Steel and Composite Structures

  • 제43권1호
  • /
  • Pages.1-17
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  • 2022
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Nonlinear dynamic analysis of porous functionally graded materials based on new third-order shear deformation theory

  • Allah, Mohamed Janane (Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM CASABLANCA), AICSE Laboratory) ;
  • Timesli, Abdelaziz (Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM CASABLANCA), AICSE Laboratory) ;
  • Belaasilia, Youssef (Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM CASABLANCA), AICSE Laboratory)
  • 투고 : 2021.10.17
  • 심사 : 2022.04.03
  • 발행 : 2022.04.10
⟨ 이전 논문 다음 논문 ⟩

초록

The free and forced nonlinear dynamic behaviors of Porous Functionally Graded Material (PFGM) plates are examined by means of a High-Order Implicit Algorithm (HOIA). The formulation is developed using the Third-order Shear Deformation Theory (TSDT). Unlike previous works, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite, and the distribution of the porosity is assumed to be gradually variable through the thickness of the PFGM plates. Using the Hamilton principle, we establish the governing equations of motion. The Finite Element Method (FEM) is used to compute approximations of the resulting equations; FEM is adopted using a four-node quadrilateral finite element with seven Degrees Of Freedom (DOF) per node. Nonlinear equations are solved by a HOIA. The accuracy and the performance of the proposed approach are verified by presenting comparisons with literature results for vibration natural frequencies and dynamic response of PFGM plates under external loading. The influences of porosity volume fraction, porosity distribution, slenderness ratio and other parameters on the vibrations of PFGM plate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of the PFGM plate.

키워드

참고문헌

  1. Al-Furjan, M.S.H., Hatami, A., Habibi, M., Shan, L. and Tounsi, A. (2020), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  2. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A.J., Benrahou, K.H., Mahmoud, S.R., Bedia, E.A.A. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concr., 26, 185-201. https://doi.org/10.12989/cac.2020.26.2.185.
  3. Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S. and Tounsi, A. (2021), "Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory", Eng. Comput. https://doi.org/10.1007/s00366-021-01382-y.
  4. Atmane, R.A., Mahmoudi, N., Bennai, R., Atmane, H.A., Tounsi, A. (2021), "Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory", Steel. Compos. Struct., 39(1), 95-107. http://dx.doi.org/10.12989/scs.2021.39.1.095.
  5. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. http://dx.doi.org/10.12989/sem.2018.65.4.453.
  6. Auada, S.P., Pracianoa, J.S.C., Barrosoa, E.S., Sousa Jr, J.B.M. and Parente Juniora, E. (2019), "Isogeometric analysis of FGM plates", Mater. Today: Proc., 8, 738-746. https://doi.org/10.21452/bccm4.2018.16.09.
  7. Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A.J., Benrahou, K. H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. R. (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concr., 27, 73-83. https://doi.org/10.12989/cac.2021.27.1.073.
  8. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A.J., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concr., 26, 439-450. https://doi.org/10.12989/cac.2020.26.5.439.
  9. Bellifa, H., Selim, M.M., Chikh, A, Bousahla, A.A., Bourada, F., Tounsi, A.J., Benrahou, K.H., Al-Zahrani, M.M. and Tounsi, A. (2021), "Influence of porosity on thermal buckling behavior of functionally graded beams", Smart Struct. Syst., 27, 719-728. https://doi.org/10.12989/sss.2021.27.4.719.
  10. Bouafia, H., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A.J., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Hussain, M. (2021), "Natural frequencies of FGM nanoplates embedded in an elastic medium", Adv. Nano Res., 11, 239-249. https://doi.org/10.12989/anr.2021.11.3.239.
  11. Bourihane, O., Hilali, Y. and Mhada, K. (2020), "Nonlinear dynamic response of functionally graded material plates using a highorder implicit algorithm", Appl. Math. Mech., 100, e202000087. https://doi.org/10.1002/zamm.202000087.
  12. Croce, L.D. and Venini, P. (2004), "Finite elements for functionally graded ReissnerMindlin plates", Comput. Methods Appl. Mech. Eng., 193(9), 705-725. https://doi.org/10.1016/j.cma.2003.09.014.30.
  13. Damanpack, A.R., Bodaghi, M., Ghassemi, H., Sayehbani, M. (2013), "Boundary element method applied to the bending analysis of thin functionally graded plates", Latin Am. J. Solids Struct., 10(3), 549-570. https://doi.org/10.1590/S1679-78252013000300006
  14. Fu, T., Chen, Z., Yu, H., Wang, Z. and Liu, X. (2018), "An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material", Compos. B. Eng., 151, 161-172. https://doi.org/10.1016/j.compositesb.2018.06.010.
  15. Ghannadpour, S.A.M., Ovesy, H.R. and Nassirnia, M. (2012), "Buckling analysis of functionally graded plates under thermal loadings using the finite strip method", Comput. Struct., 108-109, 93-99. https://doi.org/10.1016/j.compstruc.2012.02.011.
  16. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., Hussain and M., Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38, 1-15. https://doi.org/10.12989/scs.2021.38.1.001.
  17. Hachemi, H., Bousahla, A. A., Kaci, A., Bourada, F., Tounsi, A.J., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39, 51-64. https://doi.org/10.12989/SCS.2021.39.1.051.
  18. Hassan, A.H.A. and Kurgan, N. (2020), "Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multiterm extended Kantorovich method", Int. J. Eng. Sci. Technol., 23, 788-800. https://doi.org/10.1016/j.jestch.2020.03.009.
  19. Huang, X.L. and Shen, H.S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solids Struct., 41, 240-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012.
  20. Huang, Y., Karami, B., Shahsavari, D. and Tounsi, A. (2021), "Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels", Archiv. Civ. Mech. Eng., 21, 139. https://doi.org/10.1007/s43452-021-00291-7.
  21. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A.J., Bedia, E.A.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis", Comput. Concr., 25, 37-57. https://doi.org/10.12989/CAC.2020.25.1.037.
  22. Kar, U.K. and Srinivas, J. (2020), "Material modeling and analysis of hydroxyapatite/titanium FGM plate under thermos mechanical loading conditions", Mater. Today: Proc., 33, 5498-5504. https://doi.org/10.1016/j.matpr.2020.03.312.
  23. Karami, B. and Janghorban, M. (2019), "On the dynamics of porous nanotubes with variable material properties and variable thickness", Int. J. Eng. Sci., 136, 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002.
  24. Karami, B. and Janghorban, M. (2019), "A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams", Thin-Walled Struct., 143, 106227. https://doi.org/10.1016/j.tws.2019.106227
  25. Karami, B., Janghorban, A. and Rabczuk, T. (2020), "Forced vibration analysis of functionally graded anisotropic Nanoplates resting on winkler/pasternak-foundation", Comput. Mater. Contin., 62, 607-629. https://doi.org/10.32604/cmc.2020.08032.
  26. Karami, B., Janghorban, A. and Rabczuk, T. (2019), "Static analysis of functionally graded anisotropic nanoplates using nonlocal strain gradient theory", Compos. Struct., 227, 111249. https://doi.org/10.1016/j.compstruct.2019.111249.
  27. Karami, B., Janghorban, M. and Li, L. (2018b), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011.
  28. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2021), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28, 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  29. 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, 1047-1057. https://doi.org/10.1080/15376494.2017.1323143.
  30. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019a), "Influence of homogenization schemes on vibration of functionally graded curved microbeams", Compos. Struct., 216, 67-79. https://doi.org/10.1016/j.compstruct.2019.02.089.
  31. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019b), "On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory", Int. J. Eng. Sci., 144, 103143. https://doi.org/10.1016/j.ijengsci.2019.103143.
  32. Katili, I., Batoz, J.L., Maknun, I.J. and Katili, A.M. (2021), "On static and free vibration analysis of FGM plates using an efficient quadrilateral finite element based on DSPM", Compos. Struct., 261, 113514. https://doi.org/10.1016/j.compstruct.2020.113514.
  33. Kim, S.E., Duc, N.D., Nam, V.H. and Van Sy, N. (2019), "Nonlinear vibration and dynamic buckling of eccentrically oblique stiffened FGM plates resting on elastic foundations in thermal environment", Thin Walled Struct., 142, 287-296. https://doi.org/10.1016/j.tws.2019.05.013.
  34. Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res., 11, 1-17. https://doi.org/10.12989/anr.2021.11.1.001.
  35. Li, M., Yan, R., Xu, L. and Guedes Soares, C. (2021), "A general framework of higherorder shear deformation theories with a novel unified plate model for composite laminated and FGM plates", Compos. Struct., 261, 941-1006. https://doi.org/10.1016/j.compstruct.2021.113560.
  36. Liu, X., Karami, B., Shahsavari, D. and Civalek, O. (2021), "Elastic wave characteristics in damped laminated composite nano-scaled shells with different panel shapes", Compos. Struct., 267, 113924. https://doi.org/10.1016/j.compstruct.2021.113924.
  37. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A.J., Benrahou, K.H., Tounsi, A., Bedia, E.A.A. and 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, 355-367. https://doi.org/10.12989/scs.2020.36.3.355.
  38. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A.J., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39, 631-643. https://doi.org/10.12989/scs.2021.39.5.631.
  39. Minh, P.P. and Duc, N.D. (2021), "The effect of cracks and thermal environment on free vibration of FGM plates", Thin-Walled Struct., 159, 107291. https://doi.org/10.1016/j.tws.2020.107291.
  40. Minh, P.P., Manh, D.T. and Duc, N.D. (2021), "Free vibration of cracked FGM plates with variable thickness resting on elastic foundations", Thin-Walled Struct., 161, 107425. https://doi.org/10.1016/j.tws.2020.107425.
  41. Mohammadi, M., Said, A.R. and Jomehzadeh, E. (2010), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Compos. Mater., 17(2), 81-93. https://doi.org/10.1007/s104430099100z.
  42. Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Structures, 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  43. Nguyen, D.D. and Hoang, V.T. (2010), "Mechanical and thermal postbuckling of sheardeformable FGM plates with temperature-dependent properties", Mech. Compos. Mater., 46(5), 461-476. https://doi.org/10.1007/s1102901091639.
  44. Nguyen, T.K., Sab, K. and Bonnet, G. (2008), "Firstorder shear deformation plate models for functionally graded materials", Compos. Struct., 83(1), 25-36. https://doi.org/10.1016/j.compstruct.2007.03.004.
  45. Pan, Q., Rabczuk, T. and Yang, X. (2021), "Subdivision-based isogeometric analysis for second order partial differential equations on surfaces", Comput. Mech., 68, 1205-1221. https://doi.org/10.1007/s00466-021-02065-7.
  46. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AIDNME787>3.0.CO;28.
  47. Saidi, H. and Sahla, M. (2019), "Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium", Frat. ed Integrita Strutt., 50, 286-299. https://doi.org/10.3221/IGFESIS.50.24.
  48. Shaaban, A.M., Anitescu, C., Atroshchenko, E. and Rabczuk, T. (2022), "An isogeometric Burton-Miller method for the transmission loss optimization with application to mufflers with internal extended tubes", Appl. Acoust., 185, 108410. https://doi.org/10.1016/j.apacoust.2021.108410.
  49. Shafei, E., Shirzad, A. and Rabczuk, T. (2022), "Dynamic stability optimization of laminated composite plates: An isogeometric HSDT formulation and PSO algorithm", Compos. Struct., 280, 114935. https://doi.org/10.1016/j.compstruct.2021.114935.
  50. 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.
  51. Sharma, P., Meena, M. and Khinchib, A. (2021), "Modal study of bi direction FGM plate", Mater. Today: Proc., 44, 1604-1608. https://doi.org/10.1016/j.matpr.2020.11.814.
  52. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
  53. Slimane, M., Adda, H.M., Mohamed, M., Hakima, B., Hadjira, H. and Sabrina, B. (2020), "Effects of even pores distribution of functionally graded plate porous rectangular and square", Procedia Struct. Integr., 26, 35-45. https://doi.org/10.1016/j.prostr.2020.06.006.
  54. Song, J., Karami, B., Shahsavari, D. and Civalek, O. (2021), "Wave dispersion characteristics of grapheme reinforced nanocomposite curved viscoelastic panels", Compos. Struct., 277, 114648. https://doi.org/10.1016/j.compstruct.2021.114648.
  55. Tahir, S.I., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021b), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
  56. Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021a), "An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation", Waves Random Complex Media, 1-14. https://doi.org/10.1080/17455030.2021.1942310.
  57. Thai, H.T. and Choi, D.H. (2013), "A simple first order shear deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct., 101, 332-340. https://doi.org/10.1016/j.compstruct.2013.02.019
  58. Timesli, A. (2021a), "Analytical modeling of buckling behavior of porous FGM cylindrical shell embedded within an elastic foundation", Gazi Univ. J. Sci., 35, 148-165. https://doi.org/10.35378/gujs.860783.
  59. Timesli, A. (2021b), "Optimized radius of influence domain in meshless approach for modeling of large deformation problems", Iran J. Sci. Technol. Trans. Mech. Eng., https://doi.org/10.1007/s40997-021-00427-3.
  60. Timesli, A., Braikat, B., Lahmam, H. and Zahrouni, H. (2015), "A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding", Eng. Anal. Bound. Elem., 50, 372-380. https://doi.org/10.1016/j.enganabound.2014.09.011.
  61. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29, 901-916. https://doi.org/10.1016/0020-7225(91)90165Y.
  62. Tran, T.T., Nguyen, P.C. and Pham, Q.H. (2021), "Vibration analysis of FGM plate in thermal environment resting on elastic foundation using ESMITC3 element and prediction of ANN", Case Stud. Therm. Eng., 24, 100852. https://doi.org/10.1016/j.csite.2021.100852.
  63. Valizadeh, N. and Rabczuk, T. (2022), "Isogeometric analysis of hydrodynamics of vesicles using a monolithic phase-field approach", Comput. Methods Appl. Mech. Eng., 388, 114191. https://doi.org/10.1016/j.cma.2021.114191.
  64. Vinh, P.V., Dung, N.T., Tho, N.C., Thom, D.V. and Hoa, L.K. (2021), "Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates", Structures, 29, 1435-1444. https://doi.org/10.1016/j.istruc.2020.12.027.
  65. Vu, T.V., Nguyen, N.H., Khosravifard, A., Hematiyan, M.R., Tanaka, S. and Bui, T.Q. (2017), "A simple FSDTbased meshfree method for analysis of functionally graded plates", Eng. Anal. Boundary Elem., 79, 1-12. https://doi.org/10.1016/j.enganabound.2017.03.002.
  66. Xu, X., Shahsavari, D. and Karami, B. (2021), "On the forced mechanics of doubly-curved nanoshell", Int. J. Eng. Sci., 168, 103538. https://doi.org/10.1016/j.ijengsci.2021.103538.
  67. Yahiaoui, M., Tounsi, A., Fahsi, B., Bouiadjra, R.B., Benyoucef, S. (2018), "The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams", Struct. Eng. Mech., 68(1), 53-66. http://dx.doi.org/10.12989/sem.2018.68.1.053.
  68. Yang, H.S., Dong, C.Y. and Wu, Y.H. (2020), "Postbuckling analysis of multi directional perforated FGM plates using NURBSbased IGA and FCM", Appl. Math. Model., 84, 466-500. https://doi.org/10.1016/j.apm.2020.03.043.
  69. Yin, S., Hale, J.S., Yu, T., Bui, T.Q. and Bordas, S.P.A. (2014), "Isogeometric locking free plate element: A simple first order shear deformation theory for functionally graded plates", Compos. Struct., 118, 121-138. https://doi.org/10.1016/j.finel.2014.11.003.
  70. Yu, T.T., Yin, S., Bui, T.Q. and Hirose, S. (2015), "A simple FSDT based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates", Finite Elem. Anal. Des., 96, 1-10. https://doi.org/10.1016/j.finel.2014.11.003.
  71. Zaitoun, M.W., Chikh, A., Tounsi, A., Sharif, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2021)", "An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects", Eng. Comput. https://doi.org/10.1007/s00366-021-01498-1.
  72. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part2-Buckling and free vibration", Int. J. Solids Struct., 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  73. Zheng, H., Sladek, J., Sladek, V., Wang, S.K. and Wen, P.H. (2021), "Hybrid meshless/displacement discontinuity method for FGM Reissner's plate with cracks", Appl. Math. Model., 90, 1226-1244. https://doi.org/10.1016/j.apm.2020.10.023.
  74. Zine, A., Bousahla, A. A., Bourada, F., Benrahou, K.H., Tounsi, A.J., Bedia, E.A.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concr., 26, 63-74. https://doi.org/10.12989/cac.2020.26.1.063.