Advances in materials Research

  • 제7권2호
  • /
  • Pages.119-136
  • /
  • 2018
  • /
  • 2234-0912(pISSN)
  • /
  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates

  • 투고 : 2019.01.10
  • 심사 : 2019.03.13
  • 발행 : 2018.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, static and vibration analysis for anti-symmetric cross-ply and angle- ply carbon/glass hybrid laminates rectangular composite plate are presented. In this analysis, the equations of motion for simply supported thick laminated hybrid rectangular plates are derived and obtained through the use of Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle- ply laminates are obtained using Navier solution. The effects of side-to-thickness ratio, aspect ratio, and lamination schemes on the fundamental frequencies loads are investigated. The study concludes that shear deformation laminate theories accurately predict the behavior of composite laminates, whereas the classical laminate theory over predicts natural frequencies. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behaviors of anti-symmetric cross-ply and angle- ply hybrid laminated composite plates.

키워드

과제정보

연구 과제 주관 기관 : Ministry of Foreign Affairs and International Development (MAEDI), Ministry of National Education, Higher Education and Research (MENESR)

참고문헌

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/SCS.2017.25.6.693
  2. Abdelhak, Z., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Thermal buckling of functionally graded plates using a n-order four variable refined theory", Adv. Mater. Res., 4(1), 31-44. https://doi.org/10.12989/amr.2015.4.1.31
  3. Abdelhak, Z., Hadji, L., Khelifa, Z., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory", Wind Struct., 22(3), 291-305. https://doi.org/10.12989/was.2016.22.3.291
  4. Abderezak, R., Hassaine Daouadji, T., Abbes, B., Rabia, B., Belkacem, A. and Abbes, F. (2017), "Elastic analysis of interfacial stress concentrations in CFRP-RC hybrid beams: Effect of creep and shrinkage", Adv. Mater. Res., 6(3), 257-278. https://doi.org/10.12989/AMR.2017.6.3.257
  5. Abualnour, M., Houari, M.S.A., Tounsi, 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
  6. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech.., 65(4), 453-464.
  7. Bakhadda, B., Bouiadjra, M.B., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/WAS.2018.27.5.311
  8. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/EAS.2018.14.2.103
  9. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-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
  10. Belkacem, A. and Hassaine Daouadji, T. (2016c), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223
  11. Belkacem, A., Hassaine Daouadji, T. and Rabahi, A. (2016b), "A simple higher order shear deformation theory for bending, buckling, and dynamic of laminated composite plates", J. Adv. Struct. Eng, 8, 103-117. https://doi.org/10.1007/s40091-016-0109-x
  12. Belkacem, A., Hassaine Daouadji, T., Abbas, B. and Rabahi, A. (2016), "Buckling and free vibration analysis of laminated composite plates using an efficient and simple higher order shear deformation theory", J. Mech. Industry, 17(5), 512. https://doi.org/10.1051/meca/2015112
  13. Belkacem, A., Hassaine Daouadji, T., Benferha, R. and Hadji, L. (2016a), "An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions", Earthq. Struct., 11(1), 63-82. https://doi.org/10.12989/eas.2016.11.1.063
  14. Belkacem, A., Hassaine Daouadji, T., Rabia, B. and Hadji, L. (2016), "An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions", Earthq. Struct., 11(1), 63-82. https://doi.org/10.12989/eas.2016.11.1.063
  15. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/SEM.2018.66.6.761
  16. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "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
  17. Benachour, A., Hassaine Daouadji, T., Ait atman, H., Tounsi, A, Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient using", Compos. Part B Eng., 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  18. Benferhat, R., Hassaine Daouadji, T. and Mansour, M.S. (2014), "A higher order shear deformation model for bending analysis of functionally graded plates", Transact. Indian Inst. Metal, 68(1), 7-16. https://doi.org/10.1007/s12666-014-0428-1
  19. Benhenni, M., Hassaine Daouadji, T., Abbes, B., LI, Y.M. and Abbes, F. (2018), "Analytical and numerical results for free vibration of laminated composites plates", J. Chem. Molecul. Eng., 12(6), 300-304.
  20. Bensattalah, T., Bouakkaz, K., Zidour, M. and Hassaine Daouadji, T. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339
  21. Bensattalah, T., Zidour, M., Meziane, M.A.A., Hassaine Daouadji, T. and Tounsi, A. (2018), "Critical buckling load of carbon nanotube with non-local Timoshenko beam using the differential transform method", Int. J. Civil Environ. Eng., 12(6).
  22. Berthelot, J.M. (1992), Materiaux Composites: Comportement Mecanique et Analyse Des Structures, Tec & Doc Lavoisier, Paris.
  23. Bouadi, A., Bousahla, A. A., Houari, M. S. A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/ANR.2018.6.2.147
  24. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech.., 66(1), 61-73.
  25. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech.., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
  26. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  27. 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
  28. Chedad, A., Hassaine Daouadji, T., Abderezak, R., Belkacem, A., Abbes, B., Rabia, B. and Abbes, F. (2017), "A high-order closed-form solution for interfacial stresses in externally sandwich FGM plated RC beams", Adv. Mater. Res., 6(4), 317-328. https://doi.org/10.12989/AMR.2017.6.4.317
  29. 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
  30. 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
  31. 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.
  32. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/SCS.2018.27.1.109
  33. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015b), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., 9(3), 361-372. https://doi.org/10.12989/gae.2015.9.3.361
  34. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Dynamic behavior of FGM beam using a new first shear deformation theory", Earthq. Struct., 10(2), 451-461. https://doi.org/10.12989/eas.2016.10.2.451
  35. Hadji, L., Hassaine Daouadji, T., Tounsi, A. and Adda Bedia, E.A., (2015a), "A n-order refined theory for bending and free vibration of functionally graded beams", Struct. Eng. Mech.., 54(5), 923-936. https://doi.org/10.12989/sem.2015.54.5.923
  36. Hadji, L., Hassaine Daouadji, T., Tounsi, A. and Adda 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
  37. Hadji, L., Khalifa, Z., Hassaine Daouadji, T., Tounsi, A. and Adda bedia, E.A. (2015), "Static bending and free vibration of FGM beam using an exponential shear deformation theory", Coupled Syst. Mech., 4(1), 99-114. https://doi.org/10.12989/csm.2015.4.1.099
  38. Hassaine Daouadj, T. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Design, 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057
  39. Hassaine Daouadji, T. and Adim, B. (2016a), "Theoretical analysis of composite beams under uniformly distributed load", Adv. Mater. Res., 5(1), 1-9. https://doi.org/10.12989/amr.2016.5.1.001
  40. Hassaine Daouadji, T. and Belkacem, A. (2016c), "An analytical approach for buckling of functionally graded plates" Adv. Mater. Res., 5(3), 141-169. https://doi.org/10.12989/amr.2016.5.3.141
  41. Hassaine Daouadji, T. and Belkacem, A. (2017), "Mechanical behaviour of FGM sandwich plates using a quasi-3Dhigher order shear and normal deformation theory", Struct. Eng. Mech., 61(1), 49-63. https://doi.org/10.12989/sem.2017.61.1.049
  42. Hassaine Daouadji, T. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631
  43. Hassaine Daouadji, T. and Tounsi, A. and Adda Bedia, E.A. (2013), "Analytical solution for bending analysis of functionally graded plates", Scientia Iranica, Transactions B Mech. Eng., 20, 516-523.
  44. Hassaine Daouadji, T., Abdelaziz, H.H., Tounsi, A. and Adda bedia, E.A. (2012), "A new hyperbolic shear deformation theory for bending analysis of functionally graded plates", Modelling Simul. Eng., 10, 1-10.
  45. Hassaine Daouadji, T., Abdelaziz, H.H., Tounsi, A. and Adda bedia, E.A. (2013a), "Elasticity solution of a Cantilever functionally graded beam", Appl. Compos. Mater., 20(1), 1-15. https://doi.org/10.1007/s10443-011-9243-6
  46. Hassaine Daouadji, T., Belkacem, A. and Benferha, R. (2016a), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035
  47. Hassaine Daouadji, T., Benferha, R. and Belkacem, A. (2016b), "A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load", Adv. Mater. Res., 5(2), 107-120. https://doi.org/10.12989/amr.2016.5.2.107
  48. Hassaine Daouadji, T., Benferha, R. and Belkacem, A. (2016b), "Bending analysis of an imperfect advanced composite plates resting on the elastic foundations", Coupled Syst. Mech., 5(3), 269-285. https://doi.org/10.12989/csm.2016.5.3.269
  49. Hassaine Daouadji, T., Tounsi, A, Hadji, L., Abdelaziz, H.H. and Adda bedia, E.A. (2012), "A theoretical analysis for static and dynamic behavior of functionally graded plates", Mater. Phys. Mech., 14, 110-128.
  50. Hassaine Daouadji, T., Tounsi, A. and Adda bedia, E.A. (2013b), "A new higher order shear deformation model for static behavior of functionally graded plates", Adv. Appl. Math. Mech., 5(3), 351-364. https://doi.org/10.4208/aamm.11-m11176
  51. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., 65(5), 621-631 https://doi.org/10.12989/SEM.2018.65.5.621
  52. Kant, T. and Pandya, B.N. (1988), "A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates", Compos. Struct., 9(3), 215-264. https://doi.org/10.1016/0263-8223(88)90015-3
  53. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Solids Struct., 40, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  54. Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", Proc. IMechE, 223(2), 53-62.
  55. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Walled Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  56. Khalifa, Z., Hadji, L., Hassaine Daouadji, T. and Bourada, M. (2018), "Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. https://doi.org/10.12989/SEM.2018.67.2.125
  57. Khalifa, Z., Hassaine Daouadji, T., Hadji, L. Tounsi, A. and Adda Bedia, E.A. (2016), "A new higher order shear deformation model of functionally graded beams based on neutral surface position", Transact. Indian Inst. Metal, 69(3), 683-691. https://doi.org/10.1007/s12666-015-0540-x
  58. Mantari, J.L., Oktem, A.S. and Soares, C.G. (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. of Solid. Struct., 49(1), 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008
  59. Mazari, M., Hadji, L., Hassaine Daouadji, T., 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
  60. 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
  61. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38.
  62. Mohan, P.R., Naganarayana, B.P. and Prathap, G. (1994), "Consistent and variationally correct finite elements for higher-order laminated plate theory", Compos. Struct., 29(4), 445-456. https://doi.org/10.1016/0263-8223(94)90113-9
  63. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/SSS.2018.21.4.397
  64. Noor, A.K. (1975), "Stability of multilayered composite plate", Fibre Sci. Technol., 8, 81-89. https://doi.org/10.1016/0015-0568(75)90005-6
  65. Noor, K. (1973), "Free vibrations of multilayered composite plates", AIAA J., 11(7), 1038-1039. https://doi.org/10.2514/3.6868
  66. Oktem, A.S. and Chaudhuri, R. (2007), "A Fourier solution to a thick cross-ply Levy type clamped plate problem", Compos. Struct., 79(4), 481-492. https://doi.org/10.1016/j.compstruct.2006.02.007
  67. Oktem, A.S. and Chaudhuri, R. (2008), "Boundary discontinuous Fourier analysis of thick cross-ply clamped plates", Compos. Struct., 82(4), 539-548. https://doi.org/10.1016/j.compstruct.2007.02.001
  68. Rabahi, A., Hassaine Daouadji, T., Rabia, B. and Adim, B. (2018), "Nonlinear analysis of damaged RC beams strengthened with glass fiber reinforced polymer plate under symmetric loads", Earthq. Struct., 15(2), 113-122. https://doi.org/10.12989/EAS.2018.15.2.113
  69. Rabia, B., Hassaine Daouadji, T. and Mansour, M.S. (2016a), "Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory", Comptes Rendus Mecanique, 344(9), 631-641. https://doi.org/10.1016/j.crme.2016.03.002
  70. Rabia, B., Hassaine Daouadji, T., Hadji, L. and Mansour, M.S. (2016b), "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
  71. Rabia, B., Hassaine Daouadji, T., Mansour, M.S. and Hadji, L. (2016c), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(5), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429
  72. Rabia, B., Rabahi, A., Hassaine Daouadji, T., Abbes, B., Adim, B. and Abbes, F. (2018), "Analytical analysis of the interfacial shear stress in RC beams strengthened with prestressed exponentially-varying properties plate", Adv. Mater. Res., 7(1), 29-44. https://doi.org/10.12989/amr.2018.7.1.029
  73. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl Mech, Trans ASME, 51, 745-752. https://doi.org/10.1115/1.3167719
  74. Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", Handbook of Ceramics and Composites, Marcel Dekker, New York, U.S.A., 413-450.
  75. 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
  76. Sayyad, A.S. and Ghugal, Y.M. (2014), "Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory", Struct. Eng. Mech., 51(5), 867-891. https://doi.org/10.12989/sem.2014.51.5.867
  77. Srinivas, S. and Rao, A.K. (1970), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates", Int. J. Solids Struct., 6, 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4
  78. Stavski, Y. (1965), "On the theory of symmetrically heterogeneous plates having the same thickness variation of the elastic moduli", Topics in Applied Mechanics, Elsevier, New York, U.S.A.
  79. Swaminathan, K. and Patil, S.S. (2007), "Higher order refined computational model with 12 degrees of freedom for the stress analysis of antisymmetric angle-ply plates: Analytical solutions", Compos, Struct., 80(4), 595-608. https://doi.org/10.1016/j.compstruct.2006.07.006
  80. Tlidji, Y., Hassaine Daouadji, T., Hadji, L., Tounsi, A. and Adda bedia, E.A. (2014), "Elasticity solution for bending response of functionally graded sandwich plates under thermo mechanical loading", J. Thermal Stress, 37, 852-869. https://doi.org/10.1080/01495739.2014.912917
  81. Tounsi, A., Sid Ahmed, H., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  82. Whiteney, J.M. (1972), "Stress analysis of thick laminated composite and sandwich plates", J. Compos. Mater., 6(3), 426-440. https://doi.org/10.1177/002199837200600301
  83. Whitney, J.M. and Sun, C.T. (1973), "A higher-order theory for extensional motion of laminated composites", J. Sound Vib., 30(1), 85-97. https://doi.org/10.1016/S0022-460X(73)80052-5
  84. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/SSS.2018.21.1.015
  85. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/SSS.2018.21.1.065
  86. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519
  87. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  88. Zenkour, A.M. (2004), "Analytical solution for bending of cross-ply laminated plates under thermomechanical loading", Compos. Struct., 65(3-4), 367-379. https://doi.org/10.1016/j.compstruct.2003.11.012
  89. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Modell., 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  90. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/SCS.2018.26.2.125
  91. Zooubida, K., Hassaine Daouadji, T., Hadji, L., Tounsi, A. and Adda bedia, E.A., (2016), "A new higher order shear deformation model of functionally graded beams based on neutral surface position", Transact. Indian Inst. Metal, 69(3), 683-691. https://doi.org/10.1007/s12666-015-0540-x

피인용 문헌

  1. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2018, https://doi.org/10.12989/amr.2020.9.4.265
  2. Thermo-mechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation vol.9, pp.6, 2018, https://doi.org/10.12989/csm.2020.9.6.499
  3. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  4. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2018, https://doi.org/10.12989/sem.2021.77.2.217
  5. Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations vol.77, pp.6, 2018, https://doi.org/10.12989/sem.2021.77.6.797
  6. Modeling and analysis of the imperfect FGM-damaged RC hybrid beams vol.6, pp.2, 2018, https://doi.org/10.12989/acd.2021.6.2.117
  7. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2018, https://doi.org/10.12989/amr.2021.10.3.169