Wind and Structures

  • 제22권4호
  • /
  • Pages.429-454
  • /
  • 2016
  • /
  • 1226-6116(pISSN)
  • /
  • 1598-6225(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory

  • Mouaici, Fethi (Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Benyoucef, Samir (Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Atmane, Hassen Ait (Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Tounsi, Abdelouahed (Department of Civil Engineering, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
  • 투고 : 2015.11.11
  • 심사 : 2016.03.03
  • 발행 : 2016.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a shear deformation plate theory based on neutral surface position is developed for free vibration analysis of functionally graded material (FGM) plates. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. During manufacture, defects such as porosities can appear. It is therefore necessary to consider the vibration behavior of FG plates having porosities in this investigation. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The equation of motion for FG rectangular plates is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Numerical results are presented and the influences of the volume fraction index and porosity volume fraction on frequencies of FGM plates are clearly discussed.

키워드

참고문헌

  1. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B-Eng., 39, 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  2. 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. Sandwich Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  3. Ait Atmane, H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6, 113-121. https://doi.org/10.1007/s10999-010-9110-x
  4. Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  5. 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., (In press).
  6. 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
  7. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  8. 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
  9. Allahverdizadeh, A., Naei, M.H. and Nikkhah Bahrami, M. (2008), "Nonlinear free and forced vibration analysis of thin circular functionally graded plates", J. Sound Vib., 310, 966-984. https://doi.org/10.1016/j.jsv.2007.08.011
  10. Amin, MH., Soleimani, M. and Rastgoo, A. (2009), "Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation". Smart. Mater. Struct., 18, 1-9.
  11. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 569-672.
  12. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  13. 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. Stresses, 35, 677-694. https://doi.org/10.1080/01495739.2012.688665
  14. 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
  15. Baferani, A.H., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020
  16. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  17. 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", Composites: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  18. 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 Braz. Soc. Mech. Sci. Eng., 38, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  19. 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
  20. 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-Eng., 42, 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  21. 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
  22. 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
  23. 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
  24. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  25. 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
  26. 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. https://doi.org/10.1142/S0219876213500825
  27. 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
  28. Bouguenina, O., Belakhdar, K, Tounsi, A. and Adda Bedia, E.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  29. 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
  30. 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
  31. Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193
  32. Chattibi, F., Benrahou, K.H., Benachour, A., Nedri, K. and Tounsi, A. (2015), "Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory", Steel Compos. Struct., 19(1), 93-110. https://doi.org/10.12989/scs.2015.19.1.093
  33. Cunedioglu, Y. (2015), "Free vibration analysis of edge cracked symmetric functionally graded sandwich beams", Struct. Eng. Mech., 56(6), 1003-1020. https://doi.org/10.12989/sem.2015.56.6.1003
  34. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  35. Dehghan, H., Baradaran, GH. (2011),"Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method", Appl. Math. Comput., 218, 2772-2784.
  36. 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
  37. Ebrahimi, F. and Dashti, S. (2015), "Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., 19(5), 1279-1298. https://doi.org/10.12989/scs.2015.19.5.1279
  38. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  39. 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
  40. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039
  41. 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
  42. Hadji. L., Atmane, H., 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.-Eng. Ed., 32(7), 925-942. https://doi.org/10.1007/s10483-011-1470-9
  43. Hadji, L. and Adda Bedia, E.A. (2015), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., 21(3), 273-287. https://doi.org/10.12989/was.2015.21.3.273
  44. Hadji, L., Hassaine Daouadji, T., Ait Amar Meziane, M., Tlidji, Y. and Adda Bedia, E.A. (2016), "Analysis of functionally graded beam using a new first-order shear deformation theory", Struct. Eng. Mech., 57(2), 315-325. https://doi.org/10.12989/sem.2016.57.2.315
  45. 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
  46. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech.-ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  47. Hosseini Hashemi, S.H., Rokni Damavandi Taher, H. and Omidi. M. (2008), "3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Ritz method", J. Sound. Vib., 311, 1114-1140. https://doi.org/10.1016/j.jsv.2007.10.020
  48. Hosseini-Hashemi, S., Fadaee, M., Rokni, D. and Taher, H. (2011a), "Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory", Appl. Math. Model., 35, 708-727. https://doi.org/10.1016/j.apm.2010.07.028
  49. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007
  50. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011c), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002
  51. 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.
  52. Huang, X.L. and Shen, H.S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solids Struct., 41, 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012
  53. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  54. 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
  55. 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. Meth, 11(5), 135007.
  56. Kirkland, B. and Uy, B. (2015), "Behaviour and design of composite beams subjected to flexure and axial load", Steel Compos. Struct., 19(3), 615-633. https://doi.org/10.12989/scs.2015.19.3.615
  57. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "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. https://doi.org/10.12989/scs.2015.18.2.425
  58. Lee, D., Waas, A.M. and Karnopp. B.H. (1998), "Analysis of a rotating multi layer annular plate modeled via layer wise zig-zag theory: free vibration and transient analysis", Comput. Struct., 66, 313-335. https://doi.org/10.1016/S0045-7949(97)00063-1
  59. Liang, X., Wang, Z., Wang, L. and Liu, G. (2014), "Semi-analytical solution for three-dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation", J. Sound Vib., 333(12), 2649-2663. https://doi.org/10.1016/j.jsv.2014.01.021
  60. Liang, X., Wu, Z., Wang, L., Liu, G., Wang, Z. and Zhang, W. (2015a), "Semi analytical three-dimensional solutions for the transient response of functionally graded material rectangular plates", J. Eng. Mech.-ASCE, 141(9),
  61. Liang, X., Kou, H., Liu, G., Wang, L., Wang, Z. and Wu, Z. (2015b), "A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells", J. Zhejiang Univ. Sci.A, 16(7), 525-540. https://doi.org/10.1631/jzus.A1500016
  62. Li, Q., Iu, V.P. and Kou, K.P. (2009), "Three dimensional vibration analysis of functionally graded material plates in thermal environment", J. Sound. Vib., 324, 733-750. https://doi.org/10.1016/j.jsv.2009.02.036
  63. Liew, K.M. and Yang, B. (2000), "Elasticity solutions for free vibrations of annular plates from three-dimensional analysis", J. Sound. Vib., 37, 7689-7702.
  64. Lin, C.C. and Tseng, C.S. (1998), "Free vibration of polar orthotropic laminated circular and annular plates", J. Sound. Vib., 209, 797-810. https://doi.org/10.1006/jsvi.1997.1293
  65. Liu, D.Y., Wang, C.Y. and Chen, W.Q. (2010), "Free vibration of FGM plates with in-plane material inhomogeneity", Compos. Struct., 92, 1047-1051. https://doi.org/10.1016/j.compstruct.2009.10.001
  66. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions", Int. J. Numer. Meth. Eng., 79(1), 25-44. https://doi.org/10.1002/nme.2555
  67. 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
  68. Mahmoud, S.R., Abd-Alla, A.M., Tounsi, A. and Marin, M. (2014), "The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium", J. Vib. Control, 21(16), 3281-3291. https://doi.org/10.1177/1077546314521443
  69. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  70. Mansouri, M.H. and Shariyat, M. (2014), "Thermal buckling predictions of three types of high-order theories for the heterogeneous orthotropic plates, using the new version of DQM", Compos. Struct, 113(1), 40-55. https://doi.org/10.1016/j.compstruct.2014.02.032
  71. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  72. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  73. Miamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally graded materials: design, processing and applications, Kluwer Academic Publishers, Boston.
  74. Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., 57(3), 441-456. https://doi.org/10.12989/sem.2016.57.3.441
  75. Morimoto, T., Tanigawa, Y. and Kawamura, R. (2006), "Thermal buckling of functionally graded rectangular plates subjected to partial heating", Int. J. Mech. Sci., 48(9), 926-937. https://doi.org/10.1016/j.ijmecsci.2006.03.015
  76. 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
  77. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  78. 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. Based Des. Struc., 41, 421-433. https://doi.org/10.1080/15397734.2013.763713
  79. Ould Youcef, D., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., 3(4), 177-191. https://doi.org/10.12989/anr.2015.3.4.177
  80. Ozturk, H. (2015), "Vibration analysis of a pre-stressed laminated composite curved beam", Steel Compos. Struct., 19(3), 635-659. https://doi.org/10.12989/scs.2015.19.3.635
  81. 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
  82. Praveen, GN. and Reddy, J.N. (1998), "Non linear transient thermoelastic analysis of functionally graded ceramic metal plates", Int. J. Solids. Struct., 35, 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  83. 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
  84. Saidi, A.R. and Jomehzadeh, E. (2009), "On analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported", Proc. I. Mech. E., Part C: J. Mech. Eng. Sci., 223, 2009-2016. https://doi.org/10.1243/09544062JMES1431
  85. Sallai, B., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Analytical solution for bending analysis of functionally graded beam", Steel Compos. Struct., 19(4), 829-841. https://doi.org/10.12989/scs.2015.19.4.829
  86. Shufrin, I. and Eisenburger, M. (2005), "Stability and vibration of shear deformable plates-first order and higher order analysis", Int. J. Solid Struct., 42, 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067
  87. Sofiyev, A.H. and Kuruoglu, N. (2015), "Buckling of non-homogeneous orthotropic conical shells subjected to combined load", Steel Compos. Struct., 19(1), 1-19. https://doi.org/10.12989/scs.2015.19.1.001
  88. Sundararajan, N., Prakash, T. and Ganapathi, M. (2005), "Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments", Finite. Elem. Anal. Des., 42, 152-168. https://doi.org/10.1016/j.finel.2005.06.001
  89. Suresh, S. and Mortensen, A. (1998), "Fundamentals of Functionally Graded Materials", (IOM Communications Ltd., London).
  90. Tagrara, S.H., Benachour, A., Bachir Bouiadjra, M. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  91. 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
  92. Tounsi, A., Houari Mohammed, 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, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  93. Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound. Vib., 272, 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7
  94. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  95. 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
  96. Woo, J., Meguid, S.A. and Ong. L.S. (2006), "Nonlinear free vibration of functionally graded plates", J. Sound Vib., 289, 595-611. https://doi.org/10.1016/j.jsv.2005.02.031
  97. Yahoobi, H. and Feraidoon, A. (2010), "Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load", World Appl. Sci. J., 10(3), 337-341.
  98. Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loading using VIM", Steel Compos. Struct., 17(5), 753-776. https://doi.org/10.12989/scs.2014.17.5.753
  99. Yang, J. and Shen, H.S. (2001), "Dynamic response of initially stressed functionally graded rectangular thin plates", Compos. Struct., 54, 497-508. https://doi.org/10.1016/S0263-8223(01)00122-2
  100. Yang, J. and Shen, H.S. (2002), "Vibration characteristic and transient response of shear deformable functionally graded plates in thermal environment", J. Sound. Vib., 255, 579-602. https://doi.org/10.1006/jsvi.2001.4161
  101. 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
  102. Zhang, D.G. and Zhou, Y.H., (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comp. Mater. Sci., 44, 716-720.
  103. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of $ZrO_2$-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2
  104. 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

피인용 문헌

  1. A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations vol.11, pp.2, 2016, https://doi.org/10.12989/gae.2016.11.2.289
  2. Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation vol.22, pp.1, 2016, https://doi.org/10.12989/scs.2016.22.1.091
  3. Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1287
  4. Vibration analysis of non-uniform porous beams with functionally graded porosity distribution pp.2041-3076, 2018, https://doi.org/10.1177/1464420718780902
  5. Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions vol.24, pp.10, 2018, https://doi.org/10.1177/1077546316672788
  6. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation vol.12, pp.1, 2016, https://doi.org/10.12989/gae.2017.12.1.009
  7. A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams vol.19, pp.2, 2017, https://doi.org/10.12989/sss.2017.19.2.115
  8. Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities vol.6, pp.1, 2017, https://doi.org/10.12989/amr.2017.6.1.045
  9. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  10. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  11. An analytical solution for bending and vibration responses of functionally graded beams with porosities vol.25, pp.4, 2016, https://doi.org/10.12989/was.2017.25.4.329
  12. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  13. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  14. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  15. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  16. Free vibration of FGM plates with porosity by a shear deformation theory with four variables vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.353
  17. Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations vol.66, pp.6, 2016, https://doi.org/10.12989/sem.2018.66.6.729
  18. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2016, https://doi.org/10.12989/was.2018.27.1.059
  19. Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory vol.15, pp.4, 2018, https://doi.org/10.12989/eas.2018.15.4.369
  20. An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.247
  21. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  22. Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory vol.55, pp.2, 2016, https://doi.org/10.1007/s11029-019-09805-0
  23. Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution vol.72, pp.4, 2016, https://doi.org/10.12989/sem.2019.72.4.513
  24. Higher-order semi-layerwise models for doubly curved delaminated composite shells vol.91, pp.1, 2021, https://doi.org/10.1007/s00419-020-01755-7
  25. A compressive study for porous FG curved nanobeam under various boundary conditions via a nonlocal strain gradient theory vol.136, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-021-01238-w
  26. Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates vol.5, pp.11, 2016, https://doi.org/10.3390/jcs5110305
  27. Influence of porosity distribution on static and buckling responses of porous functionally graded plates vol.34, pp.None, 2016, https://doi.org/10.1016/j.istruc.2021.08.050