Structural Engineering and Mechanics

  • 제57권1호
  • /
  • Pages.127-140
  • /
  • 2016
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Static and dynamic behavior of FGM plate using a new first shear deformation plate theory

  • Hadji, Lazreg (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Meziane, M. Ait Amar (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelhak, Z. (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Daouadji, T. Hassaine (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bedia, E.A Adda (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • 투고 : 2015.10.30
  • 심사 : 2015.12.11
  • 발행 : 2016.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a new first shear deformation plate theory based on neutral surface position is developed for the static and the free vibration analysis of functionally graded plates (FGPs). Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present shear deformation plate theory and the neutral surface concept, the governing equations are derived from the principle of Hamilton. There is no stretching-bending coupling effect in the neutral surface based formulation. Numerical illustrations concern flexural and dynamic behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

키워드

참고문헌

  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 Atmane, H., Tounsi, A. and Bernard, F. (2016), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 1-14.
  3. 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., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  4. 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
  5. 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
  6. 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
  7. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng. (in Press)
  8. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  9. Benachour, A., Hassaine Daouadji, 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: Eng., 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  10. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. B, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020
  11. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  12. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", ASME Appl. Mech. Rev., 60, 195-216. https://doi.org/10.1115/1.2777164
  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, 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. Chi, S. and Chung, Y. (2006), "Mechanical behavior of functionally graded material plates under transverse load-Part I1", Numer. Res. Int. J. Solid. Struct., 43, 3675-3691. https://doi.org/10.1016/j.ijsolstr.2005.04.010
  18. Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  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, 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  20. Fekrar, A., El Meiche, N., Bessaim, A., Tounsi, A. and Adda Bedia, E.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct., 13(1), 91-107. https://doi.org/10.12989/scs.2012.13.1.091
  21. 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, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  22. Hadji, L., Atmane, H.A., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four variable refined plate theory", Appl. Math. Mech., 32, 925-942. https://doi.org/10.1007/s10483-011-1470-9
  23. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theorywith 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
  24. 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, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  25. Houari, M.S.A., Benyoucef, S., Mechab, I., Tounsi, A. and Adda Bedia, E.A., (2011), "Two variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates", J. Therm. Stress., 34, 315-334. https://doi.org/10.1080/01495739.2010.550806
  26. Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "An-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., 17(1), 21-46. https://doi.org/10.12989/scs.2014.17.1.021
  27. Koizumi, M., (1993), "The concept of FGM", Ceram Tran. Funct. Grad. Mater., 34, 3-10.
  28. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2014), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442.
  29. 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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  30. Merazi, M., Hadji, L., T.H. Daouadji, Tounsi, A. and Adda Bedia, E.A., (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  31. Nedri, K., El Meiche, N. and Tounsi, A., (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650. https://doi.org/10.1007/s11029-013-9380-0
  32. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  33. Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., 17(3), 321-338. https://doi.org/10.12989/scs.2014.17.3.321
  34. Taj, M.N.A., Chakrabarti, A. and Sheikh, A. (2013), "Analysis of functionally graded plates using higher order shear deformation theory", Appl. Math. Model., 30, 1-11.
  35. Vel, SS. and Batra, RC., (2004), 'Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J Sound Vib., 272, 703-30. https://doi.org/10.1016/S0022-460X(03)00412-7
  36. 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
  37. Tounsi, A., Houari, M.S.A. and Kaci, A. (2015), "Comment on 'A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface'", Compos. Struct., 131, 842-842. https://doi.org/10.1016/j.compstruct.2015.06.053
  38. 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. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

피인용 문헌

  1. Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials vol.63, pp.2, 2016, https://doi.org/10.12989/sem.2017.63.2.161
  2. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  3. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  4. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  5. An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations vol.66, pp.5, 2016, https://doi.org/10.12989/sem.2018.66.5.665
  6. Nonlinear thermoelastic analysis of FGM thick plates vol.8, pp.5, 2016, https://doi.org/10.12989/csm.2019.8.5.439
  7. Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load vol.968, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/msf.968.496
  8. Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study vol.72, pp.4, 2019, https://doi.org/10.12989/sem.2019.72.4.409
  9. Effect of material transverse distribution profile on buckling of thick functionally graded material plates according to TSDT vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.083