DOI QR코드

DOI QR Code

Influence of porosity on the hygro-thermo-mechanical bending response of an AFG ceramic-metal plates using an integral plate model

  • Al-Osta, Mohammed A. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Saidi, Hayat (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Al-Dulaijan, S.U. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Al-Zahrani, M.M. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Sharif, Alfarabi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2020.09.16
  • 심사 : 2021.07.29
  • 발행 : 2021.10.25

초록

In this project, the hygro-thermo-mechanical bending behavior of perfect and imperfect advanced functionally graded (AFG) ceramic-metal plates is analytically investigated using an integral plate model for the first time. The plate is assumed to be supported by a two-parameter elastic foundation. Because of the technical problems encountered in the manufacture of AFG, porosities and micro-voids can occur in AFG specimens, which can result in reduced density and strength of materials. Thus, due to the presence of porosity, a modified rule of mixture is adopted to predict the material properties of the AFG plates. The governing equations are deduced by adopting the "principle of virtual work" and an integral plate model. The analytical Navier's method is considered to solve the obtained differential equations for simply supported AFG porous plate. The results obtained are checked by comparing them for non-porous and porous AFG plates with those available in the open literature. Finally, this work will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.

키워드

과제정보

The authors would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia for funding this work through Project No. DF181032. The support provided by the Department of Civil and Environmental Engineering is also acknowledged.

참고문헌

  1. Abdalla, J.A. and Ibrahim, A.M. (2006), "Development of a discrete Reissner-Mindlin element on Winkler foundation", Finite Elem. Anal. Des., 42, 740-748. https://doi.org/10.1016/j.finel.2005.11.004
  2. Abdulrazzaq, M.A. Kadhim, Z.D., Faleh, N.M. and Moustafa, N.M. (2020a), "A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads", Struct. Monitor. Maint., Int. J., 7(1), 27-42. https://doi.org/10.12989/smm.2020.7.1.027
  3. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020b), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., Int. J., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147
  4. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Computat. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107
  5. Akbas, S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load", Eng. Comput. https://doi.org/10.1007/s00366-020-01070-3
  6. Arefi, M. and Zur, K.K. (2020), "Free vibration analysis of functionally graded cylindrical nanoshells resting on Pasternak foundation based on two-dimensional analysis", Steel Compos. Struct., Int. J., 34(4), 615-623. http://dx.doi.org/10.12989/scs.2020.34.4.615
  7. Ashraf, M.A., Liu, Z., Zhang, D. and Pham, B.T. (2020), "Effects of elastic foundation on the large-amplitude vibration analysis of functionally graded GPL-RC annular sector plates", Eng. Comput. https://doi.org/10.1007/s00366-020-01068-x
  8. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J.of Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011
  9. 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
  10. 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
  11. Barati, M.R. and Zenkour, A.M. (2017), "Investigating postbuckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions", Compos. Struct., 182, 91-98. https://doi.org/10.1016/j.compstruct.2017.09.008
  12. Behravan Rad, A. and Shariyat, M. (2015), "Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations", Compos. Struct., 125, 558-574. https://doi.org/10.1016/j.compstruct.2015.02.049
  13. Bennai, R., Fourn, H., Ait Atmane, H., Tounsi, A. and Bessaim, A. (2019), "Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory", Wind Struct., Int. J., 28(1), 49-62. http://dx.doi.org/10.12989/was.2019.28.1.049
  14. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60, 195-216. https://doi.org/10.1115/1.2777164
  15. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., Int. J., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209
  16. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46, 194-203. https://doi.org/10.2514/1.32490
  17. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B, 42, 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005
  18. Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025
  19. Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008
  20. Chucheepsakul, S. and Chinnaboon, B. (2002), "An alternative domain/boundary element technique for analyzing plates on two-parameter elastic foundations", Eng. Anal. Bound. Elem., 26, 547-555. https://doi.org/10.1016/S0955-7997(02)00007-3
  21. Civalek, O. (2007a), "Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSCHDQ methods", Appl. Math. Model., 31, 606-624. https://doi.org/10.1016/j.apm.2005.11.023
  22. Civalek, O. (2007b), "Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method", Int. J. Mech. Sci., 49, 752-765. https://doi.org/10.1016/j.ijmecsci.2006.10.002
  23. Daouadji, T.H., Adim, B. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., Int. J., 5(1), 35-53. http://dx.doi.org/10.12989/amr.2016.5.1.035
  24. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., Int. J., 8(2), 115-134. http://dx.doi.org/10.12989/anr.2020.8.2.115
  25. Duc, N.D. and Tung, H.V. (2011), "Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations", Compos. Struct., 93, 2874-2881. https://doi.org/10.1016/j.compstruct.2011.05.017
  26. Fadoun, O.O. (2019), "Analysis of axisymmetric fractional vibration of an isotropic thin disc in finite deformation", Comput. Concrete, Int. J., 23(5), 303-309. http://dx.doi.org/10.12989/cac.2019.23.5.303
  27. 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
  28. Farzaneh Joubaneh, E., Mojahedin, A., Khorshidvand, A.R. and Jabbari, M. (2015), "Thermal buckling analysis of porous circular plate with piezoelectric sensor-actuator layers under uniform thermal load", J. Sandw. Struct. Mater., 17, 3-25. https://doi.org/10.1177/1099636214554172
  29. Fenjan, N.M., Moustafa, N.M. and Faleh, N.M. (2020), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano Res., Int. J., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283
  30. Fesharaki, J.J. and Roghani, M. (2019), "Elastic behavior of functionally graded two tangled circles chamber", J. Appl. Computat. Mech., 5(4), 667-679. https://doi.org/10.22055/JACM.2019.27058.1372
  31. Feyzi, M.R. and Khorshidvand, A.R. (2017), "Axisymmetric post-buckling behavior of saturated porous circular plates", Thin-Wall. Struct., 112, 149-158. https://doi.org/10.1016/j.tws.2016.11.026
  32. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., Int. J., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037
  33. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Nonlinear and post-buckling responses of FGM plates with oblique elliptical cutouts using plate assembly technique", Steel Compos. Struct., Int. J., 34(2), 227-239. http://dx.doi.org/10.12989/scs.2020.34.2.227
  34. Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., Int. J., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253
  35. Han, J.B. and Liew, K.M. (1997), "Numerical differential quadrature method for Reissner /Mindlin plates on two-parameter foundations", Int. J. Mech. Sci., 39, 977-989. https://doi.org/10.1016/S0020-7403(97)00001-5
  36. Heidari, F., Afsari, A. and Janghorban, M. (2020), "Several models for bending and buckling behaviors of FG-CNTRCs with piezoelectric layers including size effects", Adv. Nano Res., Int. J., 9(3), 193-210. http://doi.org/10.12989/anr.2020.9.3.193
  37. Jena, S.K., Chakraverty, S. and Malikan, M. (2020), "Application of shifted Chebyshev polynomial-based Rayleigh-Ritz method and Navier's technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation", Eng. Comput. https://doi.org/10.1007/s00366-020-01018-7
  38. Kasaeian, A.B., Vatan, SH.N. and Daneshmand, S. (2011), "FGM materials and finding an appropriate model for the thermal conductivity", Procedia Eng., 14, 3199-3204. https://doi.org/10.1016/j.proeng.2011.07.404
  39. Kertesz, S., Szerencses, S.G., Vereb, G., Csanadi, J., Laszlo, Z. and Hodur, C. (2020), "Single- and multi-stage dairy wastewater treatment by vibratory membrane separation processes", Membr. Water Treat., Int. J., 11(6), 383-389. http://doi.org/10.12989/mwt.2020.11.6.383
  40. Khorshidvand, A.R., Farzaneh Joubaneh, E., Jabbari, M. and Eslami, M.R. (2014), "Buckling analysis of a porous circular plate with piezoelectric sensoractuator layers under uniform radial compression", Acta Mech., 225, 179-193. https://doi.org/10.1007/s00707-013-0959-2
  41. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  42. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., Int. J., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427
  43. Mahmoud, S.R., Al-Solami, H.M., Alkenani, N., Alhebshi, A.M.S., Alwabli, A.S. and Bahieldin, A. (2020), "A mechanical model to investigate Aedesaegypti mosquito bite using new techniques and its applications", Membr. Water Treat., Int. J., 11(6), 399-406. http://doi.org/10.12989/mwt.2020.11.6.399
  44. Mehar, K. and Panda, S.K. (2017a), "Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads", Compos. Struct., 161, 287-298. https://doi.org/10.1016/j.compstruct.2016.10.135
  45. Mehar, K. and Panda, S.K. (2017b), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings", Int. J. Comput. Meth., 14(2), 1750019. https://doi.org/10.1142/S0219876217500190
  46. Mojahedin, A., Farzaneh Joubaneh, E. and Jabbari, M. (2014), "Thermal and mechanical stability of a circular porous plate with piezoelectric actuators", Acta Mech., 225, 3437-3452. https://doi.org/10.1007/s00707-014-1153-x
  47. Mojahedin, A., Jabbari, M., Khorshidvand, A.R. and Eslami, M.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin-Wall. Struct., 99, 83-90. https://doi.org/10.1016/j.tws.2015.11.008
  48. Natanzi, A.J., Jafari, G.S. and Kolahchi, R. (2018), "Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation", Comput. Concrete, Int. J., 21(5), 569-582. http://doi.org/10.12989/cac.2018.21.5.569
  49. Ozgan, K. and Daloglu, A.T. (2007), "Alternative plate finite elements for the analysis of thick plates on elastic foundations", Struct. Eng. Mech., Int. J., 26(1), 69-86. https://doi.org/10.12989/sem.2007.26.1.069
  50. Pabst, W. (2014), "Youngs modulus of isotropic porous materials with spheroidal pores", J. Eur. Ceram. Soc., 34, 3195-3207. https://doi.org/10.1016/j.jeurceramsoc.2014.04.009
  51. Pabst, W. and Gregorova, E. (2004a), "Effective elastic properties of alumina-zirconia composite ceramics Part 2. Micromechanical modeling", Ceramics Silikaty, 48, 14-23.
  52. Pabst, W. and Gregorova, E. (2004b), "Mooney-type relation for the porosity dependence of the effective tensile modulus of ceramics", J. Mater. Sci., 39, 3213-3215. https://doi.org/10.1023/B:JMSC.0000025863.55408.c9
  53. Pabst, W., Gregorova, E., Ticha, G. and Tynova, E. (2004), "Effective elastic properties of aluminazirconia composite ceramicsPart 4. Tensile modulus of porous alumina and zirconia", Ceramics Silikaty, 48, 165-174.
  54. Pabst, W., Gregorova, E. and Ticha, G. (2006), "Elasticity of porous ceramics: a critical study of modulus porosity relations", J. Eur. Ceram. Soc., 26, 1085-1097. https://doi.org/10.1016/j.jeurceramsoc.2005.01.041
  55. Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civil Eng. Architect., 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151
  56. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, Int. J., 23(5), 361-376. http://doi.org/10.12989/cac.2019.23.5.361
  57. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  58. Rezaei, A.S. and Saidi, A.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125
  59. Rezaei, A.S. and Saidi, A.R. (2016), "Application of Carrera unified formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates", Compos. B, 91, 361-370. https://doi.org/10.1016/j.compositesb.2015.12.050
  60. Rezaei, A.S. and Saidi, A.R. (2017), "Buckling response of moderately thick fluid-infiltrated porous annular sector plates", Acta Mech., 228, 3929-3945. https://doi.org/10.1007/s00707-017-1908-2
  61. Sahoo, B., Sahoo, B., Sharma, N., Mehar, K. and Panda, S.K. (2020), "Numerical buckling temperature prediction of graded sandwich panel using higher order shear deformation theory under variable temperature loading", Smart Struct. Syst., Int. J., 26(5), 641-656. http://doi.org/10.12989/sss.2020.26.5.641
  62. Saini, R. and Lal, R. (2020), "Axisymmetric vibrations of temperature-dependent functionally graded moderately thick circular plates with two-dimensional material and temperature distribution", Eng. Comput. https://doi.org/10.1007/s00366-020-01056-1
  63. Sayyad, A. and Ghumare, S. (2019), "A new quasi-3D model for functionally graded plates", J. Appl. Computat. Mech., 5(2), 367-380. https://doi.org/10.22055/jacm.2018.26739.1353
  64. Selmi, A. (2020), "Dynamic behavior of axially functionally graded simply supported beams", Smart Struct. Syst., Int. J., 25(6), 669-678. http://doi.org/10.12989/sss.2020.25.6.669
  65. 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
  66. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016), "On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007
  67. Shafiei, N., Mirjavadi, S.S., Mohasel Afshari, B., Rabby, S. and Kazemi, M. (2017), "Vibration of two dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Methods Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007
  68. Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40. https://doi.org/10.12691/ajn-6-1-4
  69. Shen, H-S. (2000), "Nonlinear analysis of simply supported Reissner-Mindlin plates subjected to lateral pressure and thermal loading and resting on two-parameter elastic foundations", Eng. Struct., 23, 1481-1493. https://doi.org/10.1016/S0141-0296(99)00086-3
  70. Shen, H.S., Yang, J. and Zhang, L. (2001), "Free and forced vibration of Reissner-Mindlin plates with free edges resting on elastic foundations", J. Sound Vib., 244, 299-320. https://doi.org/10.1006/jsvi.2000.3501
  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., Int. J., 36(1), 1-16. http://doi.org/10.12989/scs.2020.36.1.001
  72. Sofiyev, A.H. (2011), "Thermal buckling of FGM shells resting on a two parameter elastic foundation", Thin-Wall. Struct., 49, 1304-1311. https://doi.org/10.1016/j.tws.2011.03.018
  73. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., Int. J., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135
  74. Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel-Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput. https://doi.org/10.1007/s00366-020-01154-0
  75. Thanh, C.L., Nguyen, K.D., Nguyen, T.N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2021), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216
  76. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, Int. J., 26(1), 53-62. http://doi.org/10.12989/cac.2020.26.1.053
  77. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044
  78. Wang, Z.X. and Shen, H.-S. (2013), "Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments", Ocean Eng., 57, 99-110. https://doi.org/10.1016/j.oceaneng.2012.09.004
  79. Winkler, E. (1867), "Die Lehre von der Elastizitat and Festigkeit", Prag. Dominicus.
  80. Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023
  81. Xiang, Y. (2003), "Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations", Int. J. Mech. Sci., 45, 1229-1244. https://doi.org/10.1016/S0020-7403(03)00141-3
  82. Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets", Compos. Struct., 252, 112700. https://doi.org/10.1016/j.compstruct.2020.112700
  83. Yang, B., Ding, H.J. and Chen, W.Q. (2012), "Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported", Appl. Math. Model., 36, 488-503. https://doi.org/10.1016/j.apm.2011.07.020
  84. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  85. Yas, M.H. and Tahouneh, V. (2012), "3-D Free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM)", Acta. Mech., 223, 43-62. https://doi.org/10.1007/s00707-011-0543-6
  86. Yeghnem, R., Guerroudj, H.Z., Amar, L.H.H., Meftah, S.A., Benyoucef, S., Tounsi, A. and 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, Int. J., 19(5), 579-588. http://doi.org/10.12989/cac.2017.19.5.579
  87. Yuan, Y., Zhao, K., Zhao, Y. and Kiani, K. (2020), "Nonlocal-integro-vibro analysis of vertically aligned monolayered nonuniform FGM nanorods", Steel Compos. Struct., Int. J., 37(5), 551-569. http://doi.org/10.12989/scs.2020.37.5.551
  88. Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Methods. Eng., 59, 1313-1334. https://doi.org/10.1002/nme.915
  89. Zhu, X., Lu, Z., Wang, Z., Xue, L. and Ebrahimi-Mamaghani, A. (2020), "Vibration of spinning functionally graded nanotubes conveying fluid", Eng. Comput. https://doi.org/10.1007/s00366-020-01123-7