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Buckling analysis of bidirectional FG porous beams in thermal environment under general boundary condition

  • Abdeljalil Meksi (Department of Civil Engineering, Faculty of Architecture and Civil Engineering, University of Sciences and Technology Mohamed Boudiaf) ;
  • Mohamed Sekkal (University of Science and Technology Houari Boumediene (USTHB)) ;
  • Rabbab Bachir Bouiadjra (Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Samir Benyoucef (Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2023.03.22
  • Accepted : 2023.09.25
  • Published : 2024.03.25

Abstract

This work presents a comprehensive investigation of buckling behavior of bidirectional functionally graded imperfect beams exposed to several thermal loading with general boundary conditions. The nonlinear governing equations are derived based on 2D shear deformation theory together with Von Karman strain-displacement relation. The beams are composed of two different materials. Its properties are porosity-dependent and are continuously distributed over the length and thickness of the beams following a defined law. The resulting equations are solved analytically in order to determine the thermal buckling characteristics of BDFG porous beams. The precision of the current solution and its accuracy have been proven by comparison with works previously published. Numerical examples are presented to explore the effects of the thermal loading, the elastic foundation parameters, the porosity distribution, the grading indexes and others factors on the nonlinear thermal buckling of bidirectional FG beam rested on elastic foundation.

Keywords

References

  1. Abouelregal, A.E., Mohammad-Sedighi, H., Faghidian, S.A. and Shirazi, A.H. (2021), "Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load", Facta Univ. Ser.: Mech. Eng., 19(4), 633-656. https://doi.org/10.22190/FUME201222024A.
  2. Alimoradzadeh, M. and Akbas S.D. (2022), "Nonlinear thermal vibration of FGM beams resting on nonlinear viscoelastic foundation", Steel Compos. Struct., 44(4), 557-567. https://doi.org/10.12989/scs.2022.44.4.557.
  3. Akbas, S.D. (2022a), "Moving-load dynamic analysis of AFG beams under thermal", Steel Compos. Struct., 42(5), 649-655. https://doi.org/10.12989/scs.2022.42.5.649.
  4. Akbas, S.D. (2018), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059.
  5. Akbas, S.D. (2019a), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459.
  6. Akbas, S.D. (2019b), "Hygro-thermal nonlinear analysis of a functionally graded beam", J. Appl. Comput. Mech., 5(2), 477-485. https://doi.org/10.22055/jacm.2018.26819.1360.
  7. Akbas, S.D. (2020), "Geometrically nonlinear analysis of axially functionally graded beams by using finite element method", JCAMECH, 51(2), 411-416. https://doi.org/10.22059/jcamech.2020.309019.548.
  8. Akbas, S.D. (2021), "Dynamic analysis of axially functionally graded porous beams under a moving load", Steel Compos. Struct., 39(6), 811-821. https://doi.org/10.12989/scs.2021.39.6.811.
  9. Akbas, S.D. (2022b), "Moving-load dynamic analysis of AFG beams under thermal effect", Steel Compos. Struct., 42(5), 649-655. https://doi.org/10.12989/scs.2022.42.5.649.
  10. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2021), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. https://doi.org/10.1177/1077546320947302.
  11. Asiri, S.S., Akbas, S.D. and Eltaher, M.A. (2020a), "Dynamic analysis of layered functionally graded viscoelastic deep beams with different boundary conditions due to a pulse load", Int. J. Appl. Mech., 12(5), 2050055. https://doi.org/10.1142/S1758825120500556.
  12. Asiri, S.S., Akbas, S.D. and Eltaher, M.A. (2020b), "Damped dynamic responses of a layered functionally graded thick beam under a pulse load", Struct. Eng. Mech., 75(6), 713-722. https://doi.org/10.12989/sem.2020.75.6.713.
  13. Akbas, S.D. (2017), "Post-buckling responses of functionally graded beams with porosities", Steel Compos Struct., 24(5), 579-589. https://doi.org/10.12989/scs.2017.24.5.579.
  14. Al Rjoub, Y.S. and Hamad, A.G. (2017), "Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method", KSCE J Civil Eng., 21(3), 792-806. https://doi.org/10.1007/s12205-016-0149-6.
  15. Ansari, R., Faraji Oskouie, M. and Zargar, M. (2022), "Hygrothermally induced vibration analysis of bidirectional functionally graded porous beams", Transp. Porous Media, 142, 41-62. https://doi.org/10.1007/s11242-021-01700-4.
  16. Assie, A., Akbas, S.D., Kabeel, A.M., Abdelrahman, A.A. and Eltaher, M.A. (2022), "Dynamic analysis of porous functionally graded layered deep beams with viscoelastic core", Steel Compos. Struct., 43(1), 79-90. https://doi.org/10.12989/scs.2022.43.1.079.
  17. Attia, M.A. and Salwa, A.M. (2022), "Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory", Eng. Comput., 38, 525-554. https://doi.org/10.1007/s00366-020-01080-1.
  18. Avcar, M., Hadji, L. and Akan, R. (2022), "The influence of Winkler-Pasternak elastic foundations on the natural frequencies of imperfect functionally graded sandwich beams", Geomech. Eng., 31(1), 99-112. https://doi.org/10.12989/gae.2022.31.1.099.
  19. Babaei, H., Eslami, M.R. and Khorshidv, A.R. (2020), "Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane", J. Therm. Stress., 43(1), 109-131. https://doi.org/10.1080/01495739.2019.1660600.
  20. Barati, M.R. (2017), "Investigating dynamic response of porous inhomogeneous nanobeams on hybrid Kerr foundation under hygro-thermal loading", Appl. Phys. A., 123(5), 332. https://doi.org/10.1007/s00339-017-0908-3.
  21. Belarbi, MO., Daikh, A.A., Garg, A., Hirane, H., Houari, M.S.A., Civalak, O. and Chalak, H.D. (2023), "Bending and free vibration analysis of porous functionally graded sandwich plate with various porosity distributions using an extended layerwise theory", Arch. Civil Mech. Eng., 23, 15. https://doi.org/10.1007/s43452-022-00551-0.
  22. Daikh, AA. and Zenkour, AM. (2019), "Effect of porosity on the bending analysis of various functionally graded sandwich plates", Mater. Res. Express, 6(6), 065703. https://doi.org/10.1088/2053-1591/ab0971.
  23. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature- dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343.
  24. Ebrahimi, F. and Reza Barati, M. (2016), "Thermal buckling analysis of size-dependent FG nanobeams based on the third-order shear deformation beam theory", Acta Mechanica Solida Sinica, 29(5), 547-554. https://doi.org/10.1016/S0894-9166(16)30272-5.
  25. Ellali, M., Bouazza, M. and Amara, K. (2022), "Thermal buckling of a sandwich beam attached with piezoelectric layers via the shear deformation theory", Arch. Appl. Mech., 92, 657-665. https://doi.org/10.1007/s00419-021-02094-x.
  26. Esen, I., Abdelrhmaan, A.A. and Eltaher M.A. (2022),"Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 38, 3463-3482. https://doi.org/10.1007/s00366-021-01389-5.
  27. Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos. B: Eng., 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  28. Fu, Y., Wang, J. and Mao, Y. (2012), "Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment", Appl. Mathemat. Model., 36, 4324-4340. https://doi.org/10.1016/j.apm.2011.11.059.
  29. Hadji, L. and Avcar, M. (2021), "Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory", Adv. Nano Res., 10(3), 281-293. http://doi.org/10.12989/anr.2021.10.3.281.
  30. Karamanli, A. (2017), "Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3D shear deformation theory", Compos. Struct., 174, 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046.
  31. Kirlangic, O. and Akbas, S.D. (2021), "Dynamic responses of functionally graded and layered composite beams", Smart Struct. Syst., 27(1), 115-122. https://doi.org/10.12989/sss.2021.27.1.115.
  32. Kirlangic, O. and Akbas S.D. (2020), "Comparison study between layered and functionally graded composite beams for static deflection and stress analyses", JCAMECH, 51(2), 294-301. https://doi.org/10.22059/jcamech.2020.296319.473.
  33. Le, C.I., Le, N.A.T. and Nguyen, D.K. (2021), "Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element", Compos. Struct., 261, 113309. https://doi.org/10.1016/j.compstruct.2020.113309.
  34. Li, L., Li, X. and Hu Y. (2018), "Nonlinear bending of a two-dimensionally functionally graded beam", Compos. Struct., 184, 1049-1061. https://doi.org/10.1016/j.compstruct.2017.10.087.
  35. Liu, H. and Chen, S. (2021), "Dynamic response of double-microbeam system made of transverse, longitudinal, and two-dimensional functionally graded materials", Eur. Phys. J. Plus, 136(10), 1046. https://doi.org/10.1140/epjp/s13360-021-02032-4.
  36. Liu, H. and Zhang, Q. (2021), "Nonlinear dynamics of two-directional functionally graded microbeam with geometrical imperfection using unified shear deformable beam theory", Appl. Mathemat. Model., 98, 783-800. https://doi.org/10.1016/j.apm.2021.05.029.
  37. Mao, J.J. and Zhang, W. (2019), "Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces", Compos. Struct., 216, 392-405. https://doi.org/10.1016/j.compstruct.2019.02.095.
  38. Mao, J.J., Guo, L.J. and Zhang, W. (2023), "Vibration and frequency analysis of edge-cracked functionally graded graphene reinforced composite beam with piezoelectric actuators", Eng. Comput., 39, 1563-1582. https://doi.org/10.1007/s00366-021-01546-w.
  39. Meksi, A., Benyoucef, S., Sekkal, M., Bachir Bouiadjra, R., Selim, M.M., Tounsi, A. and Hussain, M. (2021), "Influence of micromechanical models on the bending response of bidirectional FG beams under linear, uniform, exponential and sinusoidal distributed loading", Steel Compos. Struct., 39(2), 215-228. https://doi.org/10.12989/scs.2021.39.2.215.
  40. Merzouki, T., Houari, M.S.A., Bessaim, A., Haboussi, M., Dimitri, R. and Tornabene, F. (2022), "Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory", Math. Mech. Solid., 27(1), 66-92. https://doi.org/10.1177/10812865211011759.
  41. Mirjavadi, S.S., Rabby, S., Shafiei, N., Afshari, B.M. and Kazemi, M. (2017), "On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment", Appl. Phys. A Mater. Sci. Pr., 123, 315. https://doi.org/10.1007/s00339-017-0918-1.
  42. Osofero, AI., Vo, T.P., Nguyen, T.K. and Lee, J. (2016), "Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories", J. Sandw. Struct. Mater., 18(1), 3-29. https://doi.org/10.1177/1099636215582217.
  43. Ouyang, Z.Y. (2020), "Exact solution for bending analysis of two-directional functionally graded Timoshenko beams", Arch. Appl. Mech., 90, 1005-1023. https://doi.org/10.1007/s00419-019-01655-5.
  44. Patil, H.B., Pitchaimani, J. and Chinnapandi, L.J.P. (2021), "Buckling and free vibration of porous functionally graded metal ceramic beams under thermal and mechanical loading: A comparative study". J. Inst. Eng. India Ser.: C, 102(5), 1107-1117. https://doi.org/10.1007/s40032-021-00742-3.
  45. Paul, A. and Das, D. (2016), "Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness", Eng. Sci. Technol. Int. J., 19, 1608-1625. http://doi.org/10.1016/j.jestch.2016.05.014.
  46. Ren, L.L, Zhang, W. and Zhang, Y.F. (2023), "Dynamic snap-through and nonlinear vibrations of bistable asymmetric cross-ply composite laminated cantilever shell under external excitation", Mech. Syst. Signal Pr., 195, 110193. https://doi.org/10.1016/j.ymssp.2023.110193.
  47. Pham, Q.H., Tran, V.K. and Nguyen, P.C. (2022), "Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method", Case Stud. Therm. Eng., 40, 102478. https://doi.org/10.1016/j.csite.2022.102478.
  48. Robinson, M.T.A. and Adali, S. (2018), "Buckling of nonuniform and axially functionally graded nonlocal Timoshenko nanobeams on Winkler-Pasternak foundation", Compos. Struct., 206, 95-103. https://doi.org/10.1016/j.compstruct.2018.07.046.
  49. Shahsavari, D., Shahsavari, M., Li, L. and Karami B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  50. Simonetti, S.K., Turkalj, G. and Lanc, D. (2022), "Thermal buckling analysis of thin-walled closed section FG beam-type structures", Thin Wall. Struct., 181, 110075. https://doi.org/10.1016/j.tws.2022.110075.
  51. Taati, E. (2018), "On buckling and post-buckling behavior of functionally graded micro-beams in thermal environment", Int. J. Eng. Sci., 128, 63-78. https://doi.org/10.1016/j.ijengsci.2018.03.010.
  52. Tang, H., Li, L. and Hu, Y. (2018), " Buckling analysis of two-directionally porous beam", Aerosp. Sci. Technol., 78, 471-479. https://doi.org/10.1016/j.ast.2018.04.045.
  53. Tang, Y. and Ding, Q. (2019), "Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads", Compos. Struct., 225, 111076. https://doi.org/10.1016/j.compstruct.2019.111076.
  54. Tran, T.T. and Nguyen, D.K. (2018), "Free vibration analysis of 2-DFGM beams in thermal environment based on a new third-order shear deformation theory", Viet. J. Mech., 40(2), 121-140. https://doi.org/10.15625/0866-7136/10503.
  55. 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.
  56. Van Vinh, P., Duoc, N.Q. and Phuong, N.D. (2022), "A new enhanced first-order beam element based on neutral surface position for bending analysis of functionally graded porous beams", Iran. J. Sci. Technol. Trans. Mech. Eng., 46(4), 1141-1156. https://doi.org/10.1007/s40997-022-00485-1.
  57. Wang, Y., Yang, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Nonlinear dynamic analysis of thermally deformed beams subjected to uniform loading resting on nonlinear viscoelastic foundation", Eur. J. Mech. A Solid., 95, 104638. https://doi.org/10.1016/j.euromechsol.2022.104638.
  58. Wang, Y. and Zhang, W. (2022), "On the thermal buckling and postbuckling responses of temperature-dependent graphene platelets reinforced porous nanocomposite beams", Compos. Struct., 296, 115880. https://doi.org/10.1016/j.compstruct.2022.115880.
  59. Wang, A., Chen, H., Hao, Y. and Zhang, W. (2018), "Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets", Result. Phys., 9, 550-559. https://doi.org/10.1016/j.rinp.2018.02.062.
  60. Xu, C., Li, Y., Lu, M. and Dai, Z. (2022), "Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress driven nonlocal elasticity", Appl. Math. Mech., 43(3), 355-370. https://doi.org/10.1007/s10483-022-2828-5.
  61. Zghal, S., Ataoui, D. and Dammak, F. (2022), "Static bending analysis of beams made of functionally graded porous materials", Mech. Based Des. Struct. Mach., 50(3), 1012-1029. https://doi.org/10.1080/15397734.2020.1748053.