Structural Engineering and Mechanics

  • 제86권4호
  • /
  • Pages.443-459
  • /
  • 2023
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Theoretical buckling analysis of inhomogeneous plates under various thermal gradients and boundary conditions

  • Laid Lekouara (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Belgacem Mamen (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelhakim Bouhadra (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abderahmane Menasria (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Kouider Halim Benrahou (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Mohammed A. Al-Osta (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • 투고 : 2022.11.01
  • 심사 : 2023.03.16
  • 발행 : 2023.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

키워드

참고문헌

  1. Akavci, S.S. (2014), "Thermal buckling analysis of functionally graded plates on an elastic foundation according to a hyperbolic shear deformation theory", Mech. Compos. Mater., 50(2), 197-212. https://doi.org/10.1007/s11029-014-9407-1.
  2. Azandariani, M.G., Gholami, M. and Nikzad, A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037.
  3. Bodaghi, M. and Saidi, A. (2011), "Thermoelastic buckling behavior of thick functionally graded rectangular plates", Arch. Appl. Mech., 81(11), 1555-1572. https://doi.org/10.1007/s00419-010-0501-0.
  4. Bouhadra, A., Benyoucef, S., Tounsi, A., Bernard, F., Bouiadjra, R.B. and Sid Ahmed Houari, M. (2015), "Thermal buckling response of functionally graded plates with clamped boundary conditions", J. Therm. Stress., 38(6), 630-650. https://doi.org/10.1080/01495739.2015.1015900.
  5. Bouiadjra, M.B., Ahmed Houari, M.S. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stress., 35(8), 677-694. https://doi.org/10.1080/01495739.2012.688665.
  6. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Wahab, M.A. (2022), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condens. Matt., 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  7. Do, V.N.V., Tran, M.T. and Lee, C.H. (2018), "Nonlinear thermal buckling analyses of functionally graded plates by a mesh-free radial point interpolation method", Eng. Anal. Bound. Elem., 87, 153-164. https://doi.org/10.1016/j.enganabound.2017.12.001.
  8. Du, M., Liu, J., Ye, W., Yang, F. and Lin, G. (2022), "A new semi-analytical approach for bending, buckling and free vibration analyses of power law functionally graded beams", Struct. Eng. Mech., 81(2), 179-194. https://doi.org/10.12989/sem.2022.81.2.179.
  9. Ghamkhar, M., Harbaoui, I., Hussain, M., Ayed, H., Khadimallah, M.A. and Alshoaibi, A. (2022), "Structural monitoring of layered FGM distribution ring support: Analysis with and without internal pressure", Adv. Nano Res., 12(3), 337-344. https://doi.org/10.12989/anr.2022.12.3.337.
  10. Guptaa, S. and Chalak, H.D. (2022), "Bending and free vibration analysis of FG sandwich beams using higher-order zigzag theory", Steel Compos. Struct., 45(4), 483-499. https://doi.org/10.12989/scs.2022.45.4.483
  11. Hao, Y., Zhang, W. and Yang, J. (2011), "Nonlinear oscillation of a cantilever FGM rectangular plate based on third-order plate theory and asymptotic perturbation method", Compos. Part B: Eng., 42(3), 402-413. https://doi.org/10.1016/j.compositesb.2010.12.010.
  12. Hao, Y.X., Chen, L.H., Zhang, W. and Lei, J.G. (2008), "Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate", J. Sound Vib., 312(4), 862-892. https://doi.org/10.1016/j.jsv.2007.11.033.
  13. Huang, X., Shan, H., Chu, W. and Chen, Y. (2022). Computational and mathematical simulation for the size-dependent dynamic behavior of the high-order FG nanotubes, including the porosity under the thermal effects", Adv. Nano Res., 12(1), 101-115. https://doi.org/10.12989/anr.2022.12.1.101.
  14. Javaheri, R. and Eslami, M.R. (2002a), "Thermal buckling of functionally graded plates", AIAA J., 40(1), 162-169. https://doi.org/10.2514/2.1626.
  15. Javaheri, R. and Eslami, M.R. (2002b), "Thermal buckling of functionally graded plates based on higher order theory", J. Therm. Stress., 25(7), 603-625. https://doi.org/10.1080/01495730290074333.
  16. Kiani, Y., Bagherizadeh, E. and Eslami, M. (2011), "Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation (Three approximate analytical solutions)", ZAMM-J. Appl. Math. Mech., 91(7), 581-593. https://doi.org/10.1002/zamm.201000184.
  17. Kumar, H.S. and Kattimani, S. (2022). "Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities", Struct. Eng. Mech., 82(4), 477-490. https://doi.org/10.12989/sem.2022.82.4.477.
  18. Lanhe, W. (2004), "Thermal buckling of a simply supported moderately thick rectangular FGM plate", Compos. Struct., 64(2), 211-218. https://doi.org/10.1016/j.compstruct.2003.08.004.
  19. Man, Y. (2022). "On the dynamic stability of a composite beam via modified high-order theory", Comput. Concrete, 30(2), 151-164. https://doi.org/10.12989/cac.2022.30.2.151.
  20. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004.
  21. Mekerbi, M., Benyoucef, S., Mahmoudi, A., Bourada, F. and Tounsi, A. (2019), "Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution", Struct. Eng. Mech., 72(4), 513-524. https://doi.org/10.12989/sem.2019.72.4.513.
  22. Merdaci, S., Tounsi, A. and Bakora, A. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., 22(4), 713-732. https://doi.org/10.12989/scs.2016.22.4.713.
  23. Moradi, A., Poorveis, D. and Khajehdezfuly, A. (2022). "Buckling of FGM elliptical cylindrical shell under follower lateral pressure", Steel Compos. Struct., 45(2), 175-191. https://doi.org/10.12989/scs.2022.45.2.175.
  24. Nguyen-Xuan, H., Tran, L. V., Nguyen-Thoi, T. and Vu-Do, H. C. (2011), "Analysis of functionally graded plates using an edge-based smoothed finite element method", Compos. Struct., 93(11), 3019-3039. https://doi.org/10.1016/j.compstruct.2011.04.028
  25. Pasternak, P. (1954), "On a new method of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi Po Stroitelstuve i Arkhitekture.
  26. Polat, A. and Kaya, Y. (2022). "Analysis of discontinuous contact problem in two functionally graded layers resting on a rigid plane by using finite element method", Comput. Concrete, 29(4), 247-253. https://doi.org/10.12989/cac.2022.29.4.247.
  27. Radwan, A.F. (2019), "Effects of non-linear hygrothermal conditions on the buckling of FG sandwich plates resting on elastic foundations using a hyperbolic shear deformation theory", J. Sandw. Struct. Mater., 21(1), 289-319. https://doi.org/10.1177/1099636217693557.
  28. Saad, M. and Hadji, L. (2022), "Thermal buckling analysis of porous fgm plates", Mater. Today: Proc., 53, 196-201. https://doi.org/10.1016/j.matpr.2021.12.550.
  29. Singh, S. and Harsha, S. (2020), "Thermal buckling of porous symmetric and non-symmetric sandwich plate with homogenous core and S-FGM face sheets resting on Pasternak foundation", Int. J. Mech. Mater. Des., 16(4), 707-731. https://doi.org/10.1007/s10999-020-09498-7.
  30. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  31. Tao, C. and Dai, T. (2021), "Analyses of thermal buckling and secondary instability of post-buckled S-FGM plates with porosities based on a meshfree method", Appl. Math. Model., 89, 268-284. https://doi.org/10.1016/j.apm.2020.07.032.
  32. Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-020-01154-0.
  33. 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.
  34. Winkler, E. (1867), Die Lehre von der Elasticitaet und Festigkeit: mit besonderer Rucksicht auf ihre Anwendung in der Technik, fur polytechnische Schulen, Bauakademien, Ingenieure, Maschinenbauer, Architecten, etc. H. Dominicus.
  35. 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.
  36. Yaghoobi, H. and Torabi, M. (2013), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stress., 36(9), 869-894. https://doi.org/10.1080/01495739.2013.770356.
  37. Zenkour, A.M. and Mashat, D.S. (2010), "Thermal buckling analysis of ceramic-metal functionally graded plates", Nat. Sci., 02(09), 968-978. https://doi.org/10.4236/ns.2010.29118.
  38. Zenkour, A.M. and Sobhy, M. (2011), "Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory", J. Therm. Stress., 34(11), 1119-1138. https://doi.org/10.1080/01495739.2011.606017.
  39. Zhang, L. and Ko, T.H. (2022). Bending and buckling of spinning FG nanotubes based on NSGT", Comput. Concrete, 30(4), 243. https://doi.org/10.12989/cac.2022.30.4.243.
  40. Zhang, L., Zhu, P. and Liew, K. (2014), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492. https://doi.org/10.1016/j.compstruct.2013.09.043.
  41. Zhang, W, Hao, Y. and Yang, J. (2012), "Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges", Compos. Struct., 94(3), 1075-1086. https://doi.org/10.1016/j.compstruct.2011.11.004.
  42. Zhang, Wei, Hao, Y., Guo, X. and Chen, L. (2011), "Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations", Meccanica, 47, 985-1014. https://doi.org/10.1007/s11012-011-9491-4.
  43. Zhang, Wei, Yang, J. and Hao, Y. (2010), "Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory", Nonlin. Dyn., 59, 619-660. https://doi.org/10.1007/s11071-009-9568-y.
  44. Zhang, Z., Yang, Q. and Jin, C. (2022). Axisymmetric vibration analysis of a sandwich porous plate in thermal environment rested on Kerr foundation", Steel Compos. Struct., 43(5), 581-601. https://doi.org/10.12989/scs.2022.43.5.581.
  45. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005 .