382 (2023)

    MathSciNet  Google Scholar 

  62. Mohammadi, M., Saidi, A., Jomehzadeh, E.: A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 224(9), 1831–1841 (2010)

    Google Scholar 

  63. Bodaghi, M., Saidi, A.: Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory. Appl. Math. Model. 34(11), 3659–3673 (2010)

    MathSciNet  Google Scholar 

  64. Thai, H.-T., Choi, D.-H.: An efficient and simple refined theory for buckling analysis of functionally graded plates. Appl. Math. Model. 36(3), 1008–1022 (2012)

    MathSciNet  Google Scholar 

  65. Sobhy, M.: A comprehensive study on FGM nanoplates embedded in an elastic medium. Compos. Struct. 134, 966–980 (2015)

    Google Scholar 

  66. Barati, M.R., Zenkour, A.M., Shahverdi, H.: Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos. Struct. 141, 203–212 (2016)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the reviewers for their comments and suggestions to improve this article’s clarity.

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Farzad Ebrahimi.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

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 (e.g. a society or other partner) 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

Ebrahimi, F., Ahari, M.F. On the buckling of meta-graphene-origami-enabled magnetostrictive nanoplates under temperature gradient. Acta Mech 235, 2611–2628 (2024). https://doi.org/10.1007/s00707-024-03861-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-024-03861-x

Navigation