Steel and Composite Structures

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Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory

  • Bouamoud, Ahmed (Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Djilali Liabes of Sidi Bel Abbes) ;
  • Boucham, Belhadj (Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Djilali Liabes of Sidi Bel Abbes) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2019.04.04
  • Accepted : 2019.06.24
  • Published : 2019.09.10
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Abstract

In this work, a four-variable refined plate model is applied to study the thermomechanical bending of two kinds of functionally graded material (FGM) sandwich plates. The sandwich core of one kind is isotropic with the FGM face sheets whereas in the second kind, the sandwich core is FGM with the isotropic and homogeneous face sheets. By considering only four unknown variables, the governing equations are written based on the principle of virtual work and then Navier method is employed to solve these equations. Deflections and stresses of two kinds of FGM sandwich structures are analyzed and discussed. The validity and efficiency of the proposed model is checked by comparing it with various available solutions in the literature. The effects of volume fraction distribution, geometric ratio and thermal load on thermomechanical bending properties of FGM sandwich plate are investigated in detail.

Keywords

References

  1. Abazid, M.A., Alotebi, M.S. and Sobhy, M. (2018), "A novel shear and normal deformation theory for hygrothermal bending response of FGM sandwich plates on Pasternak elastic foundation", Struct. Eng. Mech., Int. J., 67(3), 219-232. https://doi.org/10.12989/sem.2018.67.3.219
  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 ree vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 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. 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
  4. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and 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., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  7. Ait Atmane, H., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x
  8. Ait Sidhoum, I., Boutchicha, D., Benyoucef, S. and Tounsi, A. (2017), "An original HSDT for free vibration analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(6). 735-745. https://doi.org/10.12989/scs.2017.25.6.735
  9. Akbas, S.D. (2017), "Thermal effects on the vibration of functionally graded deep beams with porosity", Int. J. Appl. Mech., 9(5), 1750076. https://doi.org/10.1142/S1758825117500764
  10. 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
  11. Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140
  12. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, Int. J., 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  13. 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., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  14. 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., Int. J., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453
  15. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  16. Avcar, M. and Alwan, H.H.A. (2017), "Free vibration of functionally graded Rayleigh beam", Int. J. Eng. Appl. Sci., 9(2), 127-137. http://dx.doi.org/10.24107/ijeas.322884
  17. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2
  18. Bakhadda, B., Bachir Bouiadjra, M., 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., Int. J., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311
  19. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Computat. Des., Int. J., 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213
  20. 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
  21. 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., Int. J., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103
  22. Belalia, S.A. (2017), "Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates", J. Sandw. Struct. Mater., 109963621770129. https://doi.org/10.1177/1099636217701299
  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., Int. J., 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., Int. J.,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, 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. (2017a), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695
  27. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017b), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270. https://doi.org/10.12989/scs.2017.25.3.257
  28. Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., Int. J.,13(3), 255-265. https://doi.org/10.12989/eas.2017.13.3.255
  29. 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., Int. J., 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., Int. J., 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., Int. J., 7(4), 277-292. https://doi.org/10.12989/anr.2019.7.4.277
  32. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  33. 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
  34. 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., Int. J., 7(5). [In press]
  35. 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
  36. 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., Int. J., 19(6), 601-614. https://doi.org/10.12989/sss.2017.19.6.601
  37. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, Int. J., 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  38. Birman, V., Keil, T. and Hosder, S. (2013), "Functionally graded materials in engineering", In: Thomopoulus S, Birman V, Genin GM, Editors, Structural Interfaces and Attachments in Biology, Springer, New York, USA, pp. 19-41.
  39. 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., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
  40. 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., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  41. Bouanati, S., Benrahou, K.H., Ait Atmane, H., Ait Yahia, S., Bernard, F., Tounsi, A. and Adda Bedia, E.A. (2019), "Investigation of wave propagation in anisotropic plates via quasi 3D HSDT", Geomech. Eng., Int. J., 18(1), 85-96. https://doi.org/10.12989/gae.2019.18.1.085
  42. 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., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  43. 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., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  44. 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., Int. J., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061
  45. 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., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  46. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
  47. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and 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., Int. J., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
  48. 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., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  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., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  50. 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., Int. J., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  51. 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., Int. J., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
  52. 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., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  53. 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
  54. 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., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  55. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.189
  56. Brischetto, S. (2009), "Classical and mixed advanced models for sandwich plates embedding functionally graded cores", J. Mech. Mater. Struct., 4(1), 13-33. https://doi.org/10.2140/jomms.2009.4.13
  57. Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T. and Kroplin, B. (2008), "Thermo-mechanical bending of functionally graded plates", J. Therm. Stress., 31(3), 286-308. https://doi.org/10.1080/01495730701876775
  58. Carrera, E. and Brischetto, S. (2009), "A comparison of various kinematic models for sandwich shell panels with soft core", J. Compos. Mater., 43(20), 2201-2221. https://doi.org/10.1177/0021998309343716
  59. Carrera, E. and Petrolo, M. (2010), "Guidelines and recommendations to construct theories for metallic and composite plates", AIAA J., 48(12), 2852-2866. https://doi.org/10.2514/1.J050316
  60. Carrera, E., Filippi, M. and Zappino, E. (2013), "Free vibration analysis of rotating composite blades via Carrera Unified Formulation", Compos. Struct., 106(106), 317-325. https://doi.org/10.1016/j.compstruct.2013.05.055
  61. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
  62. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "Vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., Int. J., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251
  63. Cheng, Z.Q. and Batra, R.C. (2003), "Three-dimensional thermoelastic deformations of a functionally graded elliptic plate", Compos. Part B-Eng., 31(2), 97-106. https://doi.org/10.1016/S1359-8368(99)00069-4
  64. Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and 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
  65. 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., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  66. Daouadji, T.H. and Adim, B. (2017), "Mechanical behaviour of FGM sandwich plates using a quasi-3D higher order shear and normal deformation theory", Struct. Eng. Mech., Int. J., 61(1), 49-63. https://doi.org/10.12989/sem.2017.61.1.049
  67. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2019), "Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel", Earthq. Struct., Int. J., 16(1), 55-67. https://doi.org/10.12989/eas.2019.16.1.055
  68. 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., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  69. Draoui, A., Zidour, M., Tounsi, A. and 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
  70. Ebrahimi, F. and Daman, M. (2017), "Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment", Struct. Eng. Mech., Int. J., 64(1), 121-133. https://doi.org/10.12989/sem.2017.64.1.121
  71. Ebrahimi, F. and Farazmandnia, N, (2018), "Thermal buckling analysis of functionally graded carbon nanotube-reinforced composite sandwich beams", Steel Compos. Struct., Int. J., 27(2), 149-159. https://doi.org/10.12989/scs.2018.27.2.149
  72. 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., Int. J., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585
  73. Elmossouess, B., Kebdani, S., Bachir Bouiadjra, M. and Tounsi, A. (2017), "A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 62(4), 401-415. https://doi.org/10.12989/sem.2017.62.4.401
  74. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "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
  75. 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., Int. J., 13(3), 385-410. https://doi.org/10.12989/gae.2017.13.3.385
  76. Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036
  77. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  78. Fazzolari, F.A. and Carrera, E. (2013), "Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core", J. Sound Vib., 333(5), 1485-1508. https://doi.org/10.1016/j.jsv.2013.10.030
  79. Fourn, H., Ait Atmane, H., 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., Int. J., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109
  80. Golabchi, H., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, Int. J., 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431
  81. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, A., Tounsi, A. and 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., Int. J., 25(6), 717-726. https://doi.org/10.12989/scs.2017.25.6.717
  82. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373. https://doi.org/10.1177/1099636217720373
  83. Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018a), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260-270. https://doi.org/10.1016/j.ast.2018.04.030
  84. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018b), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002
  85. Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018c), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004
  86. 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., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  87. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  88. Hirwani, C.K. and Panda, S.K. (2018), "Numerical and experimental validation of nonlinear deflection and stress responses of pre-damaged glass-fibre reinforced composite structure", Ocean Eng., 159, 237-252. https://doi.org/10.1016/j.oceaneng.2018.04.035
  89. Hirwani, C.K. and Panda, S.K. (2019), "Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure", Appl. Math. Model., 65, 303-317. https://doi.org/10.1016/j.apm.2018.08.014
  90. Hirwani, C.K., Panda, S.K. and Mahapatra, T.R. (2018a), "Thermomechanical deflection and stress responses of delaminated shallow shell structure using higher-order theories", Compos. Struct., 184, 135-145. https://doi.org/10.1016/j.compstruct.2017.09.071
  91. Hirwani, C.K., Panda, S.K. and Patle, B.K. (2018b), "Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories", Acta Mechanica, 229(8), 3453-3473. https://doi.org/10.1007/s00707-018-2173-8
  92. Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E: Low-dimens. Syst. Nanostruct., 102, 101-109. https://doi.org/10.1016/j.physe.2018.04.037
  93. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  94. 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., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  95. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631. https://doi.org/10.12989/sem.2018.65.5.621
  96. 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
  97. Kar, V.R. and Panda, S.K. (2015), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212. https://doi.org/10.1016/j.compstruct.2015.04.006
  98. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361
  99. Karami, B., Shahsavari, D. and Janghorban, M. (2018a), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143
  100. Karami, B., Janghorban, M. and Tounsi, A. (2018b), "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
  101. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  102. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201
  103. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018e), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099
  104. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019a), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036
  105. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., Int. J., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055
  106. Karami, B., Janghorban, M. and Tounsi, A. (2019c), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., Int. J., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487
  107. Katariya, P.V. and Panda, S.K. (2019), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: a finite element approach", Arab. J. Sci. Eng., 44(2), 1631-1648. https://doi.org/10.1007/s13369-018-3633-0
  108. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2018), "Bending and vibration analysis of skew sandwich plate", Aircr. Eng. Aerosp. Technol., 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087
  109. 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
  110. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and 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
  111. 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., Int. J., 63(4), 439-446. https://doi.org/10.12989/sem.2017.63.4.439
  112. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B-Eng., 28(1), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  113. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  114. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlinear Dyn., 90, 479-492. https://doi.org/10.1007/s11071-017-3676-x
  115. Kolahchi, R. and Moniri Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  116. Kolahchi, R., Safari, M. and Esmailpour, M. (2016a), "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
  117. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016b), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  118. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017a), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater. [In press] https://doi.org/10.1177/1099636217731071
  119. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  120. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017c), "Wave propagation of embedded viscoelastic FG-CNTreinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  121. Lal, A., Jagtap, K.R. and Singh, B.N. (2017), "Thermomechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Computat. Des., Int. J., 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165
  122. 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., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  123. Li, D., Deng, Z. and Xiao, H. (2016), "Thermomechanical bending analysis of functionally graded sandwich plates using fourvariable refined plate theory", Compos. Part B-Eng., 106, 107-119. https://doi.org/10.1016/j.compositesb.2016.08.041
  124. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  125. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016), "Large amplitude bending behaviour of laminated composite curved panels", Eng. Computat., 33(1), 116-138. https://doi.org/10.1108/EC-05-2014-0119
  126. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  127. Mantari, J.L. and Granados, E.V. (2015a), "Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns", Compos. Part B-Eng., 69, 317-334. https://doi.org/10.1016/j.compositesb.2014.10.009
  128. Mantari, J.L. and Granados, E.V. (2015b), "A refined FSDT for the static analysis of functionally graded sandwich plates", Thin-Wall. Struct., 90, 150-158. https://doi.org/10.1108/AEAT-11-2015-0237
  129. Mantari, J.L. and Monge, J.C. (2016), "Buckling, free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation", Int. J. Mech. Sci., 119, 170-186. https://doi.org/10.1016/j.ijmecsci.2016.10.015
  130. Marur, P.R. (1999), "Fracture behavior of functionally graded materials", Ph.D. Thesis; Auburn University, Tuscaloosa, AL, USA.
  131. Mehar, K. and Panda, S.K. (2018a), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., Int. J., 67(6), 565-578. https://doi.org/10.12989/sem.2018.67.6.565
  132. Mehar, K. and Panda, S.K. (2018b), "Thermoelastic flexural analysis of FG-CNT doubly curved shell panel", Aircr. Eng. Aerosp. Technol., 90(1), 11-23. https://doi.org/10.1108/AEAT-11-2015-0237
  133. Mehar, K. and Panda, S.K. (2019), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B: Eng., 167, 317-328. https://doi.org/10.1016/j.compositesb.2018.12.058
  134. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranica, 25(5), 2722-2737. https://doi.org/10.24200/SCI.2017.4525
  135. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443. https://doi.org/10.1177/1099636217698443
  136. 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., Int. J., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157
  137. 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
  138. 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., Int. J., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397
  139. 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., Int. J., 20(3), 369-383. https://doi.org/10.12989/sss.2017.20.3.369
  140. Na, K.S. and Kim, J.H. (2006), "Nonlinear bending response of functionally graded plates under thermal loads", J. Therm. Stress., 29(3), 245-261. https://doi.org/10.1080/01495730500360427
  141. 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. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B: Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
  142. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C. and Jorge, R.M.N. (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
  143. Nguyen, K., Thai, H.T. and Vo, T. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  144. Panyatong, M., Chinnaboon, B. and Chucheepsakul, S. (2016), "Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity", Compos. Struct., 153, 428-441. https://doi.org/10.1016/j.compstruct.2016.06.045
  145. Petrolo, M., Cinefra, M., Lamberti, A. and Carrera, E. (2015), "Evaluation of mixed theories for laminated plates through the axiomatic/asymptotic method", Compos. Part B-Eng., 76(3)-260-272. https://doi.org/10.1016/j.compositesb.2015.02.027
  146. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A-Solids, 20(5), 841-855. https://doi.org/10.1016/S0997-7538(01)01174-3
  147. 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 Institution of Mechanical Engineers, Part L: J. Mater. Des., 231(5), 463-478. https://doi.org/10.1177/1464420715600191
  148. Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., Int. J., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053
  149. Sharma, N., Mahapatra, T.R., Panda, S.K. and Katariya, P. (2018), "Thermo-acoustic analysis of higher-order shear deformable laminated composite sandwich flat panel", J. Sandw. Struct. Mater., [In press] https://doi.org/10.1177/1099636218784846
  150. Shaw, L.L. (1998), "Thermal residual stresses in plates and coatings composed of multilayered and functionally graded materials", Compos. Part B-Eng., 29(3), 199-210. https://doi.org/10.1016/S1359-8368(97)00029-2
  151. Sekkal, M., Fahsi, B., Tounsi, A. and 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., Int. J., 25(4), 389-401. https://doi.org/10.12989/scs.2017.25.4.389
  152. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017b), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., Int. J., 64(6), 737-749. https://doi.org/10.12989/sem.2017.64.6.737
  153. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445
  154. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  155. Sepahi, O., Forouzan, M.R. and Malekzadeh, P. (2010), "Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM", Compos. Struct., 92(10), 2369-2378. https://doi.org/10.1016/j.compstruct.2010.03.011
  156. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004
  157. Shen, H.S. (2002), "Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments", Int. J. Mech. Sci., 44(3), 561-584. https://doi.org/10.1016/S0020-7403(01)00103-5
  158. Suman, S.D., Hirwani, C.K., Chaturvedi, A. and Panda, S.K. (2017), "Effect of magnetostrictive material layer on the stress and deformation behaviour of laminated structure", IOP Conference Series: Mater. Sci. Eng., 178(1), 012026. https://doi.org/10.1088/1757-899X/178/1/012026
  159. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M. and Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM platesda state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070
  160. 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
  161. Tahouneh, V. (2018), "Vibration analysis of sandwich sectorial plates considering FG wavy CNT-reinforced face sheets", Steel Compos. Struct., Int. J., 28(5), 541-557. https://doi.org/10.12989/scs.2018.28.5.541
  162. Thai, H.T., Nguyen, T.K. and Vo, T. (2014), "Analysis of functionally graded sandwich plates using a new first- order shear deformation theory", Eur. J. Mech.-A/Solids., 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
  163. Tian, A., Ye, R. and Chen, Y. (2016), "A new higher order analysis model for sandwich plates with flexible core", J. Compos. Mater., 50(7), 949-961. https://doi.org/10.1177/0021998315584650
  164. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (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
  165. Tung, H.V. and Duc, N.D. (2014), "Nonlinear response of shear deformable FGM curved panels resting on elastic foundations and subjected to mechanical and thermal loading conditions", Appl. Math. Model., 38(11), 2848-2866. https://doi.org/10.1016/j.apm.2013.11.015
  166. Vel, S.S. and Batra, R.C. (2002), "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates", AIAA J., 40(7), 1421-1433. https://doi.org/10.2514/2.1805
  167. Vinson, J.R. (2001), "Sandwich structures", Appl. Mech. Rev., 54(3), 201-214. https://doi.org/10.1115/1.3097295
  168. Vinson, J.R. (2005), "Sandwich structures: past, present, and future", In: Sandwich structures 7: advancing with sandwich structures and materials, (Thomsen OT, Bozhevolnaya E, Lyckegaard A, editors), Springer, Netherlands, pp. 3-12.
  169. 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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  170. Yang, J. and Shen, H.S. (2003), "Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions", Compos. Part B-Eng., 34(2), 103-115. https://doi.org/10.1016/S1359-8368(02)00083-5
  171. 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., Int. J., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015
  172. 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., Int. J., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065
  173. 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., Int. J., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519
  174. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_2$ nano-particles", Wind Struct., Int. J., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043
  175. 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
  176. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  177. 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., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  178. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: part 1 Deflection and stresses", Int. J. Solids Struct., 42(18), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  179. Zenkour, A.M. (2013), "Bending analysis of functionally graded sandwich plates using a simple four unknown shear and normal deformations theory", J. Sandw. Struct. Mater., 15(6), 629-656. https://doi.org/10.1177/1099636213498886
  180. Zenkour, A.M. and Alghamdi, N.A. (2008), "Thermoelastic bending analysis of functionally graded sandwich plates", J. Mater. Sci., 43(8), 2574-2589. https://doi.org/10.1007/s10853-008-2476-6
  181. Zenkour, A.M and Alghamdi, N.A. (2010), "Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads", Mech. Adv. Mater. Struct., 17(6), 419-432. https://doi.org/10.1080/15376494.2010.483323
  182. Zhao, X. and Liew, K.M. (2009), "Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method", Comput. Meth. Appl. Mech. Eng., 198(33), 2796-2811. https://doi.org/10.1016/j.cma.2009.04.005
  183. Zhu, P., Zhang, L.W. and Liew, K.M. (2014), "Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrove-Galerkin approach with moving Kriging interpolation", Compos. Struct., 107, 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001
  184. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermomechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  185. 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., Int. J., 64(2), 145-153. https://doi.org/10.12989/sem.2017.64.2.145
  186. 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., Int. J., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125