Skip to main content
SpringerLink
Log in

Thermoelastic analysis of functionally graded sandwich plates with a homogeneous core

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

Abstract

This paper is concerned with the thermoelastic analysis of functionally graded (FG) sandwich plates with a homogeneous core by a numerical method. The core layer is homogeneous ceramic while two facesheets are inhomogeneous metal-ceramic FGMs having the power-law volume fractions. The metal-ceramic FG sandwich plates are characterized by the relative thicknesses of three layers, the width-thickness and aspect ratios of plate, and the volume fractions of metal and ceramic. Meanwhile, the problem is formulated using the hierarchical models exhibiting the spectral model accuracy and implemented by 2-D natural element method (NEM). The hierarchical models are based upon the 3-D elasticity and NEM is applied to the mid-surface of plate to approximate the triple-vectored in-plane displacement field. The accuracy of hierarchical models are examined with respect to the model order, from which the (3, 3, 4) hierarchical model is chosen for the thermoelastic analysis. The thermoelastic responses obtained by the present method are compared with the existing analytic solutions, and those are parametrically investigated with respect to the above-mentioned design parameters. It is found that the present method shows a reasonable accuracy and the thermoelastic responses of FG sandwich plates are remarkably influenced by the design parameters.

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. J. R. Cho and J. T. Oden, Functionally graded material: a parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme, Comput. Methods Appl. Mech. Engrg., 188 (2000) 17–38.

    Article  Google Scholar 

  2. Y. Miyamoto, W. W. Kaysser, B. H. Rabin, A. Kawasaki and A. R. G. Ford, Functionally Graded Materials: Design, Processing and Applications, Springer Science+ Business Media, New York (1999).

    Book  Google Scholar 

  3. A. M. Zenkour, A comprehensive analysis of functionally graded sandwich plates: part 1 — deflection and stresses, Int. J. Solids Struct., 42 (2005) 5224–5242.

    Article  Google Scholar 

  4. J. R. Cho and D. Y. Ha, Volume fraction optimization for minimizing thermal stress in Ni−Al2O3 functionally graded materials, Mater. Sci. Eng. A, 334 (2002) 147–155.

    Article  Google Scholar 

  5. G. J. Nie, Z. Zhong and R. C. Batra, Material tailoring for reducing stress concentration factor at a circular hole in a functionally graded materials (FGM) panel, Composite Struct., 205 (2018) 49–57.

    Article  Google Scholar 

  6. M. Chmielewski and K. Pietrzak, Metal-ceramic functionally graded materials — manufacturing, characterization, application, Bulletin Polish Academy Sci., 64(1) (2016) 151–160.

    Google Scholar 

  7. M. Kashtalyan and M. Menshykova, Three-dimensional elasticity solution for sandwich panels with a functionally graded core, Composite Struct., 87(1) (2009) 36–43.

    Article  Google Scholar 

  8. D. Li, Z. Deng, H. Xiao and P. Jin, Bending analysis of sandwich plates with different face sheet materials and functionally graded soft core, Thin-Walled Struct., 122 (2018) 8–16.

    Article  Google Scholar 

  9. M. Das, B. Barut, E. Madenci and D. R. Ambur, A triangular plate element for thermoelastic analysis of sandwich panels with a functionally graded core, Int. J. Numer. Methods Engng., 68 (2006) 940–966.

    Article  Google Scholar 

  10. M. Bennoun, M. S. A. Houari and A. Tounsi, A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates, Mech. Adv. Mater. Struct., 23(4) (2016) 423–431.

    Article  Google Scholar 

  11. Q. Li, V. P. Iu and K. P. Kou, Three-dimensional vibration analysis of functionally graded material sandwich plates, J. Sound Vib., 311 (2008) 498–515.

    Article  Google Scholar 

  12. H. Yaghoobi and P. Yaghoobi, Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach, Meccanica, 48 (2013) 2019–2035.

    Article  MathSciNet  Google Scholar 

  13. A. A. Daikh and A. Megueni, Thermal buckling analysis of functionally graded sandwich plates, Journal of Thermal Stresses, 41(2) (2018) 139–159.

    Article  Google Scholar 

  14. N. ElMeiche, A. Tounsi, N. Ziane, I. Mechab and E. A. Adda Bedia, A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, Int. J. Mech. Sci., 53 (2011) 237–247.

    Article  Google Scholar 

  15. S. S. Akavci, Mechanical behavior of functionally graded sandwich plates on elastic foundation, Composites Part B, 96 (2016) 136–152.

    Article  Google Scholar 

  16. E. Carrera, S. Brischetto, M. Cinefra and M. Soave, Effects of thickness stretching in functionally graded plates and shells, Composites Part B, 42 (2011) 123–133.

    Article  Google Scholar 

  17. S. Xiang, G. Kang, M. Yang and Y. Zhao, Natural frequencies of sandwich plate with functionally graded face and homogeneous core, Composite Struct., 96 (2013) 226–231.

    Article  Google Scholar 

  18. T. N. Nguyen, C. H. Thai and H. Nguyen-Xuan, A novel computational approach for functionally graded isotropic and sandwich plate structures based on a rotation-free meshfree method, Thin-Walled Struct., 107 (2016) 473–488.

    Article  Google Scholar 

  19. A. M. Zenkour and N. A. Alghamdi, Bending analysis of functionally graded sandwich plates uder the effect of mechanical and thermal loads, Mech. Adv. Mater. Struct., 17(6) (2010) 419–432.

    Article  Google Scholar 

  20. M. S. A. Houari, S. Benyoucef, I. Mechab, A. Tounsi and E. A. Adda Bedia, Two variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates, J. Thermal Stress., 34 (2011) 315–334.

    Article  Google Scholar 

  21. M. Cetkovic, Thermo-mechanical bending of laminated composite and sandwich plates using layerwise displacement model, Composite Struct., 125 (2015) 388–399.

    Article  Google Scholar 

  22. A. S. Sayyard and Y. M. Ghugal, Modeling and analysis of functionally graded sandwich beams: a review, Mech. Adv. Mater. Struct., 26(21) (2019) 1776–1795.

    Article  Google Scholar 

  23. N. Sukumar and B. Moran, C1 natural neighbor interpolant for partial differential equations, Numer. Methods Partial Diff. Equ., 15 (1999) 417–447.

    Article  Google Scholar 

  24. J. R. Cho and H. W. Lee, A Petrov-Galerkin natural element method securing the numerical integration accuracy, J. Mech. Sci. Technol., 20(1) (2006) 94–109.

    Article  Google Scholar 

  25. F. Chinesta, C. Cescotto, E. Cueto and P. Lorong, Natural Element Method for the Simulation of Structures and Processes, Wiley (2013).

  26. P. Lu, Y. Shu, D. Lu, K. Jiang, B. Liu and C. Huang, Research on natural element method and the application to simulate metal forming processes, Procedia Eng., 207 (2017) 1087–1092.

    Article  Google Scholar 

  27. M. A. Bennaceur and Y. Xu, Application of the natural element method for the analysis of composite laminated plates, Aero. Space Technol., 87 (2019) 244–253.

    Article  Google Scholar 

  28. J. R. Cho, A numerical evaluation of SIFs for 2-D functionally graded materials by enriched natural element method, Appl. Sci., 9(17) (2019) 3581.

    Article  Google Scholar 

  29. I. Babuska, B. A. Szabo and R. L. Actis, Hierarchical models for laminated composites, Int. J. Numer. Methods Engng., 33 (1992) 503–535.

    Article  Google Scholar 

  30. J. R. Cho and J. T. Oden, A priori error estimates of hierarchical models for elasticity problems for plate- and shell-like structures, Math. Comput. Modell., 23(10) (1996) 117–133.

    Article  MathSciNet  Google Scholar 

  31. E. Stein and S. Ohnimus, Dimensional adaptivity in linear elasticity with hierarchical test-spaces for h- and p-refinement processes, Eng. Comput., 12 (1996) 107–119.

    Article  Google Scholar 

  32. G. Kuhlmann and R. Rolfes, A hierarchic finite element for laminated composites, Int. J. Numer. Methods Engng., 61 (2004) 96–116.

    Article  Google Scholar 

  33. L. G. Nallim, S. Oller, E. Onate and F. G. Flores, A hierarchic finite element for composite laminates beams using a refined zifzag theory, Compos. Struct., 163 (2017) 168–184.

    Article  Google Scholar 

  34. J. R. Cho, Natural element approximation of hierarchical models of plate-like elastic structures, Finite Elem. Anal. Des., 180 (2020) 103439.

    Article  MathSciNet  Google Scholar 

  35. J. R. Cho, Hierarchic models for the free vibration analysis of functionally graded plates, Int. J. Mech. Mater. Des., 17 (2021) 489–501.

    Article  Google Scholar 

  36. J. R. Cho and D. Y. Ha, Averaging and finite-element discretization approaches in the numerical analysis of functionally graded materials, Mater. Sci. Eng. A, 302(2) (2001) 187–196.

    Article  Google Scholar 

  37. O. C. Zienkiewicz, R. L. Taylor and J. M. Too, Reduced integration technique in general analysis of plates and shells, Int. J. Numer. Methods Engng., 3(2) (1971) 275–290.

    Article  Google Scholar 

  38. J. N. Reddy, Analysis of functionally graded plates, Int. J. Numer. Methods Engng., 47 (2000) 663–684.

    Article  Google Scholar 

  39. J. R. Cho, Level-wise strain recovery and error estimation for natural element hierarchical plate model, Int. J. Numer. Methods Engng., 122 (2021) 3120–3136.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by 2022 Hongik University Research Fund. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924).

Author information

Authors and Affiliations

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

    Jin-Rae Cho

Authors
  1. Jin-Rae Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin-Rae Cho.

Additional information

Jin-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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cho, JR. Thermoelastic analysis of functionally graded sandwich plates with a homogeneous core. J Mech Sci Technol 36, 4583–4592 (2022). https://doi.org/10.1007/s12206-022-0821-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-022-0821-3

Keywords

Search

Navigation