Structural Engineering and Mechanics

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Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations

  • Bakora, Ahmed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2015.02.02
  • Accepted : 2015.09.15
  • Published : 2015.10.10
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Abstract

Postbuckling of thick plates made of functionally graded material (FGM) subjected to in-plane compressive, thermal and thermomechanical loads is investigated in this work. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation. Thermomechanical non-homogeneous properties are considered to be temperature independent, and graded smoothly by the distribution of power law across the thickness in the thickness in terms of the volume fractions of constituents. By employing the higher order shear deformation plate theory together the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect FGM plates are derived. The Galerkin technique is used to determine the buckling loads and postbuckling equilibrium paths for simply supported plates. Numerical examples are presented to show the influences of power law index, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.

Keywords

References

  1. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  3. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  4. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  5. Akil, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ. Infrastr. Eng. Res. Develop., 4(2), 59-64.
  6. Bachir Bouiadjra, M., 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, 677-694. https://doi.org/10.1080/01495739.2012.688665
  7. 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, 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  8. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  9. Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  10. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  11. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15, 671-703. https://doi.org/10.1177/1099636213498888
  12. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  13. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013) "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  14. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  15. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  16. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082.
  17. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005
  18. 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
  19. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  20. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. https://doi.org/10.1007/s11012-013-9827-3
  21. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  22. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  23. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 467-479.
  24. Javaheri, R. and Eslami, M.R. (2002a), "Thermal buckling of functionally graded plates", AIAA, 40(1), 162-169. https://doi.org/10.2514/2.1626
  25. Javaheri, R. and Eslami, M.R. (2002b), "Thermal buckling of functionally graded plates based on higher order theory", J. Therm. Stress., 25, 603-625. https://doi.org/10.1080/01495730290074333
  26. Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Method., 11(5), 135007.
  27. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399
  28. Lanhe, W. (2004), "Thermal buckling of a simply supported moderately thick rectangular FGM plate", Compos. Struct., 64, 211-218. https://doi.org/10.1016/j.compstruct.2003.08.004
  29. Librescu, L. and Lin, W. (1997), "Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation", Int. J. Nonlin. Mech., 32(2), 211-225. https://doi.org/10.1016/S0020-7462(96)00057-1
  30. Lin, W. and Librescu, L. (1998), "Thermomechanical postbuckling of geometrically imperfect shear-deformable flat and curved panels on a nonlinear foundation", Int. J. Eng. Sci., 36(2), 189-206. https://doi.org/10.1016/S0020-7225(97)00055-4
  31. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  32. Mantari, J.L. and Granados, E.V. (2015), "Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns", Compos. Part B, 69, 317-334. https://doi.org/10.1016/j.compositesb.2014.10.009
  33. Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Bas. Des. Struct. Mach., 41, 421-433. https://doi.org/10.1080/15397734.2013.763713
  34. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosuedarstvennoe Izadatelstvo Literatim po Stroitelstvu I Arkhitekture, 1, 1-56.
  35. Pradhan, K.K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., 53(2), 337-354. https://doi.org/10.12989/sem.2015.53.2.337
  36. Ramu, I. and Mohanty, S.C. (2015), "Free vibration and dynamic stability of functionally graded material plates on elastic foundation", Defence Sci. J., 65(3), 245-251. https://doi.org/10.14429/dsj.65.8621
  37. Samsam Shariat, B.A. and Eslami, M.R. (2007), "Buckling of thick functionally graded plates under mechanical and thermal loads", Compos. Struct., 78, 433-439. https://doi.org/10.1016/j.compstruct.2005.11.001
  38. Samsam Shariat, B.A. and Eslami, M.R. (2006), "Thermal buckling of imperfect functionally graded plates", Int. J. Solid. Struct., 43, 4082-4096. https://doi.org/10.1016/j.ijsolstr.2005.04.005
  39. Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Tech., 25(9), 2195-2209. https://doi.org/10.1007/s12206-011-0610-x
  40. Shen, H.S. (2007), "Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties", Int. J. Mech. Sci., 49, 466-478. https://doi.org/10.1016/j.ijmecsci.2006.09.011
  41. Shi, G. (2007), "A new simple third-order shear deformation theory of plates", Int. J. Solid. Struct., 44, 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
  42. 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
  43. Swaminathan, K. and Naveenkumar, D.T. (2014), "Higher order refined computational models for the stability analysis of FGM plates: Analytical solutions", Eur. J. Mech. A/Solid., 47, 349-361. https://doi.org/10.1016/j.euromechsol.2014.06.003
  44. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034
  45. 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. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  46. Tung, H.V. and Duc, N.D. (2010), "Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads", Compos. Struct., 92, 1184-1191. https://doi.org/10.1016/j.compstruct.2009.10.015
  47. Winkler, E. (1867), Die lehre von der elasticitaet und festigkeit, Prag Dominicus, Prague.
  48. Yaghoobi, H. and Torabi, M. (2013a), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stress., 36, 869-894. https://doi.org/10.1080/01495739.2013.770356
  49. Yaghoobi, H. and Torabi, M. (2013b), "Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation", Appl. Math. Model., 37, 8324-8340. https://doi.org/10.1016/j.apm.2013.03.037
  50. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48, 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  51. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  52. 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
  53. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

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