Structural Engineering and Mechanics

  • 제72권4호
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  • Pages.513-524
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  • 2019
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution

  • Mekerbi, Mohamed (Deartment of Civil Engineering, University of Ferhat Abbas Setif 1) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Mahmoudi, Abdelkader (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
  • 투고 : 2019.04.10
  • 심사 : 2019.06.12
  • 발행 : 2019.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present article deals with thermal buckling of functionally graded plates with porosity and resting on elastic foundation. The basic formulation is based on quasi 3D theory. The present theory contains only four unknowns and also accommodates the thickness stretching effect. Porosity-dependent material coefficients of the plate are compositionally graded throughout the thickness according to a modified micromechanical model. Different patterns of porosity distributions are considered. The thermal loads are assumed to be uniform, linear and non-linear temperature rises through the thickness direction. The plate is assumed to be simply supported on all edges. Various numerical examples are given to check the accuracy and reliability of the present solution, in which both the present results and those reported in the literature are provided. In addition, several numerous new results for thick FG plates with porosity are also presented.

키워드

참고문헌

  1. Abazid, M.A., Alotebi, M. S. and Sobhy, M. (2018), "A novel shear and normal deformation theory for hygrothermal bending response of FGM sandwich plates on Pasternak elastic foundation", Struct. Eng. Mech., 67(3), 219-232. https://doi.org/10.12989/sem.2018.67.3.219.
  2. Abolghasemi, S., Shaterzadeh, A.R., Rezaei and R. (2014), "Thermomechanical buckling analysis of functionally graded pla tes with an elliptic cutout", Aerosp. Sci. Tech., 39, 250-259. https://doi.org/10.1016/j.ast.2014.10.004.
  3. Achouri, F., Benyoucef, S., Bourada, F, Bachir Bouiadjra, R. and Tounsi, A. (2019), "Robust quasi 3D computational model for mechanical response of FG thick sandwich plate", Struct. Eng. Mech., 70(5), 571-589. https://doi.org/10.12989/sem.2019.70.5.571.
  4. Ait Atmane, H., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13, 71-84. https://doi.org/10.1007/s10999-015-9318-x.
  5. Akbarzadeh, A.H., Zad, S.H., Eslami, M.R. and Sadighi, M. (2011), "Mechanical behaviour of functionally graded plates under static and dynamic loading", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 225(2), 326-333. https://doi.org/10.1243/09544062JMES2111.
  6. Amiri Rad, A. and Panahandeh-Shahraki, D. (2014), "Buckling of cracked functionally graded plates under tension", Thin-Walled Struct., 84, 26-33. https://doi.org/10.1016/j.tws.2014.05.005.
  7. Arani, A.G., Pourjamshidian, M., Arefi, M. and Arani, M.R.G. (2019), "Thermal, electrical and mechanical buckling loads of sandwich nano-beams made of FG-CNTRC resting on Pasternak's foundation based on higher order shear deformation theory", Struct. Eng. Mech., 46, 439-445. https://doi.org/10.12989/sem.2019.69.4.439.
  8. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  9. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  10. Avcar, M. (2016a), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A., 130(1), 423-431. http://dx.doi.org/10.12693/APhysPolA.130.375.
  11. Avcar, M. (2016b), "Free Vibration of Non-Homogeneous Beam Subjected to Axial Force Resting on Pasternak Foundation", J. Polytechnic., 19(4), 507-512.
  12. Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55(4), 871-884. http://dx.doi.org/10.12989/sem.2015.55.4.871.
  13. Bachir Bouiadjra, R., Adda-Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547.
  14. Barati, M.R. (2017), "Investigating dynamic characteristics of porous double-layered FG nanoplates in elastic medium via generalized nonlocal strain gradient elasticity", Eur. Phys. J. Plus, 132, 378. https://doi.org/10.1140/epjp/i2017-11670-x.
  15. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755.
  16. Bodaghi, M. and Saidi, A.R. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34(11), 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016.
  17. Bouazza, M., Tounsi, A., Adda-Bedia, E.A. and Megueni, A. (2010), "Thermoelastic Stability Analysis of Functionally Graded Plates: An Analytical Approach", Comput. Mater. Sci., 49, 865-870. https://doi.org/10.1016/j.commatsci.2010.06.038.
  18. Bouiadjra, R.B., Mahmoudi, A., Benyoucef, S., Tounsi, A. and Bernard, F. (2018), "Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models", Struct. Eng. Mech., 66(3), 317-328. https://doi.org/10.12989/sem.2018.66.3.317.
  19. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661.
  20. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313.
  21. Chen, D., Yang, J., and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compo. Struct 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
  22. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Inart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  23. Choi, J. and Lakes, R. (1995), "Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson's ratio", Int. J. Mech. Sci., 37(1), 51-59. https://doi.org/10.1016/0020-7403(94)00047-N.
  24. Cong, P.H., Anh, V.M and Duc, N.D. (2017), "Nonlinear dynamic response of eccentrically stiffened FGM plate using Reddy's TSDT in thermal environment", J. Therm. Stresses, 40(6), 704-732. https://doi.org/10.1080/01495739.2016.1261614.
  25. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Tech., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  26. Duc, N.D., Cong, P.H. and Quang, V.D. (2016), "Thermal Stability of Eccentrically Stiffened FGM Plate on Elastic Foundation based on Reddy's Third-order Shear Deformation Plate Theory", J. Thermal Stresses., 39(7), 772-794. https://doi.org/10.1080/01495739.2016.1188638.
  27. Duc, N.D. and Quan, T.Q. (2013), "Nonlinear Postbuckling of Imperfect Eccentrically Stiffened P-FGM Double Curved Thin Shallow Shells on Elastic Foundations in Thermal Environments", Compos. Struct., 106, 590-600. https://doi.org/10.1016/j.compstruct.2013.07.010.
  28. Duc, N.D. and Tung, H.V. (2011), "Mechanical and Thermal Postbuckling of Higher Order Shear Deformable Functionally Graded Plates on Elastic Foundations", Compos. Struct., 93, 2874-2881. https://doi.org/10.1016/j.compstruct.2011.05.017.
  29. El-Hassar, S.M., Benyoucef, S., Heireche, H. and Tounsi, A. (2016) "Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory", Geomech. Eng., 10(3), 357-386. https://doi.org/10.12989/gae.2016.10.3.357.
  30. Frikha, A., Zghal, S. and Dammak, F. (2018a), "Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis", Comput. Methods Appl. Mech. Eng., 39, 289-311. https://doi.org/10.1016/j.cma.2017.10.013
  31. Frikha, A., Zghal, S. and Dammak, F. (2018b), "Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element", Aerosp. Sci. Tech., 34, 315-334. https://doi.org/10.1016/j.ast.2018.04.048.
  32. Ghiasian, S.E., Kiani, Y., Sadighi, M. and Eslami, M.R. (2014), "Thermal buckling of shear deformable temperature dependent circular annular FGM plates", Int. J. Mech. Sci., 81, 137-148. https://doi.org/10.1016/j.ijmecsci.2014.02.007.
  33. Gibson, L.J. and Ashby, M. (1982), "The mechanics of three-dimensional cellular materials", Proce. R. Soc., London A: Math Phys. Eng. Sci., 382(1782), 43-59. https://doi.org/10.1098/rspa.1982.0088.
  34. Gupta, A. and Talha, M. (2018), "Influence of porosity on the flexural and vibration response of gradient plate using nonpolynomial higher-order shear and normal deformation theory", Int. J. Mech. Mater. Des., 14(2), 277-296. https://doi.org/10.1007/s10999-017-9369-2.
  35. Lezgy-Nazargah, M. and Meshkani, Z. (2018), "An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations", Struct. Eng. Mech., 66(5), 665-676. https://doi.org/10.12989/sem.2018.66.5.665.
  36. Ma, L.S. and Wang, T.J. (2003), "Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings", Int. J. Solids Struct., 40, 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5.
  37. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2015a), "Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment", J. Sandwich Struct. Mater., 17(5), 511-545. https://doi.org/10.1177/1099636215577363.
  38. Mahapatra, T.R. and Panda, S.K. (2015b), "Effects of hygrothermal conditions on free vibration behaviour of laminated composite structures", IOP. Conf. Ser. Mater. Sci. Eng. 75, https://doi.org/10.1088/1757-899X/75/1/012016.
  39. Mahapatra, T.R., Panda, S.K. and Dash, S. (2016a), "Effect of hygrothermal environment on the nonlinear free vibration responses of laminated composite plates: A nonlinear finite element micromechanical approach", IOP. Conf. Ser. Mater. Sci. Eng. 149, https://doi.org/10.1088/1757-899X/149/1/012151.
  40. Mahapatra, T.R. and Panda, S.K. (2016b), "Nonlinear free vibration analysis of laminated composite spherical shell panel under elevated hygrothermal environment: A micromechanical approach", Aerosp. Sci. Technol., 49, 276-288. https://doi.org/10.1016/j.ast.2015.12.018.
  41. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016c), "Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment", Int. J. Struct. Stab. Dyn., 16, https://doi.org/10.1142/S0219455414501053.
  42. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A. and Adda Bedia, E.A. (2018), "On the effect of the micromechanical models on the free vibration of rectangular FGM plate resting on elastic foundation", Earthq. Struct., 14(2), 117-128. https://doi.org/10.12989/eas.2018.14.2.117.
  43. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  44. Mouaici, F., Benyoucef, S., Ait Atmane, H. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory", Wind. Struct., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429.
  45. Saidi, A.R. and Hasani Baferani, A. (2010), "Thermal buckling analysis of moderately thick functionally graded annular sector plates", Compos. Struct., 92, 1744-1752. https://doi.org/10.1016/j.compstruct.2010.01.004.
  46. Samsam Shariat, B.A. and Eslami, M.R. (2007), "Buckling of thick functionally graded plates under mechanical and thermal loads", Compos. Struct., 78(3), 433-439. https://doi.org/10.1016/j.compstruct.2005.11.001.
  47. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Compos. Struct., 25(4), 389-401. https://doi.org/10.12989/scs.2017.25.4.389.
  48. 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. Tech., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  49. Shojaeefard, M.H., Googarchin, H.S., Ghadiri, M. and Mahinzare, M. (2017), "Micro temperature-dependent FG porous plate: Free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT", Appl. Math. Model., 50, 633-655. https://doi.org/10.1016/j.apm.2017.06.022.
  50. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nano plates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., 63(3), 401-415. https://doi.org/10.12989/sem.2017.63.3.401.
  51. Sofiyev, A.H. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation", Eng., 2(4), 228-236. https://doi.org/10.4236/eng.2010.24033.
  52. Tebboune, W., Benrahou, K.H., Houari M.S.A. and Tounsi, A. (2015), "Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory", Steel Compos. Struct., 18(2), 443-465. https://doi.org/10.12989/scs.2015.18.2.443.
  53. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Technol., 71, 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016.
  54. Thai, H.T. and Kim, S.E. (2013), "Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation", Int. J. Mech. Sci., 75, 34-44. https://doi.org/10.1016/j.ijmecsci.2013.06.007.
  55. Tounsi, A., Houari, M.S.A, Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009.
  56. Trabelsi, S., Frikha, A., Zghal, S. and Dammak, F. (2018), "Thermal post-buckling analysis of functionally graded material structure using a modified FSDT", J. Mech. Sci.., 144, 74-89. https://doi.org/10.1016/j.ijmecsci.2018.05.033.
  57. Trabelsi, S., Frikha, A., Zghal, S. and Dammak, F. (2019), "A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells", Eng. Struct., 178, 444-459. https://doi.org/10.1016/j.engstruct.2018.10.047.
  58. Tran, L.V., Thai, C.H. and Nguyen-Xuan, H. (2013), "An isogeometric finite element formu-lation for thermal buckling analysis of functionally graded plates", Finite Elem. Anal. Des., 73, 65-76. https://doi.org/10.1016/j.finel.2013.05.003.
  59. Van Do, V.N. and Lee, C.H. (2018), "Quasi-3D higher-order shear deformation theory for thermal buckling analysis of FGM plates based on a meshless method", Aerosp. Sci. Tech., 82-83, 450-465. https://doi.org/10.1016/j.ast.2018.09.017.
  60. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams on timoshenko beam theory", Chebyshev Collocation Method Meccanica, 50, 1331-1342. https://doi.org/10.1007/s11012-014-0094-8.
  61. Zghal, S., Frikha, A. and Dammak, F. (2017), "Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures", Comp. Struct., 176, 1107-1123. https://doi.org/10.1016/j.compstruct.2017.06.015.
  62. Zghal, S., Frikha, A. and Dammak, F. (2018a), "Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures", Appl. Math. Modelling., 53, 132-155. https://doi.org/10.1016/j.apm.2017.08.021.
  63. Zghal, S., Frikha, A. and Dammak, F. (2018b), "Non-linear bending analysis of nanocomposites reinforced by grapheme nanotubes with finite shell element and membrane enhancement", Eng. Struct., 158, 95-109. https://doi.org/10.1016/j.engstruct.2017.12.017.
  64. Zghal, S., Frikha, A. and Dammak, F. (2018c), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B Eng., 150, 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037.
  65. Zhang, D.G. (2017), "Thermal post-buckling analysis of functionally graded material elliptical plates based on high-order shear deformation theory", Mech. Adv. Mater. Struc., 24, 142-148. https://doi.org/10.1080/15376494.2015.1124158.
  66. Zhang, L.W., Zhu, P. and Liew, K.M. (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.
  67. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90, 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005.

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