An advanced hyperbolic shear deformation plate model for the bending study of functionally graded materials

Ali MEFTAH; Mohamed BELAIDI; Atallah DEHBI

doi:10.18540/jcecvl11iss1pp21694

Authors

Ali MEFTAH University Center of Nour Bachir El-Bayadh, Algeria https://orcid.org/0000-0003-3664-3780
Mohamed BELAIDI University Center of Nour Bachir El-Bayadh, Algeria
Atallah DEHBI University Center of Nour Bachir El-Bayadh, Algeria

DOI:

https://doi.org/10.18540/jcecvl11iss1pp21694

Keywords:

Bending. Hyperbolic shear deformation. Free surface conditions.

Abstract

This study investigates the bending analysis of functionally graded plates using a unique form function. This function accounts for the parabolic transverse shear forces across the plate thickness while satisfying shear stress-free surface conditions. A key advantage of this approach is that it eliminates the need for shear correction factors, allowing for an accurate shear deformation distribution proportional to the plate's thickness. Additionally, compared to previous shear deformation theories, this higher-order shear theory involves fewer unknowns in its formulation. To derive the governing equations for functionally graded plates, the Hamiltonian principle is employed, and Navier’s technique is used to obtain solutions. These methodologies are essential for achieving the desired outcomes. Finally, the findings of this study are presented and compared with previous research results.

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References

BOUCHETA, A. et al. (2024) Bending of Sandwich FGM Plates with a Homogeneous Core Either Hard or Soft Via a Refined Hyperbolic Shear Deformation Plate Theory. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 48(5), pp. 3441–3455. doi: https://doi.org/10.1007/s40996-024-01386-w.

BRISCHETTO, S. and CARRERA, E. (2010) Advanced mixed theories for bending analysis of functionally graded plates. Computers & Structures, 88(23–24), pp. 1474–1483. doi: https://doi.org/10.1016/j.compstruc.2008.04.004.

CHUNG, Y.-L. and CHEN, W.-T. (2007) Bending behavior of FGM-coated and FGM-undercoated plates with two simply supported opposite edges and two free edges. Composite Structures, 81(2), pp. 157–167. doi: https://doi.org/10.1016/j.compstruct.2006.08.006.

DAOUADJI, T.H., ADIM, B. and BENFERHAT, R. (2016) Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation. Advances in materials Research, 5(1), pp. 35–53. doi: https://doi.org/10.12989/amr.2016.5.1.035.

DHEPE, S.N., BAMBOLE, A.N. and GHUGAL, Y.M. (2024) An elasticity solution of FGM rectangular plate under cylindrical bending. Acta Mechanica, 235(1), pp. 303–322. doi: https://doi.org/10.1007/s00707-023-03758-1.

DHURIA, M., GOYAL, K. and GROVER, N. (2025) Numerical assessment of bending and buckling analysis of sigmoid functionally graded (S-FGM) porous plates in framework of secant hyperbolic shear deformation theory: A finite element study. Mechanics Based Design of Structures and Machines, pp. 1–25. doi: https://doi.org/10.1080/15397734.2025.2473025.

DO, V.T., PHAM, V.V. and NGUYEN, H.N. (2020) On the Development of Refined Plate Theory for Static Bending Behavior of Functionally Graded Plates. Mathematical Problems in Engineering, 2020, pp. 1–13. doi: https://doi.org/10.1155/2020/2836763.

GANGUWAR, S. and NISTANE, V. (2025) Study on comparison between three point bending and four point bending test condition for functionally graded material beam with crack. Strength, Fracture and Complexity: An International Journal, 18(1), pp. 18–31. doi: https://doi.org/10.1177/15672069241304945.

HAN, M. et al. (2023) Bending Analysis of Asymmetric Functionally Graded Material Sandwich Plates in Thermal Environments. Materials, 16(13), p. 4682. doi: https://doi.org/10.3390/ma16134682.

KUMAR, R. et al. (2019) New transverse shear deformation theory for bending analysis of FGM plate under patch load. Composite Structures, 208, pp. 91–100. doi: https://doi.org/10.1016/j.compstruct.2018.10.014.

KUMAR, R., SINGH, B.N. and SINGH, J. (2023) Geometrically nonlinear analysis for flexure response of FGM plate under patch load. Mechanics Based Design of Structures and Machines, 51(11), pp. 6532–6556. doi: https://doi.org/10.1080/15397734.2022.2058015.

LI, S.-R., ZHANG, F. and LIU, R.-G. (2024) Classical and homogenized expressions for the bending solutions of FGM plates based on the four variable plate theories. Mechanics of Advanced Materials and Structures, 31(15), pp. 3413–3424. doi: https://doi.org/10.1080/15376494.2023.2177909.

LIU, B.L., LI, S. and LI, Y.S. (2023) Bending of FGM sandwich plates with tunable auxetic core using DQM. European Journal of Mechanics - A/Solids, 97, p. 104838. doi: https://doi.org/10.1016/j.euromechsol.2022.104838.

MA, L.S. and WANG, T.J. (2004) Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory. International Journal of Solids and Structures, 41(1), pp. 85–101. doi: https://doi.org/10.1016/j.ijsolstr.2003.09.008.

MEFTAH, A. et al. (2017) A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation. Steel and Composite Structures, 23(3), pp. 317–330. doi: https://doi.org/10.12989/scs.2017.23.3.317.

MEFTAH, A.M. (2023) Bending and Buckling Analysis of Functionally Graded Plates using a New Shear Strain Function with Reduced Unknowns. Journal of Mechanical Engineering, 20(3), pp. 105–129. doi: https://doi.org/10.24191/jmeche.v20i3.23903.

REDDY, J.N. (2000) Analysis of functionally graded plates. International Journal for numerical methods in engineering, 47(1?3), pp. 663–684. doi: https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.

SAH, S.K. and GHOSH, A. (2024) Effect of bi-directional material gradation on thermo-mechanical bending response of metal-ceramic FGM sandwich plates using inverse trigonometric shear deformation theory. International Journal of Structural Integrity, 15(3), pp. 561–593. doi: https://doi.org/10.1108/IJSI-02-2024-0016.

SAIDI, A.R., RASOULI, A. and SAHRAEE, S. (2009) Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory. Composite Structures, 89(1), pp. 110–119. doi: https://doi.org/10.1016/j.compstruct.2008.07.003.

SHEN, H.-S. and WANG, Z.-X. (2010) Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations. Composite Structures, 92(10), pp. 2517–2524. doi: https://doi.org/10.1016/j.compstruct.2010.02.010.

TELLI, F. et al. (2025) FGM concept used in damage analysis of heat-treated elbows under out-of-plane combined bending moment. Mechanics Based Design of Structures and Machines, 53(3), pp. 1778–1798. doi: https://doi.org/10.1080/15397734.2024.2395972.

THAI, H.-T. and CHOI, D.-H. (2013) A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates. Composite Structures, 101, pp. 332–340. doi: https://doi.org/10.1016/j.compstruct.2013.02.019.

VAFAKHAH, Z. and NAVAYI NEYA, B. (2019) An exact three dimensional solution for bending of thick rectangular FGM plate. Composites Part B: Engineering, 156, pp. 72–87. doi: https://doi.org/10.1016/j.compositesb.2018.08.036.

WANG, Y. et al. (2025) Nitsche-based isogeometric analysis of bending and free vibration of stiffened FGM plates with cutouts. Computers & Structures, 310, p. 107677. doi: https://doi.org/10.1016/j.compstruc.2025.107677.

WU, C.-P., CHIU, K.-H. and WANG, Y.-M. (2011) RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates. Composite Structures, 93(2), pp. 923–943. doi: https://doi.org/10.1016/j.compstruct.2010.07.001.

WU, C.-P.P. and LI, H.-Y.Y. (2010) An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates. Composite Structures, 92(10), pp. 2591–2605. doi: https://doi.org/10.1016/j.compstruct.2010.01.022.

YADAV, S.S. et al. (2023) Bending analysis of FGM plates using sinusoidal shear and normal deformation theory. Forces in Mechanics, 11, p. 100185. doi: https://doi.org/10.1016/j.finmec.2023.100185.

YANG, J., KITIPORNCHAI, S. and LIEW, K.M. (2008) Nonlinear local bending of FGM sandwich plates. Journal of Mechanics of Materials and Structures, 3(10), pp. 1977–1992. doi: https://doi.org/10.2140/jomms.2008.3.1977.

YANG, J. and SHEN, H.-S. (2003) Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Composites Part B: Engineering, 34(2), pp. 103–115. doi: https://doi.org/10.1016/S1359-8368(02)00083-5.

YUN, W., RONGQIAO, X. and HAOJIANG, D. (2010) Three-dimensional solution of axisymmetric bending of functionally graded circular plates. Composite Structures, 92(7), pp. 1683–1693. doi: https://doi.org/10.1016/j.compstruct.2009.12.002.

ZENKOUR, A.M. and ALGHAMDI, N.A. (2010) Bending Analysis of Functionally Graded Sandwich Plates Under the Effect of Mechanical and Thermal Loads. Mechanics of Advanced Materials and Structures, 17(6), pp. 419–432. doi: https://doi.org/10.1080/15376494.2010.483323.

ZHANG, D.-G. and ZHOU, Y.-H. (2008) A theoretical analysis of FGM thin plates based on physical neutral surface. Computational Materials Science, 44(2), pp. 716–720. doi: https://doi.org/10.1016/j.commatsci.2008.05.016.

ZIDI, M. et al. (2014) Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory. Aerospace Science and Technology, 34, pp. 24–34. doi: https://doi.org/10.1016/j.ast.2014.02.001.