Smart Structures and Systems

  • 제20권4호
  • /
  • Pages.509-524
  • /
  • 2017
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory

  • Zaoui, Fatima Zohra (Laboratoire de Modelisation Numerique et Experimentale des Phenomenes Mecaniques, Faculte des Sciences et Technologie, Departement de Genie Mecanique, Universite Abdelhamid Ibn Badis of Mostaganem) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Ouinas, Djamel (Laboratoire de Modelisation Numerique et Experimentale des Phenomenes Mecaniques, Faculte des Sciences et Technologie, Departement de Genie Mecanique, Universite Abdelhamid Ibn Badis of Mostaganem)
  • 투고 : 2017.02.28
  • 심사 : 2017.08.05
  • 발행 : 2017.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this article, a free vibration analysis of functionally graded (FG) plates resting on elastic foundations is presented using a quasi-3D hybrid-type higher order shear deformation theory. Undetermined integral terms are employed in the proposed displacement field and modeled based on a hybrid-type (sinusoidal and parabolic) quasi-3D HSDT with five unknowns in which the stretching effect is taken into account. Thus, it can be said that the significant feature of this theory is that it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameter) mathematical model. Equations of motion are obtained via the Hamilton's principles and solved using Navier's method. Accuracy of the proposed theory is confirmed by comparing the results of numerical examples with the ones available in literature.

키워드

참고문헌

  1. Abdelbari, S., Fekrar, A., Heireche, H., Saidi, H., Tounsi, A. and Adda Bedia, 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., Hassaine Daouadji, T. and Adda Bedia, 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. Adda Bedia, 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
  4. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A., 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
  5. 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
  6. 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
  7. Ait Yahia, 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
  8. Aizikovich, S.M., Mitrin, B.I., Seleznev, N.M., Wang, Y.C. and Volkov, S.S. (2016), "Influence of a soft FGM interlayer on contact stresses under a beam on an elastic foundation", Struct. Eng. Mech., 58(4), 613-625. https://doi.org/10.12989/sem.2016.58.4.613
  9. 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
  10. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct. Eng., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  11. 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, 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043
  12. Akbarov, S.D., Guliyev, H.H. and Yahnioglu, N. (2016), "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Struct. Eng. Mech., 57(2), 239-264. https://doi.org/10.12989/sem.2016.57.2.239
  13. 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
  14. Alijani, F. and Amabili, M. (2014), "Effect of thickness deformation on large-amplitude vibrations of functionally graded rectangular plates", Compos. Struct., 113, 89-107. https://doi.org/10.1016/j.compstruct.2014.03.006
  15. Arefi, M. (2015a), "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
  16. Arefi, M. (2015b), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195
  17. Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct. Syst., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16.1.081
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "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
  27. 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
  28. Benbakhti, A., Bachir Bouiadjra, 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
  29. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., (Accepted).
  30. 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
  31. 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
  32. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory forvibration analysis of functionally graded sandwich plates", Mech. Adv. Mater.Struct.,23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  33. 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
  34. 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
  35. Birman, V. and Byrd, L.W. (2007), "Modeling and Analysis of Functionally Graded Materials and Structures", Appl. Mech. Rev., 60, 195-216. https://doi.org/10.1115/1.2777164
  36. 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
  37. 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
  38. Bouderba, B., Houari, M.S.A. and 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
  39. 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
  40. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. Celebi, K., Yarimpabuc, D. and Keles, I. (2016), "A unified method for stresses in FGM sphere with exponentially-varying properties", Struct. Eng. Mech., 57(5), 823-835. https://doi.org/10.12989/sem.2016.57.5.823
  48. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, 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
  49. 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
  50. Darabi, A. and Vosoughi, A.R. (2016), "Hybrid inverse method for small scale parameter estimation of FG nanobeams", Steel Compos. Struct., 20(5), 1119-1131. https://doi.org/10.12989/scs.2016.20.5.1119
  51. 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
  52. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature- dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  53. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen\'s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  54. 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., (Accepted).
  55. 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
  56. 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., (In press).
  57. 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
  58. Ghorbanpour Arani, A., Cheraghbak, A. and Kolahchi, R. (2016), "Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory", Struct. Eng. Mech., 60(3), 489-505. https://doi.org/10.12989/sem.2016.60.3.489
  59. 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
  60. 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
  61. Hasani Baferani, A., 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, 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020
  62. 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
  63. 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
  64. Hirwani, C.K., Mahapatra, T.R., Panda, S.K., Sahoo, S.S., Singh, V.K. and Patle, B.K. (2017a), "Nonlinear free vibration analysis of laminated carbon/epoxy curved panels", Defence Sci. J., 67(2), 207-218. https://doi.org/10.14429/dsj.67.10072
  65. Hirwani, C.K., Patle, B.K., Panda, S.K., Mahapatra, T.R., Mandal, S.K., Srivastava, L. and Buragohain, M.K. (2017b), "Experimental and numerical analysis of free vibration of delaminated curved panel", Aerosp. Sci. Technol., 54, 353-370.
  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. Hosseini-Hashemi,S.H., Fadaee, M. and Rokni Damavandi Taher, H. (2011), "Exact solutions for free flexural vibration of Levytype 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
  68. Hosseini-Hashemi, S.H., Rokni Damavandi Taher, 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, 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008
  69. Jin, G., Su, Z., Shi, S., Ye, T. and Gao, S. (2014), "Threedimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions", Compos. Struct., 108, 565-577. https://doi.org/10.1016/j.compstruct.2013.09.051
  70. Kar, V.R. and Panda, S.K. (2015), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solids Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  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. Kar, V.R. and Panda, S.K. (2016a), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115-116, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014
  73. Kar, V.R. and Panda, S.K. (2016b), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Therm. Stresses, 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623
  74. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal post buckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
  75. Kar, V.R. and Panda, S.K. (2017), "Post-buckling analysis of shear deformable FG shallow spherical shell panel under uniform and non-uniform thermal environment", J. Therm. Stresses, 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  76. Kashtalyan, M. (2004), "Three-dimensional solution for bending of functionally graded rectangular plates", Eur J. Mech. A - Solids, 23, 853-864. https://doi.org/10.1016/j.euromechsol.2004.04.002
  77. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Tec., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  78. Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., (In press).
  79. 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., (In press).
  80. 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
  81. Laoufi, I., Ameur, M., Zidi, M., Adda Bedia, E.A. and Bousahla, A.A. (2016), "Mechanical and hygrothermal behaviour 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
  82. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31(3), 257-293. https://doi.org/10.1016/S0022-460X(73)80371-2
  83. Liu, F.L. and Liew, K.M. (1999), "Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method", J. Sound Vib., 225(5), 915-934. https://doi.org/10.1006/jsvi.1999.2262
  84. 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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  85. Mahmoud, S.R., Abd-Alla, A.M., Tounsi, A. and Marin, M. (2015), "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
  86. Mantari, J.L. (2015), "Free vibration of advanced composite plates resting on elastic foundations based on refined non-polynomial theory", Meccanica, 50, 2369-2390. https://doi.org/10.1007/s11012-015-0160-x
  87. Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct., 87, 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002
  88. 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
  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 - Solids, 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", Polymer Composites, (In press).
  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. and Panda, S.K. (2017a), "Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation", Adv. Polymer Technol., (In press).
  93. Mehar, K. and Panda, S.K. (2017b), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polymer Composites, (In press).
  94. 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
  95. 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
  96. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., (In press).
  97. 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., (In press).
  98. 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
  99. Merazi, M., Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  100. 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
  101. Mouaici, F., Benyoucef, S., Ait Atmane, 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
  102. Mouffoki, A., Adda Bedia, 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., (In press).
  103. Nagino, H., Mikami, T. and Mizusawa, T. (2008), "Threedimensional free vibration analysis of isotropic rectangular platesusing the B-spline Ritz method", J. Sound Vib., 317, 329-353. https://doi.org/10.1016/j.jsv.2008.03.021
  104. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higherorder 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
  105. Neves, A.M.A., Ferreira, A.J.M., et al. (2012a), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. B Eng., 43, 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
  106. Neves, A.M.A., Ferreira, A.J.M., et al. (2012b), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94, 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005
  107. 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
  108. 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 Petrov-Galerkin method", Compos. B Eng., 35, 685-697. https://doi.org/10.1016/j.compositesb.2004.02.004
  109. Raminnea, M., Biglari, H. and Vakili Tahami, F. (2016), "Nonlinear higher order Reddy theory for temperaturedependent 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
  110. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stresses, 21, 593-626. https://doi.org/10.1080/01495739808956165
  111. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016), "Static, free vibration and transient response of laminated composite curved shallow panel - An experimental approach", Eur. J. Mech. A - Solids, 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  112. 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", Proceedings of the IMechE Part L: Journal of Materials: Design and Applications, 231(5), 463-478.
  113. 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
  114. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., (In press).
  115. Sheikholeslami, S.A. and Saidi, A.R. (2013), "Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory", Compos. Struct., 106, 350-361. https://doi.org/10.1016/j.compstruct.2013.06.016
  116. Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration ofshear deformable plates-first order and higher order analyses", Int. J. Solids Struct., 42, 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067
  117. Singh, V.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
  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., Bachir Bouiadjra, R., Adda Bedia, 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. Taj, G. and Chakrabarti, A. (2013), "Static and dynamic analysis of functionally graded skew plates", J. Eng. Mech. - ASCE, 139(7), 848-857. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000523
  121. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  122. Trinh, T.H., Nguyen, D.K., Gan, B.S. and Alexandrov, S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  123. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423
  124. Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plate", J Sound Vib, 272, 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7
  125. 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
  126. Zhang, H., Jiang, J.K. and Zhang, Z.C. (2014), "Threedimensional elasticity solutions for bending of generally supported thick functionally graded plates", Appl. Math. Mech., 35(11), 1467-1478. https://doi.org/10.1007/s10483-014-1871-7
  127. 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
  128. Zhou, D., Cheung, Y.K., Au, F.T.K. and Lo, S.H. (2002), " Threedimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solids Struct., 39, 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2
  129. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, 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
  130. 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., (In press).

피인용 문헌

  1. A refined HSDT for bending and dynamic analysis of FGM plates vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.105