DOI QR코드

DOI QR Code

Non-linear thermal buckling of FG plates with porosity based on hyperbolic shear deformation theory

  • 투고 : 2021.08.21
  • 심사 : 2022.03.07
  • 발행 : 2022.03.10

초록

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

키워드

참고문헌

  1. Ait Atmane, R., Mahmoudi, N., Bennai R., Ait Atmane, H. and Tounsi, A. (2021), "Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory", Steel Compos. Struct., 39(1), 95-107. https://doi.org/10.12989/scs.2021.39.1.095.
  2. Akbas, S.D. (2018), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., 67(4), 337-346. http://dx.doi.org/10.12989/sem.2018.67.4.337.
  3. Al-Waily, M. (2015), "Analytical and numerical thermal buckling analysis investigation of unidirectional and woven reinforcement composite plate structural", Int. J. Energy, Environ. Economics, 6(2), License CC BY 4.0.
  4. Arefi, M., and Zur, K.K. (2020), "Free vibration analysis of functionally graded cylindrical nanoshells resting on Pasternak foundation based on two-dimensional analysis", Steel Compos. Struct., 34(4), 615-623. https://doi.org/10.12989/scs.2020.34.4.615.
  5. Avcar, M., (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel and Composite Structures, 30(6), 95-107. 603-615. http://dx.doi.org/10.12989/scs.2019.30.6.603.
  6. Bamdad, M., Mohammadimehr, M. and Alambeigi, K. (2020), "Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov", Steel Compos. Struct., 36(6), 671-687. https://doi.org/10.12989/scs.2020.36.6.671.
  7. Bodaghi, M. and Saidi, A.R. (2011), "Thermoelastic buckling behavior of thick functionally graded rectangular plates", Archive Appl. Mech., 81(11), 1555-1572. https://doi.org/10.1007/s00419-010-0501-0.
  8. Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2012), "Thermal Buckling of Functionally Graded Plates According to a Four-Variable Refined Plate Theory", J. Therm. Stress, 35(1), 677-694. https://doi.org/10.1080/01495739.2012.688665.
  9. Ebrahimi, F. and Jafari, A. (2016), "A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities", J. Eng., 9561504. https://doi.org/10.1155/2016/9561504.
  10. Ebrahimi, F., and Seyfi, A., (2020), "Studying propagation of wave in metal foam cylindrical shells with graded porosities resting on variable elastic substrate", Engineering with Computers. https://doi.org/10.1007/s00366-020-01069-w.
  11. Ebrahimi, F., Dabbagh, A. and Rastgoo, A. (2019), "Vibration analysis of porous metal foam shells rested on an elastic substrate", J. Strain Anal. Eng. Des., 54(3), 199-208. https://doi.org/10.1177/0309324719852555.
  12. Fazzolari, F.A., (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Composites Part B: Engineering, 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  13. Fenjan, R.M. Ahmed, R.A. and Faleh, N.M. (2021), "Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading", Struct. Eng. Mech., 78(1), 15-22. http://dx.doi.org/10.12989/sem.2021.78.1.015.
  14. Ghadiri Rad, M.H., Shahabian, F. and Hosseini, S.M. (2020), "Geometrically nonlinear dynamic analysis of FG graphene platelets-reinforced nanocomposite cylinder: MLPG method based on a modified nonlinear micromechanical model", Steel Compos. Struct., 35(1), 77-92. https://doi.org/10.12989/scs.2020.35.1.077.
  15. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Nonlinear and post-buckling responses of FGM plates with oblique elliptical cutouts using plate assembly technique", Steel Compos. Struct., 34(2), 227-239. https://doi.org/10.12989/scs.2020.34.2.227.
  16. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., Hussain, M. and Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. http://dx.doi.org/10.12989/scs.2021.38.1.001.
  17. Jahwari, F.A. and Naguib, H.E. (2016), "Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution", Appl. Mathem. Modelling, 40(3), 2190-2205. https://doi.org/10.1016/j.apm.2015.09.038.
  18. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates", AIAA J., 40(1), 162-169. https://doi.org/10.2514/2.1626.
  19. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates based on higher order theory", J. Therm. Stress, 25(1), 603-625. https://doi.org/10.1080/01495730290074333.
  20. Jena, S.K., Chakraverty, S. and Malikan, M. (2021), "Application of shifted Chebyshev polynomial-based Rayleigh-Ritz method and Navier's technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation", Eng. Comput., 37, 3569-3589. https://doi.org/10.1007/s00366-020-01018-7.
  21. Khaniki, H.B., Ghayesh, M.H., Hussain, S. and Amabili, M. (2020), "Porosity, mass and geometric imperfection sensitivity in coupled vibration characteristics of CNT-strengthened beams with different boundary conditions", Eng. Comput., https://doi.org/10.1007/s00366-020-01208-3.
  22. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  23. Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties", Steel Compos. Struct., 15(5), 481-505. http://dx.doi.org/10.12989/scs.2013.15.5.481.
  24. 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.
  25. Li, Y.S., Liu, B.L. and Zhang, J.J. (2021), "Hygro-thermal buckling of porous FG nanobeams considering surface effects", Struct. Eng. Mech., 79(3), 359-371. http://dx.doi.org/10.12989/sem.2021.79.3.359.
  26. Liang, D., Wu, Q., Lu, X. and Tahouneh, V. (2020), "Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers", Steel Compos. Struct., 36(1), 47-62. https://doi.org/10.12989/scs.2020.36.1.047.
  27. Long, V.T. and Tung, H.V. (2021), "Thermal nonlinear buckling of shear deformable functionally graded cylindrical shells with porosities, AIAA J. 1-9. https://doi.org/10.2514/1.J060026.
  28. Matsunaga, H., (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Composite Structures, 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004.
  29. Mohieddin Ghomshei, M. (2020) "A numerical study on the thermal buckling of variable thickness Mindlin circular FGM plate on a two-parameter foundation", Mech. Res. Commun., 108, 103577. https://doi.org/10.1016/j.mechrescom.2020.103577.
  30. Nejadi, M.M. and Mohammadimehr, M. (2020), "Buckling analysis of nano composite sandwich Euler-Bernoulli beam considering porosity distribution on elastic foundation using DQM", Advan. Nano Res., 8(1), 59-68. https://doi.org/10.12989/anr.2020.8.1.059.
  31. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9.
  32. Rahmani, M., Mohammadi, Y. and Kakavand, F., (2019), "Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings", Steel Compos. Struct., 32(2), 239-252. http://dx.doi.org/10.12989/scs.2019.32.2.239.
  33. Samsam Shariat, B.A. and Eslami, M.R. (2006), "Thermal buckling of imperfect functionally graded plates", Int. J. Solids Struct., 43(14), 4082-4096. https://doi.org/10.1016/j.ijsolstr.2005.04.005.
  34. 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", Aeros. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  35. Tang, H., Li, L. and Hu, Y. (2018), "Buckling analysis of two-directionally porous beam", Aeros. Sci. Technol., 78, 471-479. https://doi.org/10.1016/j.ast.2018.04.045.
  36. Trabelsi, S., Zghal, S. and Dammak, F. (2020), "Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures", J. Brazil. Soc. Mech. Sci. Eng., 42(5), 233. https://doi.org/10.1007/s40430-020-02314-5.
  37. Vel, S.S. and Batra, R.C. (2002), "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates", AIAA J., 40(7), 1421-1433. https://doi.org/10.2514/2.1805.
  38. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol, 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  39. Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2016), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM", Steel Compos. Struct., 17(5), 753-776. http://dx.doi.org/10.12989/scs.2014.17.5.753.
  40. Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell\'s shell theory", Steel Compos. Struct., 35(2), 249-260. http://dx.doi.org/10.12989/scs.2020.35.2.249.
  41. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090.
  42. Zenkour, A.M. and Mashat, D.S. (2010), "Thermal buckling analysis of ceramic-metal functionally graded plates", Nat. Sci, 2(9), 968-978. http://dx.doi.org/10.4236/ns.2010.29118.
  43. Zenkour, A.M. and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012.