Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Combined effects of partial loading and partial elastic foundation on the bending response of functionally graded structures

  • Abderrahmane Menasria (Civil Engineering Department, Faculty of Sciences and Technology, University of Khenchela) ;
  • Nabil Himeur (Mechanical Engineering Department, Faculty of Sciences and Technology, University of Khenchela) ;
  • Abdelhakim Bouhadra (Civil Engineering Department, Faculty of Sciences and Technology, University of Khenchela) ;
  • Messaoud Bazzouzi (Civil Engineering Department, Faculty of Sciences and Technology, University of Khenchela) ;
  • Abdelouahed Tounsi (Laboratory of Engineering and Sciences of Advanced Materials)
  • Received : 2025.02.17
  • Accepted : 2025.05.23
  • Published : 2025.04.25
⟨ Previous Next ⟩

Abstract

This study uniquely investigates functionally graded nanoplates under combined partial loading and non-uniform elastic support, developing a quasi-3D model, a unified analytical framework for complex foundations, and novel closed-form solutions, thereby addressing a critical yet underexplored area in structural mechanics. A simplified quasi-3D high-order shear deformation theory incorporating integral terms is used. The governing equilibrium equations consider the interaction between the loading type and the variation of Winkler-Pasternak and Kerr foundation parameters. The numerical results for non-dimensional stresses and displacements are obtained using the virtual displacement principle and Navier's solution technique. The accuracy of the non-dimensional formulas is validated against existing literature, demonstrating excellent agreement. Additionally, several parametric studies examine the effects of various geometric and material factors. This analytical model is well suited for analyzing the bending behaviour of simply supported FG plates in specific engineering applications.

Keywords

References

  1. Abdelrahman, A.A., Ashry, M., Alshorbagy, A.E., Eltaher, M.A. and Abdalla, W.S. (2024), "On the dynamic behavior of functionally graded cracked beams resting on winkler foundation under moving load", Steel Compos. Struct., 53(2), 169-194. https://doi.org/10.12989/scs.2024.53.2.169.
  2. Adiyaman, G. and Turan, M. (2025), "Bending and buckling analysis of porous 2D functionally graded beams with exponential material property variation", Iran. J. Sci. Technol. Trans. Civil Eng., 49, 1359-1386. https://doi.org/10.1007/s40996-024-01508-4.
  3. Ameur, M., Tounsi, A., Mechab, I. and El Bedia, A.A. (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15, 1405-1414. https://doi.org/10.1007/s12205-011-1361-z.
  4. Chen, W.R., Chiu, L.H. and Lin, C.H. (2024), "Vibration of elastically supported bidirectional functionally graded sandwich Timoshenko beams on an elastic foundation", Struct. Eng. Mech., 91(2), 197-209. https://doi.org/10.12989/sem.2024.91.2.197.
  5. Chitour, M., Bouhadra, A., Benguediab, M., Mansouri, K., Menasria, A. and Tounsi, A. (2022), "A new high order theory for buckling temperature analysis of functionally graded sandwich plates resting on elastic foundations", Nano-Electron. Phys., 14(3), 03028. https://doi.org/10.21272/jnep.14(3).03028.
  6. Chitour, M., Bouhadra, A., Benguediab, S., Saoudi, A., Menasria, A. and Tounsi, A. (2022), "Effect of phase contrast and geometrical parameters on bending behavior of sandwich beams with FG isotropic face sheets", J. Nano-Electron. Phys., 14(5), 05016. https://doi.org/10.21272/jnep.14(5).05016.
  7. Do, N.T. and Pham, Q.H. (2024), "Nonlinear static analysis of functionally graded porous sandwich plates resting on Kerr foundation", Mech. Adv. Mater. Struct., 31(22), 5678-5691. https://doi.org/10.1080/15376494.2023.2218845.
  8. Eghbali, M. and Hosseini, S.A. (2024), "An accurate analytical exploration for dynamic response of thermoelectric CNTRC beams under driving harmonic and constant loads resting on Pasternak foundation", Adv. Nano Res., 16(6), 549-564. https://doi.org/10.12989/anr.2024.16.6.549.
  9. Faicel, K., Abderahmane, M., Belgacem, M., Abdelhakim, B., Fouad, B., Soumia, B., ... & Abdelouahed, T. (2022), "Thickness stretching and nonlinear hygro-thermo-mechanical loading effects on bending behavior of FG beams", Struct. Eng. Mech., 84(6), 783-798. https://doi.org/10.12989/sem.2022.84.6.783.
  10. Fan, Y.H. and She, G.L. (2025), "Nonlinear transient response of graphene platelets reinforced metal foams beam considering initial geometrical imperfection and viscoelastic elastic foundation", Comput. Concrete, 35(1), 59-70. https://doi.org/10.12989/cac.2025.35.1.059.
  11. Foroutan, K. and Dai, L. (2024), "Nonlinear free and forced vibrations of oblique stiffened porous FG shallow shells embedded in a nonlinear elastic foundation", Struct. Eng. Mech., 89(1), 33-46. https://doi.org/10.12989/sem.2024.89.1.033.
  12. Han, J.B. and Liew, K. (1997), "Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations", Int. J. Mech. Sci., 39(9), 977-989. https://doi.org/10.1016/S0020-7403(97)00001-5.
  13. He, Y.J. and She, G.L. (2024), "Nonlinear forced vibration of imperfect FG beams with hygro-thermal factor", Struct. Eng. Mech., 92(2), 163-172. https://doi.org/10.12989/sem.2024.92.2.163.
  14. Himeur, N., Mamen, B., Benguediab, S., Bouhadra, A., Menasria, A., Bouchouicha, B., ... & Benguediab, M. (2022), "Coupled effect of variable Winkler-Pasternak foundations on bending behavior of FG plates exposed to several types of loading", Steel Compos. Struct., 44(3), 353-369. https://doi.org/10.12989/scs.2022.44.3.353.
  15. Hoang, V.N.V. and Thanh, P.T. (2023), "Influences of arbitrary-distributed Kerr foundation on free vibration and nonlinear transient response of functionally graded plate in thermal environment", Thin Wall. Struct., 188, 110802. https://doi.org/10.1016/j.tws.2023.110802.
  16. Hoang, V.N.V., Shi, P., Toledo, L. and Vu, H. (2024), "Thermal vibration analysis of FG-GPLRC doubly curved shells partially resting on Kerr foundation based on higher-order shear deformation theory", Thin Wall. Struct., 195, 111357. https://doi.org/10.1016/j.tws.2023.111357.
  17. Houari, M.S.A., Bessaim, A., Bezzina, S., Tounsi, A., Daikh, A.A., Garg, A. and Belarbi, M.O. (2024), "Thermoelastic bending analysis of thick functionally graded sandwich plates with arbitrary graded material properties using a novel quasi-3D HSDT", Arch. Civil Mech. Eng., 24(2), 80. https://doi.org/10.1007/s43452-024-00898-6.
  18. Huang, Z., Han, M., Wang, X. and Chu, F. (2023). Bending analysis of two different types of functionally graded material porous sandwich plates", Arch. Appl. Mech., 93(8), 3071-3091. https://doi.org/10.1007/s00419-023-02425-0.
  19. Kahya, V. and Turan, M. (2018), "Vibration and buckling of laminated beams by a multi-layer finite element model", Steel Compos. Struct., 28(4), 415-426. https://doi.org/10.12989/scs.2018.28.4.415.
  20. Kahya, V.O.L.K.A.N. and Turan, M.E.H.M.E.T. (2017), "Bending of laminated composite beams by a multi-layer finite element based on a higher-order theory", Acta Physica Polonica A, 132(3), 473-475. https://doi.org/10.12693/APhysPolA.132.473.
  21. Kumar, R., Lal, A., Sutaria, B., Dehury, R.K., Joshi, Y.G. and Gupta, V.S. (2024), "Bending analysis of a porous functionally graded sandwich plate with a hole resting on an elastic foundation", Acta Mechanica, 235(8), 5061-5078. https://doi.org/10.1007/s00707-024-03989-w.
  22. 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", Mech. Adv. Mater. Struct., 31(15), 3413-3424. https://doi.org/10.1080/15376494.2023.2177909.
  23. Mekerbi, M., Benyoucef, S., Mahmoudi, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S. (2021), "Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions", J. Sandw. Struct. Mater., 23(3), 1028-1057. https://doi.org/10.1177/1099636219851281.
  24. Meski, K., Boutrid, A., Menasria, A., Bouhadra, A., Mamen, B., Tounsi, A. and Cuong-Le, T. (2024), "Analytical modeling of flexural behavior of advanced composite sandwich beams under nonlinear hygrothermo-mechanical loads", Multiscale Multidisc. Model. Exper. Des., 7(5), 4701-4719. https://doi.org/10.1007/s41939-024-00414-6.
  25. Mohammed, A.J., Mohammed, B.A., Kadhom, H.K., Taki, A.G. and Tahouneh, V. (2024), "A semianalytical study for vibration analysis of damaged core laminated cylindrical shell with functionally graded CNTs reinforced face sheets resting on a two-parameter elastic foundation", Adv. Nano Res., 17(4), 301-313. https://doi.org/10.12989/ANR.2024.17.4.301.
  26. Najafi, M., Ahmadi, I. and Sladek, V. (2024), "A new three-dimensional model for free vibration analysis of functionally graded nanoplates resting on an elastic foundation", Steel Compos. Struct., 52(3), 273-291. https://doi.org/10.12989/scs.2024.52.3.273.
  27. Nebab, M., Ait Atmane, H., Bennai, R. and Tounsi, A. (2019), "Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation", Arab. J. Geosci., 12(24), 809. https://doi.org/10.1007/s12517-019-4871-5.
  28. Park, M. and Choi, D.H. (2018), "A simplified first-order shear deformation theory for bending, buckling and free vibration analyses of isotropic plates on elastic foundations", KSCE J. Civil Eng., 22, 1235-1249. https://doi.org/10.1007/s12205-017-1517-6.
  29. Rachid, A., Ouinas, D., Lousdad, A., Zaoui, F.Z., Achour, B., Gasmi, H., ... & Tounsi, A. (2022), "Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs", Thin Wall. Struct., 172, 108783. https://doi.org/10.1016/j.tws.2021.108783.
  30. Salehipour, H., Shahmohammadi, M.A. and Civalek, Ö . (2024), "Natural frequencies and modal shapes of folded sandwich plates made of porous core and FG-CNTRC coating layers resting on two parameters elastic foundation", Aerosp. Sci. Technol., 148, 109077. https://doi.org/10.1016/j.ast.2024.109077.
  31. She, G.L., Li, Y.P., He, Y. and Song, J.P. (2024), "Thermal post-buckling analysis of graphene platelets reinforced metal foams beams with initial geometric imperfection", Comput. Concrete, 33(3), 241-250. https://doi.org/10.12989/cac.2024.33.3.241.
  32. Shen, X., Li, T., Xu, L., Kiarasi, F., Babaei, M. and Asemi, K. (2024), "Free vibration analysis of FG porous spherical cap reinforced by graphene platelet resting on Winkler foundation", Adv. Nano Res., 16(1), 11- 26. https://doi.org/10.12989/anr.2024.16.1.011.
  33. Slimani, R., Menasria, A., Ali Rachedi, M., Mourad, C., Refrafi, S., Nimer, A.A., ... & Mamen, B. (2024), "A novel quasi-3D refined HSDT for static bending analysis of porous functionally graded plates", J. Comput. Appl. Mech., 55(3), 519-537. https://doi.org/10.22059/jcamech.2024.372417.968.
  34. Soltani, M., Momenian, M. and Civalek, O. (2024), "Stability analysis of sandwich double nanobeamsystem with varying cross-section interconnected by Kerr-type three-parameter elastic layer", Thin Wall. Struct., 204, 112249. https://doi.org/10.1016/j.tws.2024.112249.
  35. Tamrabet, A., Mamen, B., Menasria, A., Bouhadra, A., Tounsi, A., Ghazwani, M.H., ... & Mahmoud, S.R. (2023), "Buckling behaviors of FG porous sandwich plates with metallic foam cores resting on elastic foundation", Struct. Eng. Mech., 85(3), 289-304. https://doi.org/10.12989/sem.2023.85.3.289.
  36. Thai, H.T., Park, M. and Choi, D.H. (2013), "A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation", Int. J. Mech. Sci., 73, 40-52. https://doi.org/10.1016/j.ijmecsci.2013.03.017.
  37. Turan, M. (2022), "Bending analysis of two-directional functionally graded beams using trigonometric series functions", Arch. Appl. Mech., 92, 1841-1858. https://doi.org/10.1007/s00419-022-02152-y.
  38. Turan, M. (2024), "Mixed series solution for vibration and stability of porous bi-directional functionally graded beams", Arch. Appl. Mech., 94, 1785-1806. https://doi.org/10.1007/s00419-024-02611-8.
  39. Turan, M. and Adiyaman, G. (2024), "Free vibration and buckling analysis of porous two-directional functionally graded beams using a higher-order finite element model", J. Vib. Eng. Technol., 12, 1133- 1152. https://doi.org/10.1007/s42417-023-00898-5.
  40. Turan, M. and Adiyaman, G.A. (2023), "New higher-order finite element for static analysis of twodirectional functionally graded porous beams", Arab. J. Sci. Eng., 48, 13303-13321. https://doi.org/10.1007/s13369-023-07742-8.
  41. Turan, M. and Kahya, V. (2021), "Free vibration and buckling analysis of functionally graded sandwich beams by Navier method", Gazi Univ. J. Eng. Arch. Facult., 36(2), 743-758. https://doi.org/10.17341/gazimmfd.599928.
  42. Turan, M., Kahya, V., Yaylacı, E. and Yaylaci, M. (2025), "A shear deformable numerical approaches for the static analysis of bi-directional functionally graded beams", Adv. Nano Res., 18(2). https://doi.org/10.12989/anr.2025.18.2.143.
  43. Turan, M., Uzun Yaylacı, E. and Yaylacı, M. (2023), "Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods", Arch. Appl. Mech., 93, 1351-1372. https://doi.org/10.1007/s00419-022-02332-w.
  44. 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", Compos. Struct., 93(2), 923-943. https://doi.org/10.1016/j.compstruct.2010.07.001.
  45. Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory", Compos. Part B: Eng., 62, 54-64. https://doi.org/10.1016/j.compositesb.2014.02.014.
  46. Yushan, X. and Zhen, W. (2024), "Non-linear bending analysis and control of graphene-platelets-reinforced porous sandwich plates with piezoelectric layer subjected to electromechanical loading", Appl. Math. Model., 137, 115708. https://doi.org/10.1016/j.apm.2024.115708.
  47. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B: Eng., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  48. Zenkour, A., Allam, M. and Radwan, A. (2014), "Effects of transverse shear and normal strains on FG plates resting on elastic foundations under hygro-thermo-mechanical loading", Int. J. Appl. Mech., 6(05), 1450063. https://doi.org/10.1142/S175882511450063X.