SpringerLink
Log in

Numerical optimization of volume fraction distributions in FGM sandwich beams with FG-CNTRC facesheets

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

This paper presents a numerical method for the optimal tailoring of volume fraction distributions of reinforcement materials (pillars) within FGM (functionally graded material) sandwich beams with FG-CNTRC (functionally graded CNT-reinforced composite) facesheets. Since the mechanical behaviors of sandwich beams vary depending on the distribution pattern of reinforcement materials (CNT and ceramic in this paper) through the thickness, the tailoring of these distribution patterns is important to enhance the mechanical performance. In the present study, the thickness-wise distributions of CNT in the facesheets and ceramic in the core are optimized to maximize the fundamental natural frequency of sandwich beams, based on the exterior penalty-function method and the golden section method. The developed optimization method is verified and the resulting optimum distributions of CNT and ceramic are compared with the primitive functionally graded distribution patterns which are widely adopted in the literature. Moreover, the volume fraction distributions of CNT and ceramic are also individually optimized, and the optimum results between simultaneous (SO) and individual optimizations (IO) are compared.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Jedari Salami, Extended high order sandwich panel theory for bending analysis of sandwich beams with carbon nanotube reinforced face sheets, Physica E., 76 (2016) 187–197.

    Article  Google Scholar 

  2. R. Shokri-Oojghaz, R. Moradi-Dastjerdi, H. Mohammadi and K. Behdinan, Stress distributions in nanocomposite sandwich cylinders reinforced by aggregated carbon nanotube, Polym. Compos., 40 (2019) E1918–E1927.

    Article  Google Scholar 

  3. H. Wu, S. Kitipornchai and J. Yang, Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets, Int. J. Struct. Stab. Dyn., 15(7) (2015) 1540011.

    Article  MathSciNet  Google Scholar 

  4. Y. Kiani, Thermal post-buckling of temperature dependent sandwich plates with FG-CNTRC face sheets, J. Therm. Stresses, 41(7) (2018) 866–882.

    Article  Google Scholar 

  5. M. Mohammadimehr and S. Shahedi, High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM, Compos. Part B - Eng., 108 (2017) 91–107.

    Article  Google Scholar 

  6. C. Caglayan, I. Gurkan, S. Gungor and H. Cebeci, The effect of CNT-reinforced polyurethane foam cores to flexural properties of sandwich composites, Compos. Part A - Appl. Sci., 115 (2018) 187–195.

    Article  Google Scholar 

  7. M. Subramani, S. Rajeshkumar and M. Ramamoorthy, Free vibration analysis of the MWCNT reinforced hybrid laminated composite sandwich beam, Mater. Today - Proc., 22(4) (2020) 3220–3225.

    Article  Google Scholar 

  8. A. Amiri, M. Mohammadimehr and M. Anvari, Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets, Appl. Math. Mech.- Engl. Ed., 41 (2020) 1027–1038.

    Article  MathSciNet  Google Scholar 

  9. S. Kamarian, M. Bodaghi, R. B. Isfahani and J. Song, Thermal buckling analysis of sandwich plates with soft core and CNT-Reinforced composite face sheets, J. Sandw. Struct. Mater., 23(8) (2021) 3606–3644.

    Article  Google Scholar 

  10. M. E. Çetin, The effect of carbon nanotubes modified polyurethane adhesive on the impact behavior of sandwich structures, Polym. Compos., 42 (2021) 4353–4365.

    Article  Google Scholar 

  11. H. S. Shen, Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Compos. Struct., 91(1) (2009) 9–19.

    Article  Google Scholar 

  12. J. N. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, J. Mech. Phys. Solids, 59 (2011) 2382–2399.

    Article  MathSciNet  Google Scholar 

  13. J. Yang, L. L. Ke and C. Feng, Dynamic buckling of thermoelectro-mechanically loaded FG-CNTRC beams, Int. J. Struct. Stab. Dyn., 15(8) (2015) 1540017.

    Article  MathSciNet  Google Scholar 

  14. H. Wu, S. Kitipornchai and J. Yang, Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nano-tube-reinforced composite beams, Appl. Math. Model., 42 (2017) 735–752.

    Article  MathSciNet  Google Scholar 

  15. Z. X. Lei, L. W. Zhang and K. M. Liew, Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach, Appl. Math. Comput., 266 (2015) 773–791.

    MathSciNet  Google Scholar 

  16. B. A. Selim, L. W. Zhang and K. M. Liew, Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory, Compos. Struct., 156 (2016) 276–290.

    Article  Google Scholar 

  17. N. D. Duc, J. Lee, T. Nguyen-Thoi and P. T. Thang, Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations, Aero. Sci. Technol., 68 (2017) 391–402.

    Article  Google Scholar 

  18. Y. Kiani, Free vibration of functionally graded carbon nano-tube reinforced composite plates integrated with piezoelectric layers, Comput. Math. Appl., 72(9) (2016) 2433–2449.

    Article  MathSciNet  Google Scholar 

  19. R. Ansari, J. Torabi and M. Faghih Shojaei, Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading, Compos. Part B - Eng., 109 (2017) 197–213.

    Article  Google Scholar 

  20. F. Ebrahimi and N. Farazmandnia, Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory, Mech. Adv. Mater. Struct., 24(10) (2017) 820–829.

    Article  Google Scholar 

  21. F. Lin and Y. **ang, Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories, Appl. Math. Model., 38(15–16) (2014) 3741–3754.

    Article  MathSciNet  Google Scholar 

  22. M. H. Yas and N. Samadi, Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation, Int. J. Pres. Ves. Pipe, 98 (2012) 119–128.

    Article  Google Scholar 

  23. J. Xu, Z. Yang, J. Yang and Y. Li, Free vibration analysis of rotating FG-CNT reinforced composite beams in thermal environments with general boundary conditions, Aero. Sci. Technol., 118 (2021) 107030.

    Article  Google Scholar 

  24. L. L. Ke, J. Yang and S. Kitipornchai, Dynamic stability of functionally graded carbon nanotube-reinforced composite beams, Mech. Adv. Mater. Struct., 20(1) (2013) 28–37.

    Article  Google Scholar 

  25. S. Jafari Mehrabadi and B. Sobhani Aragh, Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes, Thin Wall. Struct., 80 (2014) 130–141.

    Article  Google Scholar 

  26. M. Mirzaei and Y. Kiani, Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels, Compos. Struct., 142 (2016) 45–56.

    Article  Google Scholar 

  27. A. Alibeigloo and A. A. Pasha Zanoosi, Thermo-electroelasticity solution of functionally graded carbon nanotube reinforced composite cylindrical shell embedded in piezoelectric layers, Compos. Struct., 173 (2017) 268–280.

    Article  Google Scholar 

  28. Z. Wu, Y. Zhang and G. Yao, Nonlinear forced vibration of functionally graded carbon nanotube reinforced composite circular cylindrical shells, Acta Mech., 231 (2020) 2497–2519.

    Article  MathSciNet  Google Scholar 

  29. J. E. Jam and Y. Kiani, Buckling of pressurized functionally graded carbon nanotube reinforced conical shells, Compos. Struct., 125 (2015) 586–595.

    Article  Google Scholar 

  30. N. D. Duc, P. H. Cong, N. D. Tuan, P. Tran and N. V. Thanh, Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations, Thin Wall. Struct., 115 (2017) 300–310.

    Article  Google Scholar 

  31. M. Nejati, A. Asanjarani, R. Dimitri and F. Tornabene, Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes, Int. J. Mech. Sci., 130 (2017) 383–398.

    Article  Google Scholar 

  32. M. Rezaiee-Pajand, E. Sobhani and A. R. Masoodi, Semianalytical vibrational analysis of functionally graded carbon nanotubes coupled conical-conical shells, Thin Wall. Struct., 159 (2021) 107272.

    Article  Google Scholar 

  33. J. R. Cho and H. J. Kim, Numerical optimization of CNT distribution in functionally graded CNT-reinforced composite beams, Polymers, 14(20) (2022) 4418.

    Article  Google Scholar 

  34. J. R. Cho and H. J. Kim, Optimal tailoring of CNT distribution in functionally graded porous CNTRC beams, Polymer., 15 (2023) 349.

    Article  Google Scholar 

  35. H. S. Shen and C. L. Zhang, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Mater. Des., 31(7) (2010) 3403–3411.

    Article  Google Scholar 

  36. J. R. Cho, Nonlinear bending and free vibration analyses of metal-ceramic functionally graded plates by 2-D natural element method, J. Mech. Sci. Technol., 35 (2021) 5591–5599.

    Article  Google Scholar 

  37. MIDAS IT, Analysis Manual - Midas NFX. Modelling, Integrated Design and Analysis Software, MIDAS IT, Gyeonggi-do, Korea (2020).

    Google Scholar 

  38. H. J. Kim and J. R. Cho, A numerical study on free vibration analysis of detailed and homogenized models for FG-CNTRC beams, J. Mech. Sci. Technol., 37 (2023) 229–238.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924, RS-2023-00240618).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University College London, London, WC1E 7JE, UK

    Hyeong ** Kim

  2. Department of Naval Architecture and Ocean Engineering, Hongik University, Sejong, 30016, Korea

    **-Rae Cho

Authors
  1. Hyeong ** Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **-Rae Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to **-Rae Cho.

Additional information

Hyeong ** Kim received his B.S. and M.S. degree from the Hongik University and Pusan National University in 2020 and 2022, respectively. He is currently a Ph.D. student at the Department of Mechanical Engineering in University College London. His major research field is the nonlinear structural mechanics, analysis, and design of ships and offshore structures.

**-Rae Cho received his B.S. degree in Aeronautical Engineering from Seoul National University in 1983. He then received his M.S. and Ph.D. degrees from the University of Texas at Austin in 1993 and 1995, respectively. He is currently a Professor at the Department of Naval Architecture and Ocean Engineering in Hongik University. His major research field is the computational mechanics in solid/structural mechanics, ocean engineering and materials science and engineering.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, H.J., Cho, JR. Numerical optimization of volume fraction distributions in FGM sandwich beams with FG-CNTRC facesheets. J Mech Sci Technol 38, 3533–3543 (2024). https://doi.org/10.1007/s12206-024-0626-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-024-0626-7

Keywords

Search

Navigation