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An original HSDT for free vibration analysis of functionally graded plates

  • Sidhoum, Imene Ait (Laboratoire de Mecanique Applique, Departement de Genie Mecanique, Universite des Sciences et Technologie d'ORAN Mouhamed Boudiaf) ;
  • Boutchicha, Djilali (Laboratoire de Mecanique Applique, Departement de Genie Mecanique, Universite des Sciences et Technologie d'ORAN Mouhamed Boudiaf) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, Civil Engineering Department, University of SidiBel Abbes, Faculty of Technology) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Civil Engineering Department, University of SidiBel Abbes, Faculty of Technology)
  • 투고 : 2016.12.01
  • 심사 : 2017.09.21
  • 발행 : 2017.12.30

초록

This work presents a free vibration analysis of functionally graded plates by employing an original high order shear deformation theory (HSDT). This theory use only four unknowns, which is even less than the classical HSDT. The equations of motion for the dynamic analysis are determined via the Hamilton's principle. The original kinematic allows obtaining interesting equations of motion. These equations are solved analytically via Navier procedure. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

키워드

참고문헌

  1. Abdelbari, S., Fekrar, A., Heireche, H., Saidi, H., Tounsi, A. and AddaBedia, E.A. (2016), "An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations", Wind Struct., 22(3), 329-348. https://doi.org/10.12989/was.2016.22.3.329
  2. Abdelhak, Z., Hadji, L., HassaineDaouadji, T. and AddaBedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267
  3. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B Eng., 39(1), 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  4. Abualnour, M., Houari, M.S.A., Tounsi, A., AddaBedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  5. AddaBedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Brazil. J. Phys., 45(2), 225-233. https://doi.org/10.1007/s13538-015-0306-2
  6. Ahouel, M., Houari, M.S.A., AddaBedia, E.A. and Tounsi, A. (2016) "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  7. 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
  8. AitAtmane, 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
  9. AitYahia, S., AitAtmane, 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
  10. Akavci, S.S. (2006), "Analysis of shear deformable symmetrically laminated composite plates on elastic foundation", Sci. Eng. Compos. Mater., 13, 79-91.
  11. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B, 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035
  12. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B Eng., 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043
  13. Alieldin, S.S., Alshorbagy, A.E. and Shaat, M. (2011), "A firstorder shear deformation finite element model for elastostatic analysis of laminated composite plates and the equivalent functionally graded plates", Ain Shams Eng. J., 2, 53-62. https://doi.org/10.1016/j.asej.2011.05.003
  14. Attia, A., Tounsi, A., AddaBedia, 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
  15. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical postbuckling 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
  16. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  17. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperaturedependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091
  18. 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
  19. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-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
  20. Belkorissat, I., Houari, M.S.A., Tounsi, A., AddaBedia, 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
  21. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017b), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  22. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017a), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695
  23. 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(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  24. 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
  25. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  26. Benbakhti, A., BachirBouiadjra, M., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates", Steel Compos. Struct., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975
  27. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., AddaBedia, E.A. and Mahmoud, S.R. (2017), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., (Accepted)
  28. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  29. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder 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
  30. 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
  31. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and AddaBedia, 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
  32. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/SSS.2017.19.6.601
  33. Bever, M.B. and Duwez, P.E. (1972), "Gradients in composite materials", Mater. Sci. Eng., 10, 1-8. https://doi.org/10.1016/0025-5416(72)90059-6
  34. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  35. 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
  36. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  37. Boukhari, A., AitAtmane, H., Tounsi, A., AddaBedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  38. 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
  39. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  40. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "Anew 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
  41. Bourada, M., Tounsi, A., Houari, M.S.A. and AddaBedia, 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
  42. 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
  43. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and AddaBedia, 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
  44. Castellazzi, G., Gentilini, C., Krysl, P. and Elishakoff, I. (2013), "Static analysis of functionally graded plates using a nodal integrated finite element approach", Compos. Struct., 103, 197-200. https://doi.org/10.1016/j.compstruct.2013.04.013
  45. Cheng, Z.Q. and Batra, R.C. (2000), "Deflection relationship between the homogenous Kirchhoff plate theory and different functionally graded plates theories", Arch. Appl. Mech., 52(1), 143-158.
  46. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-part I: analysis", Int. J. Solid. Struct., 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011
  47. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and AddaBedia, E.A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  48. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  49. Chinosi, C. and Croce, L.D. (2007), "Approximation of functionally graded plates with non-conforming finite elements", J. Comput. Appl. Math., 210, 106-115. https://doi.org/10.1016/j.cam.2006.10.078
  50. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  51. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  52. 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
  53. Fahsi, A., Tounsi, A., Hebali, H.,Chikh, A., AddaBedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/GAE.2017.13.3.385
  54. 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
  55. Ghannadpour, S.A.M. and Alinia, M.M. (2006), "Large deflection behavior of functionally graded plates under pressure loads", Compos. Struct., 75(1-4), 67-71. https://doi.org/10.1016/j.compstruct.2006.04.004
  56. Hadji, L., HassaineDaouadji, T., Ait Amar Meziane, M., Tlidji, Y. and AddaBedia, 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
  57. 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
  58. HanifiHachemi Amar, L., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/SEM.2017.64.5.527
  59. Hebali, H., Bakora, A., Tounsi, A. and Kaci, A. (2016), "A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates", Steel Compos. Struct., 22(3), 473-495. https://doi.org/10.12989/scs.2016.22.3.473
  60. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and AddaBedia, 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
  61. Hirwani, C.K., Mahapatra, T.R., Panda, S.K., Sahoo, S.S., Singh, V.K. and Patle, B.K. (2017b), "Nonlinear free vibration analysis of laminated carbon/epoxy curved panels", Defen. Sci. J., 67(2), 207-221. https://doi.org/10.14429/dsj.67.10072
  62. Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mahapatra, S.S. (2017a), "Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure", ASCE J. Aerosp. Eng., 30(5), 04017045. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000756
  63. Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mahapatra, S.S. (2017c), "Nonlinear transient finite element analysis of delaminated composite shallow shell panels", AIAA J., 55(5), 1734-1748. https://doi.org/10.2514/1.J055624
  64. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "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
  65. Hosseini-Hashemi, Sh., RokniDamavandiTaher, H., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., 34(5), 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008
  66. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  67. Kar, V.R. and Panda, S.K. (2015), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solid. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  68. 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
  69. Kar, V.R. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Therm. Stress., 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623
  70. Kar, V.R. and Panda, S.K. (2016b), "Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method", J. Vib. Control, 22(7), 1935-1949. https://doi.org/10.1177/1077546314545102
  71. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  72. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/SCS.2017.25.3.361
  73. Kashtalyan, M. (2004), "Three-dimensional elasticity solution for bending of functionally graded rectangular plates", Eur. J. Mech. A/Solid., 23, 853-864. https://doi.org/10.1016/j.euromechsol.2004.04.002
  74. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aerosp. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  75. Khetir, H., BachirBouiadjra, M., Houari, M.S.A., Tounsi, A. and S.R. Mahmoud, (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/SEM.2017.64.4.391
  76. Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., 63(4), 439-446. https://doi.org/10.12989/SEM.2017.63.4.439
  77. Koizumi, M. (1993), "The concept of FGM, ceramic transactions", Funct. Grad. Mater., 34, 3-10.
  78. Laoufi, I., Ameur, M., Zidi, M., AddaBedia, E.A. and Bousahla, A.A. (2016), "Mechanical and hygrothermalbehaviour of functionally graded plates using a hyperbolic shear deformation theory", Steel Compos. Struct., 20(4), 889-911. https://doi.org/10.12989/scs.2016.20.4.889
  79. LarbiChaht, 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
  80. Mahapatra, T.R. and Panda, S.K. (2015), "Thermoelastic vibration analysis of laminated doubly curved shallow panels using nonlinear FEM", J. Therm. Stress., 38(1), 39-68. https://doi.org/10.1080/01495739.2014.976125
  81. Mahapatra, T.R. and Panda, S.K. (2016), "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
  82. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2015), "Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment", J. Sandw. Struct. Mater., 17(5), 511-545. https://doi.org/10.1177/1099636215577363
  83. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016b), "Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment", Int. J. Struct. Stab. Dyn., 16(3), 1450105. https://doi.org/10.1142/S0219455414501053
  84. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016a), "Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model", Mech. Adv. Mater. Struct., 23(11), 1343-1359. https://doi.org/10.1080/15376494.2015.1085606
  85. Mahi, A., AddaBedia, 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
  86. 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
  87. Mehar, K. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038
  88. Mehar, K. and Panda, S.K. (2017), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., DOI: 10.1002/pc.24266.
  89. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech. A/Solid., 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005
  90. Mehar, K., Panda, S.K. and Patle, B.K. (2017b), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., DOI: 10.1002/pc.24409.
  91. Mehar, K., Panda, S.K. and Patle, B.K. (2017c), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466
  92. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017d), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689
  93. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324
  94. 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
  95. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., AddaBedia, E.A. and Mahmoud, SR. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443.
  96. 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
  97. 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
  98. Merdaci, S., Tounsi, A. and Bakora, A. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., 22(4), 713-732. https://doi.org/10.12989/scs.2016.22.4.713
  99. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 18, 31-38.
  100. Mouaici, F., Benyoucef, S., AitAtmane, H. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of nonhomogeneous plates using hyperbolic shear deformation theory", Wind Struct., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429
  101. Mouffoki, A., AddaBedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/SSS.2017.20.3.369
  102. Neves, AMA, Ferreira, AJM, Carrera, E, Roque, CMC, Cinefra, M, Jorge, RMN, et al. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B Eng., 43(2), 711-725.
  103. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermomechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9
  104. Panda, S.K. and Mahapatra, T.R. (2014), "Nonlinear finite element analysis of laminated composite spherical shell vibration under uniform thermal loading", Meccanica, 49(1), 191-213. https://doi.org/10.1007/s11012-013-9785-9
  105. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higherorder finite element formulation", J. Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  106. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid. Struct., 35, 4457-4471. https://doi.org/10.1016/S0020-7683(97)00253-9
  107. Qian, L.F., Batra, R.C. and Chen, L.M. (2004), "Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local PetroveGalerkin method", Compos. Part B Eng., 35(6-8), 685-697. https://doi.org/10.1016/j.compositesb.2004.02.004
  108. Raminnea, M., Biglari, H. and VakiliTahami, F. (2016), "Nonlinear higher order Reddy theory for temperature- dependent vibration and instability of embedded functionally graded pipes conveying fluid-nanoparticle mixture", Struct. Eng. Mech., 59(1), 153-186. https://doi.org/10.12989/sem.2016.59.1.153
  109. Reddy, J. (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
  110. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-77.
  111. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016a), "Static, free vibration and transient response of laminated composite curved shallow panel-An experimental approach", Eur. J. Mech. A/Solid., 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  112. Sahoo, S.S., Panda, S.K. and Sen, T.R. (2016b), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA J., 54(8), 2530-2544. https://doi.org/10.2514/1.J054908
  113. Sahoo, S.S., Panda, S.K. and Singh, V.K. (2017), "Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate", Proc. IMechE Part L: J. Mater. Des. Appl., 231(5), 463-478.
  114. Saidi, H., Tounsi, A. and Bousahla, A.A. (2016), "A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations", Geomech. Eng., 11(2), 289-307. https://doi.org/10.12989/gae.2016.11.2.289
  115. Singh, M.K. and Panda, S.K. (2017), "Geometrical nonlinear free vibration analysis of laminated composite doubly curved shell panels embedded with piezoelectric layers", J. Vib. Control, 23(13), 2078-2093. https://doi.org/10.1177/1077546315609988
  116. Singh, M.K., Mahapatra, T.R. and Panda, S.K. (2016), "Nonlinear transient analysis of smart laminated composite plate integrated with PVDF sensor and AFC actuator", Compos. Struct., 157, 121-130. https://doi.org/10.1016/j.compstruct.2016.08.020
  117. Singh, M.K., Prakash, T. and Ganapathi, M. (2011), "Finite element analysis of functionally graded plates under transverse load", Finite Elem. Anal. Des., 47, 453-460. https://doi.org/10.1016/j.finel.2010.12.001
  118. Singh, V.K. and Panda, S.K. (2015), "Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers", Smart Struct. Syst., 16(5), 853-872. https://doi.org/10.12989/sss.2015.16.5.853
  119. Taibi, F.Z., Benyoucef, S., Tounsi, A., BachirBouiadjra, R., AddaBedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17(2), 99-129. https://doi.org/10.1177/1099636214554904
  120. Tounsi, A., Houari, M.S.A., Benyoucef, S. and AddaBedia, 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
  121. Wen, P.H. and Aliabadi, M.H. (2012), "Analysis of functionally graded plates by meshless method: A purely analytical formulation", Eng. Anal. Bound. Elem., 36, 639-650. https://doi.org/10.1016/j.enganabound.2011.11.017
  122. 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
  123. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319, 918-939. https://doi.org/10.1016/j.jsv.2008.06.025
  124. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017),"A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153.
  125. Zidi, M., Tounsi, A., Houari M.S.A., AddaBedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygrothermo-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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