DOI QR코드

DOI QR Code

Thermal post-buckling analysis of graphene platelets reinforced metal foams beams with initial geometric imperfection

  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Yin-Ping Li (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Yujie He (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Jin-Peng Song (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2023.07.21
  • Accepted : 2023.08.30
  • Published : 2024.03.25

Abstract

This article investigates the thermal and post-buckling problems of graphene platelets reinforced metal foams (GPLRMF) beams with initial geometric imperfection. Three distribution forms of graphene platelet (GPLs) and foam are employed. This article utilizes the mixing law Halpin Tsai model to estimate the physical parameters of materials. Considering three different boundary conditions, we used the Euler beam theory to establish the governing equations. Afterwards, the Galerkin method is applied to discretize these equations. The correctness of this article is verified through data analysis and comparison with the existing articles. The influences of geometric imperfection, GPL distribution modes, boundary conditions, GPLs weight fraction, foam distribution pattern and foam coefficient on thermal post-buckling are analyzed. The results indicate that, perfect GPLRMF beams do not undergo bifurcation buckling before reaching a certain temperature, and the critical buckling temperature is the highest when both ends are fixed. At the same time, the structural stiffness of the beam under the GPL-A model is the highest, and the buckling response of the beam under the Foam-II mode is the lowest, and the presence of GPLs can effectively improve the buckling strength.

Keywords

References

  1. Akbas, S.D. (2018), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., 67(4), 337-346. https://doi.org/10.12989/sem.2018.67.4.337.
  2. Akbas, S.D. and Kocaturk, T. (2013), "Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature", J. Therm. Stress., 36(12), 1233-1254. https://doi.org/10.1080/01495739.2013.788397.
  3. Babaei, H., Kiani, Y. and Eslami, M.R. (2021), "Perturbation method for thermal post-buckling analysis of shear deformable FG-CNTRC beams with different boundary conditions", Int. J. Struct. Stab. Dyn., 21(13), 2150175. https://doi.org/10.1142/S0219455421501753.
  4. Baghbadorani, A.A. and Kiani, Y. (2021), "Free vibration analysis of functionally graded cylindrical shells reinforced with graphene platelets", Compos. Struct., 276, 114546. https://doi.org/10.1016/j.compstruct.2021.114546.
  5. Barati, M.R. and Zenkour, A.M. (2019), "Thermal post-buckling analysis of closed circuit flexoelectric nanobeams with surface effects and geometrical imperfection", Mech. Adv. Mater. Struct., 26(17), 1482-1490. https://doi.org/10.1080/15376494.2018.1432821.
  6. Bayat, Y. and Toussi, H.E. (2020), "Analytical layerwise solution of nonlinear thermal instability of SMA hybrid composite beam under nonuniform temperature condition", Mech. Adv. Mater. Struct., 27(19), 1673-1686. https://doi.org/10.1080/15376494.2018.1524950.
  7. Chai, Q.D. and Wang, Y.Q. (2022), "Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion", Eng. Struct., 252, 113718. https://doi.org/10.1016/j.engstruct.2021.113718.
  8. Chang, X.P., Zhou, J. and Li, Y.H. (2022), "Post-buckling characteristics of functionally graded fluid-conveying pipe with geometric ddefects on Pasternak foundation", Ocean Eng., 266(4), 113056. https://doi.org/10.1016/j.oceaneng.2022.113056.
  9. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022a), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus, 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0.
  10. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022b), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel. Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641.
  11. Dehghani, M. (2021), "Analyzing the thermal post-buckling of composite plate containing an elliptical cut-out using a particle semi-energy method", Int. J. Struct. Stab. Dyn., 21(7), 2150088. https://doi.org/10.1142/S0219455421500887.
  12. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  13. Ding, H.X. and She, G.L. (2023a), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Arch. Civil Mech. Eng., 23, 97. https://doi.org/10.1007/s43452-023-00634-6.
  14. Ding, H.X. and She, G.L. (2023b), "Nonlinear primary resonance behavior of graphene platelets reinforced metal foams conical shells under axial motion", Nonlinear Dyn., 111, 13723-13752. https://doi.org/10.1007/s11071-023-08564-x.
  15. Ding, H.X., Eltaher, M.A. and She, G.L. (2023a), "Nonlinear low-velocity impact of graphene platelets reinforced metal foams cylindrical shell: Effect of spinning motion and initial geometric imperfections", Aerosp. Sci. Technol., 140, 108435. https://doi.org/10.1016/j.ast.2023.108435.
  16. Ding, H.X., Liu, H.B., She, G.L. and Wu, F. (2023c), "Wave propagation of FG-CNTRC plates in thermal environment using the high-order shear deformation plate theory", Comput. Concrete, 32(2), 207-215. https://doi.org/10.12989/cac.2023.32.2.207.
  17. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  18. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  19. Ding, H.X., Zhang, Y.W. and She, G.L. (2023b), "Propagation characteristics of guided waves in CNTRCs plates resting on elastic foundations in a thermal environment", Wave. Random Complex Media, 2023, 1-18. https://doi.org/10.1080/17455030.2023.2235611.
  20. Esfahani, S.E., Kiani, Y. and Eslami, M.R. (2013), "Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations", Int. J. Mech. Sci., 69, 10-20. https://doi.org/10.1016/j.ijmecsci.2013.01.007.
  21. Gan, L.L. and She, G.L. (2023), "Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions", Geomech. Eng., 32(5), 541-551. https://doi.org/10.12989/gae.2023.32.5.541.
  22. Gan, L.L., Xu, J.Q. and She, G.L. (2023), "Wave propagation of graphene platelets reinforced metal foams circular plates", Struct. Eng. Mech., 85(5), 645-654. https://doi.org/10.12989/sem.2023.85.5.645.
  23. Ghayesh, M.H. (2019), "Resonant dynamics of axially functionally graded imperfect tapered Timoshenko beams", J. Vib. Control, 25(2), 336-350. https://doi.org/10.1177/1077546318777591.
  24. Gholami, R. and Ansari, R. (2018), "The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates", Appl. Math. Mech., 39(9), 1219-1238. https://doi.org/10.1007/s10483-018-2367-9.
  25. Gu, X.J., Hao, Y.X., Zhang, W. and Chen, J. (2019), "Dynamic stability of rotating cantilever composite thin walled twisted plate with initial geometric imperfection under in-plane load", Thin Wall. Struct., 144, 106267. https://doi.org/10.1016/j.tws.2019.106267.
  26. Gupta, A. and Talha, M. (2018), "Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates", Mech. Based Des. Struct., 46(6), 693-711. https://doi.org/10.1080/15397734.2018.1449656.
  27. Hajlaoui, A. and Dammak, F. (2022), "A modified first shear deformation theory for three-dimensional thermal post-buckling analysis of FGM plates", Meccanica, 57(2), 337-353. https://doi.org/10.1007/s11012-021-01427-y.
  28. Hosseini, S.M.H. and Arvin, H. (2020), "Thermo-rotational buckling and post-buckling analyses of rotating functionally graded microbeams", Int. J. Mech. Mater. Des., 17(1), 55-72. https://doi.org/10.1007/s10999-020-09509-7.
  29. Jafari, P. and Kiani, Y. (2021), "Free vibration of functionally graded graphene platelet reinforced plates: A quasi 3D shear and normal deformable plate model", Compos. Struct., 275, 114409. https://doi.org/10.1016/j.compstruct.2021.114409.
  30. Jafari, P. and Kiani, Y. (2022), "A four-variable shear and normal deformable quasi-3D beam model to analyze the free and forced vibrations of FG-GPLRC beams under moving load", Acta Mech., 233(7), 2797-2814. https://doi.org/10.1007/s00707-022-03256-w.
  31. Jafarpour, S. and Khedmati, M.R. (2021), "Vibration analysis of stiffened plates with initial geometric imperfections", Proc. Inst. Mech. Eng. M: J. Eng. Marit. Environ., 235(2), 521-531. https://doi.org/10.1177/1475090220967520.
  32. Kalkan, I., Bocek, M. and Aykac, S. (2016), "Lateral stability of reinforced-concrete beams with initial imperfections", Proc. Inst. Civil Eng, Struct, Build., 169(10), 727-740. https://doi.org/10.1680/jstbu.15.00023.
  33. Li, X.Y., Yu, K.P. and Zhao, R. (2018), "Thermal post-buckling and vibration analysis of a symmetric sandwich beam with clamped and simply supported boundary", Arch. Appl. Mech., 88(4), 543-561. https://doi.org/10.1007/s00419-017-1326-x.
  34. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B. (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel Compos. Struct., 46(5), 649-658. https://doi.org/10.12989/scs.2023.46.5.649.
  35. Liu, H., Lv, Z. and Tang, H.J. (2019), "Nonlinear vibration and instability of functionally graded nanopipes with initial imperfection conveying fluid", Appl. Math. Model., 76, 133-150. https://doi.org/10.1016/j.apm.2019.06.011.
  36. Liu, Q.Y. and Ma, J.P. (2021), "Finite element simulation for investigation on thermal post-buckling of geometrically imperfect GOP-reinforced beam", Adv. Concrete Constr., 12(2), 135-143. https://doi.org/10.12989/acc.2021.12.2.135.
  37. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  38. Mirjavadi, S.S., Forsat, M., Yahya, Y.Z., Barati, M.R., Jayasimha, A.N. and Hamouda, A.M.S. (2020), "Porosity effects on postbuckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners", Struct. Eng. Mech., 75(6), 701-711. https://doi.org/10.12989/sem.2020.75.6.701.
  39. Mirjavadi, S.S., Forsat, M., Yahya, Y.Z., Barati, M.R., Jayasimha, A.N. and Khan, I. (2020), "Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection", Adv. Concrete Constr., 9(4), 397-406. https://doi.org/10.12989/acc.2020.9.4.397.
  40. Mirzavand, B. and Pourmohammad, H. (2019), "Post-buckling analysis of non-uniformly heated functionally graded cylindrical shells enhanced by shape memory alloys using classical lamination theory", J. Intel. Mat. Syst. Struct., 30(16), 2421-2435. https://doi.org/10.1177/1045389X19861794.
  41. Moghaddasi, M. and Kiani Y. (2022), "Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load", Meccanica, 57(5), 1105-1124. https://doi.org/10.1007/s11012-022-01476-x.
  42. Rossi, A., de Souza, A.S.C., Nicoletti, R.S. and Martins, C.H. (2021), "The influence of structural and geometric imperfections on the LDB strength of steel-concrete composite beams", Thin Wall. Struct., 162, 107542. https://doi.org/10.1016/j.tws.2021.107542.
  43. She, G.L., Yuan, F.G. and Ren, Y.R. (2017), "Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory", Appl. Math. Model., 47, 340-357. https://doi.org/10.1016/j.apm.2017.03.014.
  44. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  45. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x.
  46. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615.
  47. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.
  48. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  49. Shen, H.S. and Wang, Z.X. (2014), "Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments", Int. J. Mech. Sci., 81, 195-206. https://doi.org/10.1016/j.ijmecsci.2014.02.020.
  50. Shenas, A.G., Malekzadeh, P. and Ziaee, S. (2021), "Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass", Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 235(23), 6690-6710. https://doi.org/10.1177/09544062211008471.
  51. Song, J.P. and She, G.L. (2023), "Nonlinear resonance of axially moving GPLRMF plates with different boundary conditions", Struct. Eng. Sci., 86(3), 361-371. https://doi.org/10.12989/sem.2023.86.3.361.
  52. 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.
  53. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.
  54. Wang, Y.W. 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.
  55. Wang, Y.X. and Kiani, Y. (2022), "Effects of initial compression/tension, foundation damping and pasternak medium on the dynamics of shear and normal deformable GPLRC beams under moving load", Mater. Today Commun., 33, 104938. https://doi.org/10.1016/j.mtcomm.2022.104938.
  56. Wen, C.Q., Tang, L. and Yang, G.T. (2020), "Buckling and post-buckling of pinned Euler beams on weakened Winkler foundation under thermal loading", J. Therm. Stress., 43(5), 529-542. https://doi.org/10.1080/01495739.2020.1734128.
  57. Wu, F. and She, G.L. (2023), "Wave propagation in double nanobeams in thermal environments using the Reddy's high-order shear deformation theory", Adv. Nano Res., 14(6), 495-506. https://doi.org/10.12989/anr.2023.14.6.495.
  58. Wu, H.L., Kitipornchai, S. and Yang, J. (2017), "Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite beams", Appl. Math. Model., 42, 735-752. https://doi.org/10.1016/j.apm.2016.10.045.
  59. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  60. Xu, J.Q. and She, G.L. (2023), "Thermal post-buckling of graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Struct. Eng. Mech., 87(1), 85-94. https://doi.org/10.12989/sem.2023.87.1.085.
  61. Xu, J.Q., She, G.L., Li. Y.P. and Gan, L.L. (2023), "Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection", Steel Compos. Struct., 47(6), 795-811. https://doi.org/10.12989/scs.2023.47.6.795.
  62. Yang, Z.C., Wu, H.L., Yang, J., Liu, A.R., Safaei, B., Lv, J.E. and Fu, J.Y. (2022), "Nonlinear forced vibration and dynamic buckling of FG graphene-reinforced porous arches under impulsive loading", Thin Wall. Struct., 181, 110059. https://doi.org/10.1016/j.tws.2022.110059.
  63. Yas, M.H. and Rahimi, S. (2020), "Thermal buckling analysis of porous functionally graded nanocomposite beams reinforced by graphene platelets using Generalized differential quadrature method", Aerosp. Sci. Technol., 107, 106261. https://doi.org/10.1016/j.ast.2020.106261.
  64. Ye, C. and Wang, Y.Q. (2021), "Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: internal resonances", Nonlinear Dyn., 104(3), 2051-2069. https://doi.org/10.1007/s11071-021-06401-7.
  65. Zhang, H.Y., Bai, H.F. and Zuo, Z.Y. (2022), "Post-buckling of magneto-electro-elastic porous functionally graded cylindrical shells with geometric imperfection", Int. J. Struct. Stab. Dyn., 22(13), 2250138. https://doi.org/10.1142/S0219455422501383.
  66. Zhang, Y.C., Jin, L., Shao, Y.S. and Zhao, J.Y. (2011), "Practical advanced design considering random distribution of initial geometric imperfections", Adv. Struct. Eng., 14(3), 379-389. https://doi.org/10.1260/1369-4332.14.3.379.
  67. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel. Compos, Struct., 42(3) 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  68. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlinear Dyn., 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  69. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., 2023, 1-12. https://doi.org/10.1080/15376494.2023.2180556
  70. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  71. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133.
  72. Zhang, Y.W., Ding, H.X., She, G.L. and Tounsi, A. (2023d), "Wave propagation of CNTRC beams resting on elastic foundation based on various higher-order beam theories", Geomech. Eng., 33(4), 381-391. https://doi.org/10.12989/gae.2023.33.4.381.
  73. Zhang, Y.W., She, G.L. and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  74. Zhang, Y.W., She, G.L., Gan, L.L. and Li, Y.P. (2023c), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615.
  75. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M., and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  76. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel. Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  77. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://doi.org/10.12989/anr.2022.13.5.465.
  78. Zhu, S.B., Tong, Z.Z., Sun, J.B., Li, Q.D., Zhou, Z.H. and Xu, X.S. (2021), "Electro-thermo-mechanical post-buckling of piezoelectric functionally graded cylindrical shells", Appl. Math. Model., 98, 309-322. https://doi.org/10.1016/j.apm.2021.05.011.