Finite Element Formulation for Mechanical Buckling of FGM Plate Exposed to Various Boundary Conditions

Year : 2025 | Volume : 13 | Special Issue 04 | Page : 503 513
    By

    Vineet Kumar,

  • Pankaj Sonia,

  1. Assistant Professor, Department of Mechanical Engineering, Govt. Engineering College, Bikaner, Rajasthan, India
  2. Assistant Professor, Department of Mechanical Engineering, GLA University, Mathura, Uttar Pradesh, India

Abstract

Mechanical buckling analysis of functionally graded (FG) material plates based on first-order shear deformation theory. In the real world many components manufactured by FG materials face the buckling load under certain conditions. Various types of gradation law for tailoring the material properties are applied by the researcher, out of that, presently a simple power law for material gradation is applied with shear correction factor (SCF) is used to take account of transverse shear & parabolic distribution of shear strain through z- direction of the plate. Every material has manufacturing defects at the time of production or preparation of material solutions. So, the need of simulation for the real materials based on porosity is required for factual results. In this direction there are two types of material porosities are modelled, and their effects are investigated viz. Tape I (even distributions of pores within plate) and Type II (Uneven distribution of pores). A four node iso-parametric element with five degrees of freedom at each node is used to discretize the plate element. Finite element technique in conjunction with Hamilton’s principle is used to develop the governing equations and solutions. Validation studies are performed to verify and predict the accuracy of the present formulation. Results are presented in tabulated form as well as the parametric studies are done to explore the various dimensions taken into consideration. The slenderness ratio (a/b), aspect factor (a/h), material exponent index (p), various boundary conditions (BCs), uniaxial and biaxial buckling loading is explored and discussed.

Keywords: Water treatment, calcium removal, biopolymer membrane, polylactic acid, pectin.

[This article belongs to Special Issue under section in Journal of Polymer and Composites (jopc)]

How to cite this article:
Vineet Kumar, Pankaj Sonia. Finite Element Formulation for Mechanical Buckling of FGM Plate Exposed to Various Boundary Conditions. Journal of Polymer and Composites. 2025; 13(04):503-513.
How to cite this URL:
Vineet Kumar, Pankaj Sonia. Finite Element Formulation for Mechanical Buckling of FGM Plate Exposed to Various Boundary Conditions. Journal of Polymer and Composites. 2025; 13(04):503-513. Available from: https://journals.stmjournals.com/jopc/article=2025/view=219801


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References

  1. Koizumi, M.: FGM activities in Japan. Compos. Part B Eng. 28, 1–4 (1997). https://doi.org/10.1016/S1359-8368(96)00016-9
  2. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: An analytical framework for rectangular FGM tapered plate resting on the elastic foundation. Mater. Today Proc. 28, 1719–1726 (2020). https://doi.org/10.1016/j.matpr.2020.05.136
  3. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Vibration analysis of the rectangular FG materials plate with variable thickness on Winkler-Pasternak-Kerr elastic foundation. Mater. Today Proc. 62, 184–190 (2022). https://doi.org/10.1016/j.matpr.2022.02.615
  4. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Vibration response of exponentially graded plates on elastic foundation using higher-order shear deformation theory. Indian J. Eng. Mater. Sci. 29, 181–188 (2022)
  5. Kumar, V., Singh, S.J., Harsha, S.P.: Temperature-Dependent Vibration Characteristics of Porous FG Material Plates Utilizing FSDT. Int. J. Struct. Stab. Dyn. 24, 1–35 (2023). https://doi.org/10.1142/S021945542450072X
  6. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Vibration response of the exponential functionally graded material plate with variable thickness resting on the orthotropic Pasternak foundation. Mech. Based Des. Struct. Mach. (2023). https://doi.org/10.1080/15397734.2023.2193623
  7. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak’s foundation. Eur. J. Mech. A/Solids. 85, 104124 (2021). https://doi.org/10.1016/j.euromechsol.2020.104124
  8. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. (2020). https://doi.org/10.1177/1464420720980491
  9. Hosseini-Hashemi, S., Khorshidi, K., Amabili, M.: Exact solution for linear buckling of rectangular Mindlin plates. J. Sound Vib. 315, 318–342 (2008). https://doi.org/10.1016/j.jsv.2008.01.059
  10. Mohammadi, M., Saidi, A.R., Jomehzadeh, E.: Levy solution for buckling analysis of functionally graded rectangular plates. Appl. Compos. Mater. 17, 81–93 (2010). https://doi.org/10.1007/s10443-009-9100-z
  11. Ramu, I., Mohanty, S.C.: Buckling Analysis of Rectangular Functionally Graded Material Plates under Uniaxial and Biaxial Compression Load. Procedia Eng. 86, 748–757 (2014). https://doi.org/10.1016/j.proeng.2014.11.094
  12. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Effect of elastic foundation and porosity on buckling response of linearly varying functionally graded material plate. Structures. 55, 1186–1203 (2023). https://doi.org/10.1016/j.istruc.2023.06.084
  13. Thai, H.T., Kim, S.E.: Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation. Int. J. Mech. Sci. 75, 34–44 (2013). https://doi.org/10.1016/j.ijmecsci.2013.06.007
  14. Prakash, T., Singha, M.K., Ganapathi, M.: Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates. Comput. Mech. 43, 341–350 (2009). https://doi.org/10.1007/s00466-008-0309-8
  15. Asemi, K., Shariyat, M., Salehi, M., Ashrafi, H.: A full compatible three-dimensional elasticity element for buckling analysis of FGM rectangular plates subjected to various combinations of biaxial normal and shear loads. Finite Elem. Anal. Des. 74, 9–21 (2013). https://doi.org/10.1016/j.finel.2013.05.011
  16. Uymaz, B., Aydogdu, M.: Three dimensional shear buckling of FG plates with various boundary conditions. Compos. Struct. 96, 670–682 (2013). https://doi.org/10.1016/j.compstruct.2012.08.031
  17. Afzali, M., Farrokh, M., Carrera, E.: Thermal buckling loads of rectangular FG plates with temperature-dependent properties using Carrera Unified Formulation. Compos. Struct. 295, (2022). https://doi.org/10.1016/j.compstruct.2022.115787
  18. Rezaei, A.S., Saidi, A.R.: Exact solution for free vibration of thick rectangular plates made of porous materials. Compos. Struct. 134, 1051–1060 (2015). https://doi.org/10.1016/j.compstruct.2015.08.125
  19. Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Vibration Response Analysis of Tapered Porous FGM Plate Resting on Elastic Foundation. Int. J. Struct. Stab. Dyn. 2350024, 1–31 (2022). https://doi.org/10.1142/S0219455423500244
  20. Barati, M.R., Sadr, M.H., Zenkour, A.M.: Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on elastic foundation. Int. J. Mech. Sci. 117, 309–320 (2016). https://doi.org/10.1016/j.ijmecsci.2016.09.012
  21. Dhuria, M., Grover, N., Goyal, K.: Influence of porosity distribution on static and buckling responses of porous functionally graded plates. Structures. 34, 1458–1474 (2021). https://doi.org/10.1016/j.istruc.2021.08.050
  22. N. Reddy: Theory and Analysis of Elastic Plate and Shells. (2009)
  23. Kim, S.E., Thai, H.T., Lee, J.: Buckling analysis of plates using the two variable refined plate theory. Thin-Walled Struct. 47, 455–462 (2009). https://doi.org/10.1016/j.tws.2008.08.002
  24. Rouzegar, J., Sharifpoor, R.A.: Finite element formulations for buckling analysis of isotropic and orthotropic plates using two-variable refined plate theory. Iran. J. Sci. Technol. – Trans. Mech. Eng. 41, 177–187 (2017). https://doi.org/10.1007/s40997-016-0055-z
  25. Zenkour, A.M., Aljadani, M.H.: Mechanical buckling of functionally graded plates using a refined higher-order shear and normal deformation plate theory. Adv. Aircr. Spacecr. Sci. 5, 615–632 (2018). https://doi.org/10.12989/aas.2018.5.6.615
  26. Wu, T.L., Shukla, K.K., Huang, J.H.: Post-buckling analysis of functionally graded rectangular plates. Compos. Struct. 81, 1–10 (2007). https://doi.org/10.1016/j.compstruct.2005.08.026
  27. Gupta, A.K., Kumar, A.: Buckling Analysis of Porous Functionally Graded Plates. Eng. Technol. Appl. Sci. Res. 13, 10901–10905 (2023). https://doi.org/10.48084/etasr.5943
Special Issue Subscription Review Article
Volume 13
Special Issue 04
Received 26/03/2025
Accepted 30/04/2025
Published 15/06/2025
Publication Time 81 Days
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