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Original Articles

Classical and homogenized expressions for the bending solutions of FGM plates based on the four variable plate theories

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Pages 3413-3424 | Received 18 Oct 2022, Accepted 04 Feb 2023, Published online: 16 Feb 2023

References

  • D. K. Jha, Tarun Kant, and R. K. Singh, A critical review of recent research on functionally graded plates, Compos. Struct., vol. 96, pp. 833–849, 2013. DOI: 10.1016/j.compstruct.2012.09.001.
  • K. Swaminathan, D. T. Naveenkumar, A. M. Zenkour, and E. Carrera, Stress, vibration and buckling analyses of FGM plates – a state-of-the-art review, Compos. Struct., vol. 120, pp. 10–31, 2015. DOI: 10.1016/j.compstruct.2014.09.070.
  • S. R. Li, J. H. Zhang, and Y. G. Zhao, Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection, Thin-Walled Struct., vol. 45, no. 5, pp. 528–536, 2007. DOI: 10.1016/j.tws.2007.04.002.
  • S. Abrate, Free vibration, buckling, and static deflections of functionally graded plates, Compos. Sci. Technol., vol. 66, pp. 2382–2394, 2006.
  • S. Abrate, Functionally graded plates behave like homogenous plates, Compos. Part B: Eng., vol. 39, no. 1, pp. 151–158, 2008. DOI: 10.1016/j.compositesb.2007.02.026.
  • D. G. Zhang, and Y. H. Zhou, A theoretical analysis of FGM plate based on physical neutral surface, Comput. Mater. Sci., vol. 44, no. 2, pp. 716–720, 2008. DOI: 10.1016/j.commatsci.2008.05.016.
  • S. R. Li, X. Wang, and R. C. Batra, Correspondence relations between deflection, buckling load, and frequencies of thin functionally graded material plates and those of corresponding homogeneous plates, Trans. ASME, J. Appl. Mech., vol. 82, no. 11, p. 111006, 2015. DOI: 10.1115/1.4031186.
  • Y.-L. Chung, and W.-T. Chen, Bending behavior of FGM-coated and FGM-undercoated plates with two simply supported opposite edges and two free edges, Compos. Struct., vol. 81, no. 2, pp. 157–167, 2007. DOI: 10.1016/j.compstruct.2006.08.006.
  • A. H. Hassan, and N. Kurgan, Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method, Eng. Sci. Technol., vol. 23, no. 4, pp. 788–800, 2020. DOI: 10.1016/j.jestch.2020.03.009.
  • H. S. Shen, and Z. X. Wang, Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations, Compos. Struct., vol. 92, no. 10, pp. 2517–2524, 2010. DOI: 10.1016/j.compstruct.2010.02.010.
  • L. S. Ma, and T. J. Wang, Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory, Int. J. Solids Struct., vol. 41, no. 1, pp. 85–101, 2004. DOI: 10.1016/j.ijsolstr.2003.09.008.
  • A. R. Saidi, A. Rasouli, and S. Sahraee, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory, Compos. Struct., vol. 89, no. 1, pp. 110–119, 2009. DOI: 10.1016/j.compstruct.2008.07.003.
  • D. G. Zhang, Modeling and analysis of FGM rectangular plates based on physical neutral surface and high order shear deformation theory, Int. J. Mech. Sci., vol. 68, pp. 92–104, 2013. DOI: 10.1016/j.ijmecsci.2013.01.002.
  • A. J. M. Ferreira, R. C. Batra, C. M. C. Roque, L. F. Qian, and P. A. L. S. Martins, Static analysis of functionally graded plates using higher order shear deformation theory and a meshless method, Compos. Struct., vol. 69, no. 4, pp. 449–457, 2005. DOI: 10.1016/j.compstruct.2004.08.003.
  • M. N. A. Gulshan Taj, A. Chakrabarti, and A. H. Sheikh, Analysis of functionally graded plates using higher order shear deformation theory, Appl. Math. Modell., vol. 37, no. 18–19, pp. 8484–8494, 2013. DOI: 10.1016/j.apm.2013.03.058.
  • A. M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Appl. Math. Modell., vol. 30, no. 1, pp. 67–84, 2006. DOI: 10.1016/j.apm.2005.03.009.
  • S. Benyoucef, I. Mechab, A. Tounsi, A. Fekrar, H. Ait Atmane, and El Abbas Adda Bedia, Bending of thick FGM plates resting on Winkler-Pasternak elastic foundations, Mech. Compos. Mater., vol. 46, no. 4, pp. 425–434, 2010. DOI: 10.1007/s11029-010-9159-5.
  • X. Xiang, and G. W. Kang, Static analysis of functionally graded plates by the various shear deformation theory, Compos. Struct., vol. 99, pp. 224–230, 2013. DOI: 10.1016/j.compstruct.2012.11.021.
  • R. Kumar, A. Lal, B. N. Singh, and J. Singh, New transverse shear deformation theory for bending analysis of FGM plate under patch load, Compos. Struct., vol. 208, pp. 91–100, 2019. DOI: 10.1016/j.compstruct.2018.10.014.
  • M. Zidi, A. Tounsi, M. S. A. Houari, E. A. A. Bedia, and O. A. Bég, Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory, Aerosp. Sci. Technol., vol. 34, pp. 24–34, 2014. DOI: 10.1016/j.ast.2014.02.001.
  • D.-D. Li, Z.-B. Deng, G.-P. Chen, H.-Z. Xiao, and L.-J. Zhu, Thermomechanical bending analysis of sandwich plates with both functionally graded face sheets and functionally graded core, Compos. Struct., vol. 169, pp. 29–41, 2017. DOI: 10.1016/j.compstruct.2017.01.026.
  • I. Mechab, B. Mechab, and S. Benaissa, Static and dynamic analysis of functionally graded plates using Four-variable refined plate theory by the new function, Composites: Part B., vol. 45, no. 1, pp. 748–757, 2013. DOI: 10.1016/j.compositesb.2012.07.015.
  • A. B. Benyamina, B. Bouderba, and A. Saoula, Bending responses of composite material plates with specific properties, case of a typical FGM “ceramic/metal” in thermal environments, Period. Polytech. Civil Eng., vol. 62, no. 4, pp. 930–938, 2018. DOI: 10.3311/PPci.11891.
  • L. Hadji, N. Zouatnia, and A. Kassoul, Bending analysis of FGM plates using a sinusoidal shear deformation theory, Wind Struct., vol. 23, no. 6, pp. 543–558, 2016. DOI: 10.12989/was.2016.23.6.543.
  • L. Hadji, F. Bernard, A. Safa, and A. Tounsi, Bending and free vibration analysis for FGM plates containing various distribution shape of porosity, Adv. Mater. Res., vol. 10, no. 2, pp. 115–135, 2021.
  • A. M. Zenkour, and A. F. Radwan, Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment, Archiv. Civ. Mech. Eng., vol. 20, no. 4, p. 112, 2020. DOI: 10.1007/s43452-020-00116-z.
  • V. T. Do, V. V. Pham, and H. N. Nguyen, On the development of refined plate theory for static bending behavior of functionally graded plates, Math. Prob. Eng., vol. 2020, p. 2836763, 2020. DOI: 10.1155/2020/2836763.
  • F. Boukhelf, M. B. Bouiadjra, M. Bouremana, and A. Tounsi, Hygro-thermo-mechanical bending analysis of FGM plates using a new HSDT, Smart Struct. Syst., vol. 21, pp. 75–97, 2018.
  • R. Meksi, S. Benyoucef, A. Mahmoudi, A. Tounsi, E. A. A. Bedia, and S. R. Mahmoud, An analytical solution for bending, buckling and vibration responses of FGM sandwich plates, J. Sandwich Struct. Mater., vol. 21, no. 2, pp. 727–757, 2019. DOI: 10.1177/1099636217698443.
  • A. Bouamoud, B. Boucham, F. Bourada, M. S. A. Houari, and A. Tounsi, Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory, Steel Compos. Struct., vol. 32, 5, pp. 611–632, 2019.
  • F. Zaoui, A. Tounsi, D. Ouinas, and J. A. V. Olay, A refined HSDT for bending and dynamic analysis of FGM plates, Struct. Eng. Mech., vol. 74, pp. 105–119, 2020.
  • S. S. Akavci, and A. H. Tharikulu, Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories, Composites Part B., vol. 83, pp. 203–215, 2015. DOI: 10.1016/j.compositesb.2015.08.043.
  • A. M. Zenkour, Bending of FGM plates by simplified four-unknown shear and normal, deformation theory, Int. J. Appl. Mech., vol. 05, no. 02, p. 1350020, 2013. DOI: 10.1142/S1758825113500208.
  • H. T. Thai, and S. E. Kim, A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates, Compos. Struct., vol. 99, pp. 172–180, 2013. DOI: 10.1016/j.compstruct.2012.11.030.
  • M. M. Abazid, M. S. Alotebi, and M. Sobhy, A novel shear and normal deformation theory for hygrothermal bending response of FGM sandwich plates on Pasternak elastic foundation, Struct. Eng. Mech., vol. 67, pp. 219–232, 2018.
  • A. Benbakhti, M. B. Bouiadjra, N. Retiel, and A. Tounsi, A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates, Steel Compos. Struct., vol. 22, no. 5, pp. 975–999, 2016. DOI: 10.12989/scs.2016.22.5.975.
  • A. Belarouci, and A. Fekrar, A new quasi-3D theory for the study of the bending of thick FGM’s plates on elastic foundation, Smart Struct. Syst., vol. 27, pp. 847–860, 2021.
  • Z. Z. Wang, and L. S. Ma, Effect of thickness stretching on bending and free vibration behaviors of functionally graded graphene reinforced composite plates, Appl. Sci., vol. 11, no. 23, p. 11362, 2021. DOI: 10.3390/app112311362.
  • S. R. Li, Y. Xiang, and H. S. Shen, Modelling and evaluation of thermoelastic damping of FGM micro plates based on the Levinson plate theory, Compos. Struct., vol. 278, p. 114684, 2021. DOI: 10.1016/j.compstruct.2021.114684.
  • Shi-Rong Li, and Hang-Kong Ma, Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping, Arch. Appl. Mech., vol. 90, no. 6, pp. 1285–1304, 2020. DOI: 10.1007/s00419-020-01664-9.
  • R. D. Mindlin, Influence of rotary inertia and shear on the bending of elastic plates, Trans ASME Appl Mech., vol. 18, no. 1, pp. 31–38, 1951. DOI: 10.1115/1.4010217.
  • J. R. Reddy, C. M. Wang, and S. Kitipornchai, Axisymmetric bending of functionally graded circular and annular plates, Eur. J. Mech.-A/Solids, vol. 18, no. 2, pp. 185–199, 1999. DOI: 10.1016/S0997-7538(99)80011-4.
  • S. H. Shen, Nonlinear bending of simply supported rectangular Reissner-Mindlin plates under transverse and in-plane loads and resting on elastic foundations, Eng. Struct., vol. 22, no. 7, pp. 847–856, 2000. DOI: 10.1016/S0141-0296(99)00044-9.
  • Z. Q. Cheng, and S. Kitipornchai, Exact bending solution of inhomogeneous plates from homogeneous thin-plate deflection, AIAA J., vol. 38, no. 7, pp. 1289–1291, 2000. DOI: 10.2514/3.14546.
  • M. Levinson, An accurate, simple theory of the statics and dynamics of elastic plates, Mech. Res. Commun., vol. 7, no. 6, pp. 343–350, 1980. DOI: 10.1016/0093-6413(80)90049-X.
  • J. N. Reddy, C. M. Wang, G. T. Lim, and K. H. Ng, Bending solutions of Levinson beams and plates in terms of the classical theory, Int. J. Solids Struct., vol. 38, no. 26–27, pp. 4701–4720, 2001. DOI: 10.1016/S0020-7683(00)00298-5.
  • J. N. Reddy, Analysis of functionally graded plates, Int. J. Numer. Meth. Eng., vol. 47, no. 1–3, pp. 663–684, 2000. DOI: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  • J. N. Reddy, and C. M. Wang, Deflection relationship between classical and third-order plate theories, Acta Mech., vol. 130, no. 3–4, pp. 199–208, 1998. DOI: 10.1007/BF01184311.
  • J. N. Reddy, and C. M. Wang, An overview of the relationships between solutions of the classical and shear deformation plate theories, Compos. Sci. Technol., vol. 60, no. 12–13, pp. 2327–2335, 2000. DOI: 10.1016/S0266-3538(00)00028-2.
  • R. P. Shimpi, Refined plate theory and its variants, AIAA., vol. 40, no. 1, pp. 137–146, 2002. DOI: 10.2514/3.15006.
  • R. P. Shimpi, and H. G. Patel, A two variable refined plate theory for orthotropic plate analysis, Int. J. Solids Struct., vol. 43, no. 22–23, pp. 6783–6799, 2006. DOI: 10.1016/j.ijsolstr.2006.02.007.

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