Structural Engineering and Mechanics

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A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations

  • Meksi, Abdeljalil (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Benyoucef, Samir (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Tounsi, Abdelouahed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil)
  • Received : 2014.09.02
  • Accepted : 2014.12.16
  • Published : 2015.03.25
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Abstract

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

Keywords

References

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  27. A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.717
  28. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.735
  29. Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory vol.27, pp.3, 2018, https://doi.org/10.12989/scs.2018.27.3.311
  30. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2015, https://doi.org/10.12989/gae.2018.15.1.711
  31. Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory vol.22, pp.1, 2018, https://doi.org/10.12989/sss.2018.22.1.121
  32. A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates vol.22, pp.3, 2015, https://doi.org/10.12989/sss.2018.22.3.303
  33. Robust quasi 3D computational model for mechanical response of FG thick sandwich plate vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.571
  34. Free vibration analysis of thick cylindrical MEE composite shells reinforced CNTs with temperature-dependent properties resting on viscoelastic foundation vol.70, pp.6, 2015, https://doi.org/10.12989/sem.2019.70.6.683
  35. Asymmetric Thermal Buckling of Imperfect FGM Circular Plates with Rotationally Restrained Edge vol.20, pp.12, 2015, https://doi.org/10.1142/s0219455420501278
  36. A refined HSDT for bending and dynamic analysis of FGM plates vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.105
  37. Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT vol.36, pp.3, 2015, https://doi.org/10.1007/s00366-019-00732-1
  38. Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions vol.23, pp.3, 2015, https://doi.org/10.1177/1099636219851281
  39. Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment vol.235, pp.5, 2015, https://doi.org/10.1177/1464420720986899
  40. Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT vol.264, pp.None, 2015, https://doi.org/10.1016/j.compstruct.2021.113643