DOI QR코드

DOI QR Code

An efficient shear deformation theory for wave propagation of functionally graded material plates

  • Boukhari, Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Atmane, Hassen Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Adda Bedia, E.A. (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2015.06.17
  • Accepted : 2016.01.20
  • Published : 2016.03.10

Abstract

An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching.bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

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 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
  3. 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", International Journal of Mechanics and Materials in Design. (in Press)
  4. 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
  5. 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
  6. 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
  7. Arefi, M. (2013), "Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder", Acta. Mech., 224, 2771-2783. https://doi.org/10.1007/s00707-013-0888-0
  8. Arefi, M. and Rahimi, G.H. (2011), "Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart Struct. Syst., 8(5), 433-446. https://doi.org/10.12989/sss.2011.8.5.433
  9. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  10. 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
  11. 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
  12. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A. (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
  13. 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
  14. 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
  15. 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, 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  24. 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
  25. 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
  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. 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
  28. 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
  29. Chen, W.Q., Wang, H.M. and Bao, R.H. (2007), "On calculating dispersion curves of waves in a functionally graded elastic plate", Compos. Struct., 81, 233-242. https://doi.org/10.1016/j.compstruct.2006.08.009
  30. Curiel-Sosa, J.L., Beg, O.A. and Murillo, J.L. (2013), "Finite element analysis of structural instability using an implicit/explicit switching technique", Int. J. Comput. Meth. Eng. Sci. Mech., 14(5), 452-464. https://doi.org/10.1080/15502287.2013.784383
  31. 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
  32. 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
  33. 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
  34. 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
  35. Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  36. 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
  37. Han, X. and Liu, G.R. (2002), "Effects of SH waves in a functionally graded plate", Mechanics Research Communications, 29, 327-338. https://doi.org/10.1016/S0093-6413(02)00316-6
  38. Han, X., Liu, G.R., Xi, Z.C. and Lam, K.Y. (2001), "Transient responses in a functionally graded cylinder", Int. J. Solid. Struct., 38, 3021-3037. https://doi.org/10.1016/S0020-7683(00)00219-5
  39. Han, X., Liu, G.R. and Lam, K.Y. (2002), "Transient waves in plates of functionally graded materials", Int. J. Numer. Meth. Eng., 52, 851-865.
  40. 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
  41. 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
  42. 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.
  43. Kim, Y.W. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vib., 284(3-5), 531-549. https://doi.org/10.1016/j.jsv.2004.06.043
  44. Kim, S.E., Thai, H.T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89, 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017
  45. 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
  46. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28, 1-4.
  47. 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
  48. 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
  49. 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
  50. Mansouri, M.H. and Shariyat, M. (2015), "Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations", Compos. Part B, 83, 88-104. https://doi.org/10.1016/j.compositesb.2015.08.030
  51. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  52. Mechab, I., Ait Atmane, H., Tounsi, A., Belhadj, H.A. and Adda Bedia, E.A. (2010), "A two variable refined plate theory for the bending analysis of functionally graded plates", Acta Mech Sin, 26, 941-949. https://doi.org/10.1007/s10409-010-0372-1
  53. 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
  54. 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
  55. 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
  56. 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
  57. Park, J.S. and Kim, J.H. (2006), "Thermal postbuckling and vibration analyses of functionally graded plates", J. Sound Vib., 289(1-2), 77-93. https://doi.org/10.1016/j.jsv.2005.01.031
  58. 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
  59. Rashidi, M.M., Shooshtari, A. and Beg, O.A. (2012), "Homotopy perturbation study of nonlinear vibration of Von K?rm?n rectangular plates", Compu. Struct., 106-107, 46-55. https://doi.org/10.1016/j.compstruc.2012.04.004
  60. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  61. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A/Solid., 20, 841-855.
  62. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, Wiley, New York.
  63. Reddy, J.N. and Chin, C.D. (1998), "Thermo-mechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21, 593-626. https://doi.org/10.1080/01495739808956165
  64. 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
  65. 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
  66. 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
  67. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622
  68. Shimpi, R.P. and Patel, H.G. (2006a), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct, 43(22), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007
  69. Shimpi, R.P. and Patel, H.G. (2006b), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030
  70. 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
  71. Sun, D. and Luo, S.N. (2011a), "The wave propagation and dynamic response of rectangular functionally graded material plates with completed clamped supports under impulse load", Eur. J. Mech. A/Solid., 30, 396-408. https://doi.org/10.1016/j.euromechsol.2011.01.001
  72. Sun, D. and Luo, S.N. (2011b), "Wave propagation of functionally graded material plates in thermal environments", Ultrasonics, 51, 940-952. https://doi.org/10.1016/j.ultras.2011.05.009
  73. Sun, D. and Luo, S.N. (2012), "Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments", Appl. Math. Model., 36, 444-462. https://doi.org/10.1016/j.apm.2011.07.023
  74. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, IOM Communications Ltd., London.
  75. 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
  76. 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
  77. Touloukian, T.S. (1967), Thermophysical Properties of High Temperature Solid Materials, McMillan, New York.
  78. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013a), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerospace Sci. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  79. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  80. 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
  81. Yang, J. and Shen, H.S. (2002), "Vibration characteristics and transient response of shear deformable functionally graded plates in thermal environments", J. Sound Vib., 255, 579-602. https://doi.org/10.1006/jsvi.2001.4161
  82. 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
  83. 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.
  84. 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
  85. 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
  86. Zenkour, AM. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  87. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerospace Sci. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  88. Woo, J., Meguid, S.A. and Ong, L.S. (2006), "Nonlinear free vibration behavior of functionally graded plates", J. Sound Vib., 289, 595-611. https://doi.org/10.1016/j.jsv.2005.02.031

Cited by

  1. A novel four variable refined plate theory for laminated composite plates vol.22, pp.4, 2016, https://doi.org/10.12989/scs.2016.22.4.713
  2. 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
  3. Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium vol.47, pp.6, 2017, https://doi.org/10.1007/s13538-017-0524-x
  4. Dynamic buckling of polymer–carbon nanotube–fiber multiphase nanocomposite viscoelastic laminated conical shells in hygrothermal environments 2017, https://doi.org/10.1177/1099636217743288
  5. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation vol.72, 2018, https://doi.org/10.1016/j.ast.2017.11.004
  6. Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates vol.132, pp.10, 2017, https://doi.org/10.1140/epjp/i2017-11666-6
  7. 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
  8. 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
  9. Forced vibration analysis of functionally graded porous deep beams vol.186, 2018, https://doi.org/10.1016/j.compstruct.2017.12.013
  10. Numerical analysis of acoustic radiation properties of laminated composite flat panel in thermal environment: A higher-order finite-boundary element approach 2017, https://doi.org/10.1177/0954406217735866
  11. A new non-polynomial four variable shear deformation theory in axiomatic formulation for hygro-thermo-mechanical analysis of laminated composite plates vol.182, 2017, https://doi.org/10.1016/j.compstruct.2017.09.029
  12. Shear wave in a fiber-reinforced anisotropic layer overlying a pre-stressed porous half space with self-weight vol.18, pp.5, 2016, https://doi.org/10.12989/sss.2016.18.5.911
  13. Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method 2017, https://doi.org/10.1016/j.aej.2017.06.001
  14. Buckling optimization of variable-stiffness composite panels based on flow field function vol.181, 2017, https://doi.org/10.1016/j.compstruct.2017.08.081
  15. Nonlinear bending of a two-dimensionally functionally graded beam vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.087
  16. Evaluation of heat dissipation and structural response of a cellular panel as a heat exchanger 2018, https://doi.org/10.1177/1099636217749274
  17. Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1347
  18. Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory vol.180, 2017, https://doi.org/10.1016/j.compstruct.2017.08.012
  19. A refined theory with stretching effect for the flexure analysis of laminated composite plates vol.11, pp.5, 2016, https://doi.org/10.12989/gae.2016.11.5.671
  20. Influence of various temperature distributions on critical speed and vibrational characteristics of rotating cylindrical microshells with modified lengthscale parameter vol.132, pp.6, 2017, https://doi.org/10.1140/epjp/i2017-11551-4
  21. A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates vol.22, pp.3, 2016, https://doi.org/10.12989/scs.2016.22.3.473
  22. On thermal stability of plates with functionally graded coefficient of thermal expansion vol.60, pp.2, 2016, https://doi.org/10.12989/sem.2016.60.2.313
  23. A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates vol.22, pp.2, 2016, https://doi.org/10.12989/scs.2016.22.2.257
  24. Bending analysis of FGM plates using a sinusoidal shear deformation theory vol.23, pp.6, 2016, https://doi.org/10.12989/was.2016.23.6.543
  25. A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.047
  26. Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects vol.187, 2018, https://doi.org/10.1016/j.compstruct.2017.12.004
  27. A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate vol.60, pp.4, 2016, https://doi.org/10.12989/sem.2016.60.4.547
  28. Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.052
  29. Fracture problems, vibration, buckling, and bending analyses of functionally graded materials: A state-of-the-art review including smart FGMS pp.1548-0046, 2018, https://doi.org/10.1080/02726351.2017.1410265
  30. Numerical Method to Compute Water Surface Profile for Converging Compound Channel vol.43, pp.10, 2018, https://doi.org/10.1007/s13369-018-3161-y
  31. Explicit fiber element and its application to piers under multipulse near-fault earthquake motion pp.15417794, 2018, https://doi.org/10.1002/tal.1547
  32. A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches vol.40, pp.7, 2018, https://doi.org/10.1007/s40430-018-1276-4
  33. Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media vol.29, pp.11, 2018, https://doi.org/10.1177/1045389X18770856
  34. Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1487612
  35. Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories vol.133, pp.5, 2018, https://doi.org/10.1140/epjp/i2018-12015-1
  36. Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory pp.1530-7972, 2018, https://doi.org/10.1177/1099636218760667
  37. Effect of rotation on Rayleigh waves in a fiber-reinforced solid anisotropic magneto-thermo-viscoelastic media pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1445322
  38. Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates vol.133, pp.4, 2018, https://doi.org/10.1140/epjp/i2018-11956-5
  39. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529