DOI QR코드

DOI QR Code

A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates

  • Chikr, Sara Chelahi (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique) ;
  • Kaci, Abdelhakim (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique) ;
  • Yeghnem, Redha (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2019.03.26
  • 심사 : 2019.07.30
  • 발행 : 2019.12.10

초록

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

키워드

참고문헌

  1. Aaleti, S. and Sritharan, S. (2009), "A simplified analysis method for characterizing unbonded post-tensioned precast wall systems", Eng. Strcut., 31(12), 2966-2975. https://doi.org/10.1016/j.engstruct.2009.07.024.
  2. 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.
  3. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A., 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.
  4. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T., Alhodaly, M.S. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res.,57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175.
  5. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
  6. Ahouel, M., Houari, M.S.A., Adda Bedia, 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 Atmane, H, Tounsi, A., Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", International J. Mech. Mater. Design, 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x.
  8. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B Eng., 96,136-152. https://doi.org/10.1016/j.compositesb.2016.04.035.
  9. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070.
  10. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A, 123, 296. https://doi.org/10.1007/s00339-017-0854-0
  11. Alibeigloo, A., Liew, K.M. (2014), "Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity", Compos Struct, 113, 23-30. https://doi.org/10.1016/j.compstruct.2014.03.004.
  12. Alshorbagy, A.E., Eltaher, M.A., Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006.
  13. Ambartsumian, S.A. (1958), "On the theory of bending plates", Izv Otd Tech Nauk AN SSSR, 5, 69-77. https://doi.org/10.1002/sapm1944231184.
  14. 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.
  15. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Alwabli, A.S. (2018a), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  16. Attia, M.A., Eltaher, M.A., Soliman, A., Abdelrahman, A.A., Alshorbagy, A.E. (2018b), "Thermoelastic crack analysis in functionally graded pipelines conveying natural gas by an FEM", J. Appl. Mech., 10(4), https://doi.org/10.1142/S1758825118500369.
  17. Avcar, M and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11, 232. https://doi.org/10.1007/s12517-018-3579-2.
  18. Ayat, H., Kellouche, Y., Ghrici, M., Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Design, 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  19. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A., 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.
  20. Behera, S., Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.
  21. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A., 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.
  22. Belabed, Z, Houari , MSA, Tounsi, A, Mahmoud, SR, Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. B Eng., 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. http://dx.doi.org/10.12989/scs.2015.18.4.1063.
  25. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017a), "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.
  26. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "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. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J Braz. Soc. Mech. Sci.Eng., 38, 265-275. https://doi.org/10.1007/s40430-015-0354-0.
  28. Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F., Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/eas.2017.13.3.255.
  29. Benahmed, A, Houari, MSA, Benyoucef, S, Belakhdar, K, Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomechan Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.
  30. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019.
  31. Bendaho, B., Belabed, Z., Bourada, M., Benatta, M.A., Bourada, F. and Tounsi, A. (2019), "Assessment of new 2D and quasi-3D Nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates", Adv. Nano Res., 7(4), 279-294. https://doi.org/10.12989/anr.2019.7.4.277.
  32. 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.
  33. Berghouti, H., Adda Bedia, E.A. Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  34. Bensattalah, T., Zidour, M., Daouadji, T.S. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021.
  35. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R, 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. Sandwich Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888.
  36. Besseghier, A, Houari, MSA, Tounsi, A, Mahmoud, SR. (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.
  37. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H., 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.
  38. Bouafia, K., Kaci, A., Houari, M. S. A., Benzair, A., 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.
  39. Bouanati, S., Benrahou, K.H., Ait Atmane, H., Ait Yahia, S., Bernard, F., Tounsi, A., Adda Bedia, E.A. (2019), "Investigation of wave propagation in anisotropic plates via quasi 3D HSDT", Geomech. Eng., 18(1), 85-96. https://doi.org/10.12989/gae.2019.18.1.085.
  40. 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.
  41. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Comp. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085.
  42. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S., Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061.
  43. Boukhari, A., Ait Atmane, H., Houari, M.S.A., 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.
  44. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  45. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  46. 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.
  47. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., 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.
  48. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A., 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.
  49. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409.
  50. 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.
  51. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computat. Methods, 11(6), 1350082. https://doi.org/10.1142/S0219876213500825.
  52. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191.
  53. Carrera, E, Brischetto, S, Cinefra, M, Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. B Eng, 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  54. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  55. Chen, CS, Hsu, CY, Tzou, G.J. ( 2009), "Vibration and stability of functionally graded plates based on a higher-order deformation theory", J. Reinforced Plastics Compos., 28(10), 1215-1234. https://doi.org/10.1177%2F0731684408088884. https://doi.org/10.1177/0731684408088884
  56. Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H., Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res.,54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1
  57. 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.
  58. Chih-Ping, W, Hao-Yuan, L. (2010), "An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates", Compos. Struct., 92(10), 2591-2605. https://doi.org/10.1016/j.compstruct.2010.01.022.
  59. Dai, HL, Rao, YN, Dai, T. (2016), "A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000-2015", Compos. Struct., 152, 199-225. https://doi.org/10.1016/j.compstruct.2016.05.042.
  60. Dean, J., Fallah, A.S., Brown, P.M., Louca, L.A., Clyne, T.W. (2011), "Energy absorption during projectile perforation of lightweight sandwich panels with metallic fibre cores", Compos. Struct., 93(3), 1089-1095. https://doi.org/10.1016/j.compstruct.2010.09.019.
  61. 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.
  62. Draoui, A., Zidour, M., Tounsi, A., Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  63. 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.
  64. Eltaher, M.A., Mohamed, N., Mohamed, S.A., Seddek, L.F. (2019a), "Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations", Appl. Math. Model., 75, 414-445. https://doi.org/10.1016/j.apm.2019.05.026.
  65. Eltaher, M.A., Mohamed, N., Mohamed, S., Seddek, L.F. (2019b), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, 136-157. https://doi.org/10.4028/www.scientific.net/JNanoR.57.136.
  66. Eltaher, M. A., Attia, M. A., Soliman, A. E. and Alshorbagy, A. E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097.
  67. Eltaher, M.A., Fouda, N., El-midany, T., Sadoun, A.M. (2018b), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. MEch. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.
  68. Eltaher, M.A., Khairy, A., Sadoun, A.M., Omar, F.A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.
  69. Eltaher, M.A., Alshorbagy, A.E., Mahmoud, F.F. (2013), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039.
  70. Emam, S., Eltaher, M., Khater, M., Abdalla, W. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.
  71. Emam, S., Eltaher, M.A. (2016), "Buckling and postbuckling of composite beams in hygrothermal environments", Compos. Struct., 152, 665-675. https://doi.org/10.1016/j.compstruct.2016.05.029.
  72. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, 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.
  73. Fazzolari, F.A. (2015), "Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions", Compos Struct, 121,197-210. https://doi.org/10.1016/j.compstruct.2014.10.039.
  74. Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Polit, O. (2011), "Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations", Compos. Part B Eng., 42(5), 1276-1284. https://doi.org/10.1016/j.compositesb.2011.01.031,
  75. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A., 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.
  76. Gupta, N. (2007), "A functionally graded syntactic foam material for high energy absorption under compression", Mater Lett., 61(4-5), 979-982. https://doi.org/10.1016/j.matlet.2006.06.033.
  77. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, A., Tounsi, A., Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. https://doi.org/10.12989/scs.2017.25.6.717.
  78. Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0.
  79. 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 Comp. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235.
  80. Hebali, H., Bakora, A., Tounsi, A., 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.
  81. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A., 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(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665.
  82. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A., Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636219845841.
  83. 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.
  84. Jha, D.K., Kant, T., Singh, R.K. (2012), "Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates", Nucl Eng Des, 250, 8-13. https://doi.org/10.1016/j.nucengdes.2012.05.001.
  85. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A., 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.
  86. Kadari, B., Bessaim, A., Tounsi, A., Heireche, H., Bousahla, A.A. and Houari, M.S.A. (2018), "Buckling analysis of orthotropic nanoscale plates resting on elastic foundations", J. Nano Res., 55, 42-56. https://doi.org/10.4028/www.scientific.net/JNanoR.55.42.
  87. 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.
  88. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9.
  89. Karami, B., Janghorban, M., Tounsi, A. (2019a), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.
  90. Karami, B., Janghorban, M., Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  91. Karami, B., Shahsavari, D., Janghorban, M., Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  92. Karami, B., Janghorban, M. and Tounsi, A. (2018a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput.. https://doi.org/10.1007/s00366-018-0664-9.
  93. Karami, B., Janghorban, M., Shahsavari, D., Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  94. Karami, B., Janghorban, M., Tounsi, A. (2018c), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  95. Karami, B., Janghorban, M., Tounsi, A. (2018d), "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.
  96. Karami, B., Janghorban, M., 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.
  97. Kashtalyan, M., Menshykova, M. (2009), "Three-dimensional elasticity solution for sandwich panels with a functionally graded core", Compos Struct, 87 (1), 36-43. https://doi.org/10.1016/j.compstruct.2007.12.003.
  98. 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., Int. J., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.
  99. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Touns, A., Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a fourvariable quasi 3D HSDT", Eng. Comput.., https://doi.org/10.1007/s00366-019-00732-1.
  100. Kirigulige, MS, Kitey, R, Tippur, HV. (2005), "Dynamic fracture behaviour of model sandwich structures with functionally graded core: A feasibility study", Compos Sci Technol, 65, 1052-1068. https://doi.org/10.1016/j.compscitech.2004.10.029.
  101. 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.
  102. Koizumi, M. (1997), "FGM activities in Japan", Composites Part B: Engineering, 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  103. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023.
  104. Krenich, F., Heireche, H., Houari, M.S.A., Tounsi, A. (2017), "A novel nonlocal four variable platetheory for thermal stability of single-layered graphene sheets embedded in anelastic substrate medium", Curr. Nanomater., 1, 215-222. https://doi.org/10.2174/2405461501666161130121643
  105. 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.
  106. Levinson, M. (1980), "An accurate simple theory of static and dynamics of elastic plates", Mech. Res. Commun., 7, 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  107. Levy, M. (1877), "Memoire sur la theorie des plaques elastique planes", J Math Appl, 30, 219-306.
  108. Li, R.R. and Batra, R. (2013), "Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams", Compos. Struct., 95, 5-9. https://doi.org/10.1016/j.compstruct.2012.07.027.
  109. Librescu, L., Hause, T. (2000), "Recent developments in the modeling and behavior of advanced sandwich constructions: a survey", Compos. Struct., 48(1-3), 1-17. https://doi.org/10.1016/S0263-8223(99)00068-9.
  110. Lindstrom, A., Hallstrom, S. (2010), "Energy absorption of SMC/balsa sandwich panels with geometrical triggering features", Compos Struct, 92(11), 2676-2684. https://doi.org/10.1016/j.compstruct.2010.03.018.
  111. Liu, B., Ferreira, A.J.M., Xing, Y.F., Neves, A.M.A. (2016), "Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method", Compos Struct, 136, 546-553. https://doi.org/10.1016/j.compstruct.2015.10.044.
  112. Lu, C.F., Lim, C.W., Chen, W.Q. (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16, 576-584. https://doi.org/10.1080/15376490903138888.
  113. Lu, C.F., Lim, C.W., Chen, W.Q. (2009), "Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions", Int. J. Numer. Meth. Eng., 79, 25-44. https://doi.org/10.1002/nme.2555.
  114. Mahi, A., Adda Bedia, E.A., 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.
  115. Mahmoudi, A., Benyoucef, A., Tounsi, A., Benachour, A., Adda Bedia, E.A., Mahmoud, S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636217727577.
  116. Mantari, J.L., Guedes Soares, C. (2012), "Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates", Compos. Struct., 94(8), 2561-2575. https://doi.org/10.1016/j.compstruct.2012.02.019.
  117. Mantari, J.L., Guedes Soares, C. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B Eng., 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036.
  118. Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct., 87(4), 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002.
  119. Meftah, A., Bakora, A., Zaoui, F.Z., Tounsi, A., Adda Bedia, E.A. (2017), "A non-polynomial fourvariable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Steel Compos Struct., 23(3), 317-330. https://doi.org/10.12989/scs.2017.23.3.317
  120. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct.Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  121. 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 Comp. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  122. Meziane, M.A.A., 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.
  123. Mindlin, RD. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  124. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A., Ford, R.G. (1999), "Functionally graded materials: design, processing and applications", Kluwer Academic Publishers.
  125. Mohamed, N., Eltaher, M.A., Mohamed, S., and Seddek, L.F., (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
  126. Mohammadimehr, M., Atifeh, S.J., Navi, B.R. (2018), "Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings", J. Vib. Control, 24(15), 3471-3486. https://doi.org/10.1177%2F1077546317706887. https://doi.org/10.1177/1077546317706887
  127. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A., 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.
  128. Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A., 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.
  129. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012a), "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. https://doi.org/10.1016/j.compositesb.2011.08.009.
  130. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012b), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.
  131. Neves, A.M. A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012c), "Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions", ZAMM - J. Appl. Math. Mech. 92 (9), 749-766. https://doi.org/10.1002/zamm.201100186.
  132. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  133. Pollien, A., Conde, Y., Pambaguian, L. and Mortensen, A. (2005), "Graded open-cell aluminum foam core sandwich beams", Mater. Sci. Eng. A, 404, 9-18. https://doi.org/10.1016/j.msea.2005.05.096.
  134. 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. Part B Eng., 35(6-8), 685-697. https://doi.org/10.1016/j.compositesb.2004.02.004.
  135. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, Florida, USA.
  136. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", J. Aerosp. Lightweight Struct., 1(1), 1-21. http://dx.doi.org/10.3850/S201042861100002X.
  137. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phys., 23, 184-191. https://doi.org/10.1002/sapm1944231184.
  138. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77. https://doi.org/10.1177/002199836900300316.
  139. Sekkal, M., Fahsi, B., Tounsi, A., Mahmoud, S.R. (2017a), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., 25(4), 389-401. https://doi.org/10.12989/scs.2017.25.4.389.
  140. Sekkal, M., Fahsi, B., Tounsi, A., Mahmoud, S.R. (2017b), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. https://doi.org/10.12989/sem.2017.64.6.737.
  141. Selmi, A., Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroengineering, 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445.
  142. Semmah, A., Heireche, H., Bousahla, A.A., Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.
  143. Shahsavari, D., Karami, B., Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053.
  144. Shen, H.S., Li, S.R. (2008), "Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties", Compos Pt B-Eng, 39(2), 332-344. https://doi.org/10.1016/j.compositesb.2007.01.004.
  145. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos Struct, 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  146. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech, 94, 195-200. https://doi.org/10.1007/BF01176650.
  147. Soliman, A.E., Eltaher, M.A., Attia, M.A, Alshorbagy, A.E. (2018), "Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility", Struct. Eng. Mech., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085.
  148. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M., Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070.
  149. Talha, M., Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.
  150. Thai, H.T., Kim, S.E. (2015), "A review of theories for the modeling and analysis of functionally graded plates and shells", Compos. Struct., 128, 70-86. https://doi.org/10.1016/j.compstruct.2015.03.010.
  151. Tounsi, A, Houari, MSA, Benyoucef, S., 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.
  152. Tounsi, A., Ait Atmane, H., Khiloun, M., Sekkal, M., Taleb, O., Bousahla, A.A. (2019), "On buckling behavior of thick advanced composite sandwich plates", Compos. Mater. Eng., 1(1), 1-19. https://doi.org/10.12989/cme.2019.1.1.001.
  153. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  154. Vel, S.S., Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272, 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7.
  155. Vinson, J.R. (2001), "Sandwich structures", Appl. Mech. Rev., 54(3), 201-214. https://doi.org/10.1115/1.3097295.
  156. Vinson, J.R. (2005), "Sandwich structures: past, present, and future", Sandwich Structures 7: Advancing with Sandwich Structures and Materials. Netherlands, Springer, Germany. 3-12.
  157. Wu, C.P., Huang, S.E. (2004), "Three-dimensional solutions of functionally graded piezothermo-elastic shells and plates using a modified Pagano method", Comput. Mater. Continua, 12, 251-282.
  158. Yaghoobi, H., Valipour, M.S., Fereidoon, A., Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM", Steel Compos. Struct., 17(5), 753-776. http://dx.doi.org/10.12989/scs.2014.17.5.753.
  159. Yahia, S.A., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. http://dx.doi.org/10.12989/sem.2015.53.6.1143.
  160. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A., 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.
  161. Yeghnem, R., Guerroudj, H.Z., Amar, LHH., Meftah, S.A., Benyoucef, S., Tounsi, A., Adda Bedia, E.A. (2017), "Numerical modeling of the aging effects of RC shear walls strengthened by CFRP plates: A comparison of results from different "code type" models", Comput. Concrete, 19(5), 579-588. https://doi.org/10.12989/cac.2017.19.5.579.
  162. Ying, J., Lu, C.F., Lim, C.W. (2009), "3D thermoelasticity solutions for functionally graded thick plates", J. Zhejiang Univ. Sci, A, 10(3), 327-336. https://doi.org/10.1631/jzus.A0820406.
  163. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A., 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.
  164. Younsi, A., Tounsi, A, Zaoui, F.Z., Bousahla, A.A., 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.
  165. Zaoui, F.Z., Ouinas, D., 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.
  166. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F., Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  167. Zemri, A., Houari, M.S.A., Bousahla, A.A., 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.
  168. Zenkour, A. (2007), "Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate", Archive Appl. Mech., 77(4), 197-214. https://doi.org/10.1007/s00419-006-0084-y.
  169. Zenkour, A., Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos Struct, 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012.
  170. Zenkour, A. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2 - buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  171. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A., Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153. https://doi.org/10.12989/sem.2017.64.2.145.
  172. Zidi, M., Tounsi, A., Houari, M.S.A..Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol. ,34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001.
  173. Zine, A., Tounsi, A., Draiche, K., Sekkal, M., 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.

피인용 문헌

  1. Modeling and analysis of the imperfect FGM-damaged RC hybrid beams vol.6, pp.2, 2019, https://doi.org/10.12989/acd.2021.6.2.117
  2. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2019, https://doi.org/10.12989/amr.2021.10.3.169