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Critical thermal buckling analysis of porous FGP sandwich plates under various boundary conditions

  • Received : 2021.09.26
  • Accepted : 2023.05.16
  • Published : 2023.07.10

Abstract

Critical thermal buckling of functionally graded porous (FGP) sandwich plates under various types of thermal loading is considered. It is assumed that the mechanical and thermal nonhomogeneous properties of FGP sandwich plate vary smoothly by distribution of power law across the thickness of sandwich plate. In this paper, porosity defects are modeled as stiffness reduction criteria and included in the rule of mixture. The thermal environments are considered as uniform, linear and nonlinear temperature rises. The critical buckling temperature response of FGM sandwich plates has been analyzed under various boundary conditions. By comparing several numerical examples with the reference solutions, the results indicate that the present analysis has good accuracy and rapid convergence. Further, the effects of various parameters like distribution shape of porosity, sandwich combinations, aspect ratio, thickness ratio, boundary conditions on critical buckling temperature of FGP sandwich plate have been studied in this paper.

Keywords

Acknowledgement

This research was supported by the Algerian Ministry of Higher Education and Scientific Research (MESRS) as part of the grant for the PRFU research project n° A01L02UN140120200002 and by the University of Tiaret, in Algeria.

References

  1. Abbes, B., Benhenni, M.A., Daouadji, T.H., Abbes, F., Adim, B. and Li, Y. (2019), "Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions", Struct. Eng. Mech., 70(5), 535-549. https://doi.org/10.12989/sem.2019.70.5.535.
  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. http://doi.org/10.12989/scs.2017.25.6.693.
  3. Abdelhak, Z., Hadji, L., Daouadji, T.H. and Bedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267.
  4. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021a), "Modeling and analysis of the imperfect FGM-damaged RC hybrid beams", Adv. Comput. Des., 6(2), 117-133. http://doi.org/10.12989/acd.2021.6.2.117.
  5. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021b), "Aluminum beam reinforced by externally bonded composite materials", Adv. Mater. Res., 10(1), 23-44. http://doi.org/10.12989/amr.2021.10.1.023.
  6. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021c), "Fiber reinforced polymer in civil engineering: Shear lag effect on damaged RC cantilever beams bonded by prestressed plate", Couple. Syst. Mech., 10(4), 299-316. http://doi.org/10.12989/csm.2021.10.4.299.
  7. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021d), "New solution for damaged porous RC cantilever beamsstrengthening by composite plate", Adv. Mater. Res., 10(3), 169-194. http://doi.org/10.12989/amr.2021.10.3.169.
  8. Abderezak, R., Daouadji, T.H. and Rabia, B. (2022b), "Analysis and modeling of hyperstatic RC beam bonded by composite plate symmetrically loaded and supported", Steel Compos. Struct., 45(4), 591-603. https://doi.org/10.12989/scs.2022.45.4.591.
  9. Abderezak, R., Daouadji, T.H. and Tayeb, B. (2023), "Composite aluminum-slab RC beam bonded by a prestressed hybrid carbon-glass composite material", Struct. Eng. Mech., 85(5), 573-592. https://doi.org/10.12989/sem.2023.85.5.573.
  10. Abderezak, R., Rabia, B. and Daouadji, T.H. (2022a), "Rehabilitation of RC structural elements: Application for continuous beams bonded by composite plate under a prestressing force", Adv. Mater. Res., 11(2), 91-109. https://doi.org/10.12989/amr.2022.11.2.091.
  11. Adim, B. and Daouadji, T.H. (2016a), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223.
  12. Adim, B., Daouadji, T.H. and Abbes, B. (2016b), "Buckling analysis of anti-symmetric cross-ply laminated composite plates under different boundary conditions", Int. Appl. Mech., 52(6), 126-141. https://doi.org/10.1007/s10778-016-0787-x.
  13. Adim, B., Daouadji, T.H., Abbes, B. and Rabahi, A. (2016c), "Buckling and free vibration analysis of laminated composite plates using an efficient and simple higher order shear deformation theory", Mech. Indus., 17, 512. https://doi.org/10.1051/meca/2015112.
  14. Ahmed, R.A., Al-Maliki, A.F. and Faleh, N.M. (2020a), "Dynamic characteristics of multi-phase crystalline porous shells with using strain gradient elasticity", Adv. Nano Res., 8(2), 157-167. https://doi.org/10.12989/anr.2020.8.2.157.
  15. Ahmed, R.A., Mustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020b), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. https://doi.org/10.12989/sem.2020.76.3.413.
  16. Aicha, K., Rabia, B., Daouadji, T.H. and Bouzidene, A. (2020), "Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions", Couple. Syst. Mech., 9(6), 575-597. http://doi.org/10.12989/csm.2020.9.6.575.
  17. Amine, M. (2018), "Dynamic analysis for anti-symmetric crossply and angle-ply laminates for simply supported thick hybrid rectangular plates", Adv. Mater. Res., 7(2), 83-103. https://doi.org/10.12989/amr.2018.7.2.119.
  18. Bamdad, M., Mohammadimehr, M. and Alambeigi, K. (2020), "Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov", Steel Compos. Struct., 36(6), 671-687. https://doi.org/10.12989/scs.2020.36.6.671.
  19. Batou, B. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  20. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  21. Bendenia, N., Zidour, M., Bousahla, K.H., Bourada, F., Tounsi, A., Benrahou Bedia, E. Mahmoud, S. and Tounsi, A. (2020), "Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates Pasternak elastic foundation", Comput. Concrete, 26(3), 213-226. http://doi.org/10.12989/cac.2020.26.3.213.
  22. Benferhat, R., Daouadji, T.H. and Abderezak, R. (2021), "Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations", Struct. Eng. Mech., 77(6), 797-807. http://doi.org/10.12989/sem.2021.77.6.797.
  23. Benferhat, R., Daouadji, T.H. and Abderezak, R. (2021), "Effect of porosity on fundamental frequencies of FGM sandwich plates", Compos. Mater. Eng., 3(1), 25-40. http://doi.org/10.12989/cme.2021.3.1.025.
  24. Benferhat, R., Daouadji, T.H. and Mansour, M.S. (2016b), "Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory", Comptes Rendus Mecanique, 344(9), 631-641. https://doi.org/10.1016/j.crme.2016.03.002.
  25. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016a), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(6), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429.
  26. Bensattalah, T., Hassaine Daouadji, T. and Zidour, M. (2020), "Influences the shape of the floor on the behavior of buildings under seismic effect", Proceedings of the 4th International Symposium on Materials and Sustainable Development: Volume 1: Nano Technology and Advanced Materials 4, 26-42.
  27. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163.
  28. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. http://doi.org/10.12989/cme.2019.1.1.021.
  29. Bourada, M., Tounsi, A., Houari, M.S.A. and Bedia, E.A.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1) 5-33. https://doi.org/10.1177/1099636211426386.
  30. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermo mechanical bending analysis of - different configurations of FG sandwich", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  31. Daouadji, T.H., Abderezak, R. and Rabia, B. (2022), "New technique for repairing circular steel beams by FRP plate", Adv. Mater. Res., 11(3), 171-190. https://doi.org/10.12989/amr.2022.11.3.171.
  32. Daouadji, T.H., Chedad, A. and Adim, B. (2016b), "Interfacial stresses in RC beam bonded with a functionally graded material plate", Struct. Eng. Mech., 60(4), 693-705. http://doi.org/10.12989/sem.2016.60.4.693.
  33. Daouadji, T.H., Rabahi, A., Abbes, B. and Adim, B. (2016a), "Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate", J. Adhes. Sci. Technol., 30(12), 1253-1280. https://doi.org/10.1080/01694243.2016.1140703.
  34. Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using space approach", Compos. Part B: Eng., 60, 661-676. https://doi.org/10.1016/j.compositesb.2018.12.020.
  35. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. http://doi.org/10.12989/cac.2019.24.4.369.
  36. Ebrahimi, F., Jafari, A. and Selvamani, R. (2020), "Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment", Adv. Nano Res., 8(1), 83-94. https://doi.org/10.12989/anr.2020.8.1.083.
  37. Fan, F., Safaei, B. and Sahmani, S. (2021), "Buckling and postbuckling response of nonlocal strain gradient functionally graded micro/nano-plates via NURBS-based isogeometric analysis", Thin Wall. Struct., 159, 107231. https://doi.org/10.1016/j.tws.2020.107231.
  38. Feng, H., Shen, D. and Tahouneh, V. (2020), "Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers", Steel Compos. Struct., 37(6), 711-731. https://doi.org/10.12989/scs.2020.37.6.711.
  39. Hadj, B., Rabia, B. and Daouadji, T.H. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 823-832. https://doi.org/10.12989/sem.2019.72.1.061.
  40. Hadj, B., Rabia, B. and Daouadji, T.H. (2021), "Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity", Couple. Syst. Mech., 10(1), 61-77. http://doi.org/10.12989/csm.2021.10.1.061.
  41. Hashim, H.A. and Sadiq, I.A. (2021), "A five-variable refined plate theory for thermal buckling analysis of composite", Compos. Mater. Eng., 3(2), 135-155. http://doi.org/10.12989/cme.2021.3.2.135.
  42. Hassaine Daouadji, T. (2013), "Analytical analysis of the interfacial stress in damaged reinforced concrete beams strengthened by bonded composite plates", Strength Mater., 45(5), 587-597. https://doi.org/10.1007/s11223-013-9496-4.
  43. Hassaine Daouadji, T. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Des., 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057.
  44. Henni, M.A.B., Abbes, B., Daouadji, T.H., Abbes, F. and Adim, B. (2021), "Numerical modeling of hygrothermal effect on the dynamic behavior of hybrid composite plates", Steel Compos. Struct., 39(6), 751-763. http://doi.org/10.12989/scs.2021.39.6.751.
  45. Houari, M.S.A., Tounsi, A. and Beg, O.A. (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. http://doi.org/10.1016/j.ijmecsci.2013.09.004.
  46. Ishihara, M., Yoshida, T., Ootao, Y. and Kameo, Y. (2020), "Hygro thermo elasticity in a porous cylinder under nonlinear coupling between heat and moisture", Struct. Eng. Mech., 75(1), 59-69. https://doi.org/10.12989/sem.2020.75.1.059.
  47. Kablia, A., Benferhat, R., Daouadji, T.H. and Abderezak, R. (2023), "Free vibration of various types of FGP sandwich plates with variation in porosity distribution", Struct. Eng. Mech., 85(1), 1-14. https://doi.org/10.12989/sem.2023.85.1.001.
  48. Kablia, A., Rabia, B. and Hassaine Daouadji, T. (2022), "Dynamic of behavior for imperfect FGM plates resting on elastic foundation containing various distribution rates of porosity: Analysis and modeling", Couple. Syst. Mech., 11(5), 389-409. https://doi.org/10.12989/csm.2022.11.5.389.
  49. Khaniki, H.B., Ghayesh, M.H. and Hussain, S. (2022), "Porosity, mass and geometric imperfection sensitivity in coupled vibration characteristics of CNT-strengthened beams with different boundary conditions", Eng. Comput., 38, 2313-2339. https://doi.org/10.1007/s00366-020-01208-3.
  50. Khazaei, P. and Mohammadimehr, M. (2020), "Size dependent effect on deflection and buckling analyses of porous nanocomposite plate based on nonlocal strain gradient theory", Struct. Eng. Mech., 76(1), 27-56. https://doi.org/10.12989/sem.2020.76.1.027.
  51. Khiloun, M., Bousahla, A., Kaci, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 36, 807-821. https://doi.org/10.1007/s00366-019-00732-1.
  52. Li, Z., Tang, F., Chen, Y. and Zheng, J. (2019a), "Material distribution optimization of functionally graded arch subjected to external pressure under temperature rise field", Thin Wall. Struct., 138, 64-78. https://doi.org/10.1016/j.tws.2019.01.034.
  53. Li, Z., Tang, F., Chen, Y., Tang, Y. and Chen, G. (2019b), "Elastic and inelastic buckling of thin-walled steel liners encased in circular host pipes under external pressure and thermal effects", Thin Wall. Struct., 137, 213-223. https://doi.org/10.1016/j.tws.2018.12.044.
  54. Liang, D., Wu, Q., Lu, X. and Tahouneh, V. (2020), "Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers", Steel Compos. Struct., 36(1), 47-62. https://doi.org/10.12989/scs.2020.36.1.047.
  55. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., ... & Mahmoud, S.R. (2020), "A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., 36(3), 355-367. http://doi.org/10.12989/scs.2020.36.3.355.
  56. Mirjavadi, S.S., Forsat, M., Nia, A.F., Badnava, S. and Hamouda, A.M.S. (2020), "Nonlocal strain gradient effects on forced vibrations of porous FG cylindrical nanoshells", Adv. Nano Res., 8(2), 149-156. https://doi.org/10.12989/anr.2020.8.2.149.
  57. Mohammadimehr, M. and Meskini, M. (2020), "Analysis of porous micro sandwich plate: Free and forced vibration under magneto-electro-elastic loadings", Adv. Nano Res., 8(1), 69-82. https://doi.org/10.12989/anr.2020.8.1.069.
  58. Pandit, S. and Sharma, S. (2022), "Wavelet strategy for flow and heat transfer in CNT-water based fluid with asymmetric variable rectangular channel", Eng. Comput., 38, 93-103. https://doi.org/10.1007/s00366-020-01139-z.
  59. Rabia, B., Abderezak, R., Daouadji, T.H., Abbes, B., Belkacem, A. and Abbes, F. (2018), "Analytical analysis of the interfacial shear stress in RC beams strengthened with prestressed exponentially-varying properties plate", Adv. Mater. Res., 7(1), 29-44. https://doi.org/10.12989/amr.2018.7.1.029.
  60. Rabia, B., Daouadji, T.H. and Abderezak, R. (2019a), "Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate", Earthq. Struct., 16(5), 601-609. https://doi.org/10.12989/eas.2019.16.5.601.
  61. Rabia, B., Daouadji, T.H. and Abderezak, R. (2019b), "Effect of porosity in interfacial stress analysis of perfect FGM beams reinforced with a porous functionally graded materials plate", Struct. Eng. Mech., 72(3), 293-304. https://doi.org/10.12989/sem.2019.72.3.293.
  62. Rabia, B., Daouadji, T.H. and Abderezak, R. (2020a), "Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: Study and analysis", Adv. Mater. Res., 9(4), 265-287. http://doi.org/10.12989/amr.2020.9.4.265.
  63. Rabia, B., Tahar, H.D. and Abderezak, R. (2020b), "Thermomechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation", Couple. Syst. Mech., 9(6), 499-519. http://doi.org/10.12989/csm.2020.9.6.499.
  64. Rahmani, M.C., Kaci, A., Bousahla Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  65. Rahmani, M.C., Kaci, A., Bousahla Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown integral plate theory", Comput. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  66. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightw. Struct., 1(1), 1-21. http://doi.org/10.3850/S201042861100002X.
  67. Rostami, R. and Mohammadimehr, M. (2022), "Vibration control of rotating sandwich cylindrical shell-reinforced nanocomposite face sheet and porous core integrated with functionally graded magneto-electro-elastic layers", Eng. Comput., 38, 87-100. https://doi.org/10.1007/s00366-020-01052-5.
  68. Sahmani, S., Fattahi, A.M. & Ahmed, N.A. (2020), "Analytical treatment on the nonlocal strain gradient vibrational response of postbuckled functionally graded porous micro-/nanoplates reinforced with GPL", Eng. Comput., 36, 1559-1578. https://doi.org/10.1007/s00366-019-00782-5.
  69. Shan, W., Deng, Z., Zhong, H., Mo, H., Han, Z., Yang, Z., ... & Liu, P. (2020), "Propagation characteristics of longitudinal wave, shear wave and bending wave in porous circular nanoplates", Struct. Eng. Mech., 76(4), 551-559. https://doi.org/10.12989/sem.2020.76.4.551.
  70. She, G.L., Liu, H.B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., 36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179.
  71. Si, H., Shen, D., Xia, J. and Tahouneh, V. (2020), "Vibration behavior of functionally graded sandwich beam with porous core and nanocomposite layers", Steel Compos. Struct., 36(1), 1-16. https://doi.org/10.12989/scs.2020.36.1.001.
  72. 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.
  73. Tahar, H.D., Abderezak, R. and Rabia, B. (2021a), "Hyperstatic steel structure strengthened with prestressed carbon/glass hybrid laminated plate", Couple. Syst. Mech., 10(5), 393-414. https://doi.org/10.12989/csm.2021.10.5.393.
  74. Tahar, H.D., Abderezak, R. and Rabia, B. (2021d), "A new model for adhesive shear stress in damaged RC cantilever beam strengthened by composite plate taking into account the effect of creep and shrinkage", Struct. Eng. Mech., 79(5), 531-540. http://doi.org/10.12989/sem.2021.79.5.531.
  75. Tahar, H.D., Abderezak, R., Rabia, B. and Tounsi, A. (2021b), "Performance of damaged RC continuous beams strengthened by prestressed laminates plate: Impact of mechanical and thermal properties on interfacial stresses", Couple. Syst. Mech., 10(2), 161-184. http://doi.org/10.12989/csm.2021.10.2.161.
  76. Tahar, H.D., Abderezak, R., Rabia, B. and Tounsi, A. (2021c), "Impact of thermal effects in FRP-RC hybrid cantilever beams", Struct. Eng. Mech., 78(5), 573-583. http://doi.org/10.12989/sem.2021.78.5.573.
  77. Tahar, H.D., Boussad, A., Abderezak, R., Rabia, B., Fazilay, A. and Belkacem, A. (2019), "Flexural behaviour of steel beams reinforced by carbon fiber reinforced polymer: Experimental and numerical study", Struct. Eng. Mech., 72(4), 409-419. https://doi.org/10.12989/sem.2019.72.4.409.
  78. Tang, Y., Tang, F., Zheng, J. and Li, Z. (2021), "In-plane asymmetric buckling of an FGM circular arch subjected to thermal and pressure fields", Eng. Struct., 239(15), 112268. https://doi.org/10.1016/j.engstruct.2021.112268.
  79. Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2022), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38(Suppl 1), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  80. Tlidji, Y., Benferhat, R. and Tahar, H.D. (2021a), "Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity", Struct. Eng. Mech., 77(2), 217-229. http://doi.org/10.12989/sem.2021.77.2.217.
  81. Tlidji, Y., Benferhat, R., Daouadji, T.H., Tounsi, A. and Trinh, L.C. (2022), "Free vibration analysis of FGP nanobeams with classical and non-classical boundary conditions using Statespace approach", Adv. Nano Res., 13(5), 453-463. https://doi.org/10.12989/anr.2022.13.5.453.
  82. Tlidji, Y., Benferhat, R., Trinh, L.C., Tahar, H.D. and Abdelouahed, T. (2021b), "New state-space approach to dynamic analysis of porous FG beam under different boundary conditions", Adv. Nano Res., 11(4), 347-359. https://doi.org/10.12989/.2021.11.4.347.
  83. Tounsi, A., Al-Dulaijan, S., Osta, M.A., Chikh, A., Al-Zahrani, M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  84. Tounsi, A., Atmane, H.A., Khiloun, M., Sekkal, M., Taleb, O. and 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.
  85. Wang, J.F., Cao, S.H. and Zhang, W. (2021), "Thermal vibration and buckling analysis of functionally graded carbon nanotube reinforced composite quadrilateral plate", Eur. J. Mech.-A/Solid., 85, 104105. https://doi.org/10.1016/j.euromechsol.2020.104105.
  86. Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell's shell theory", Steel Compos. Struct., 35(2), 249-260. https://doi.org/10.12989/scs.2020.35.2.249.
  87. Zhou, C., Zhan, Z., Zhang, J., Fang, Y. and Tahouneh, V. (2020), "Vibration analysis of FG porous rectangular plates reinforced by graphene platelets", Steel Compos. Struct., 34(2), 215-226. https://doi.org/10.12989/scs.2020.34.2.215.