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A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates

  • Hebali, Habib (Universite Ibn Khaldoun) ;
  • Bakora, Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Kaci, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2016.05.30
  • Accepted : 2016.10.02
  • Published : 2016.10.30
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Abstract

This work presents a bending, buckling, and vibration analysis of functionally graded plates by employing a novel higher-order shear deformation theory (HSDT). This theory has only four unknowns, which is even less than the first shear deformation theory (FSDT). A shear correction coefficient is, thus, not needed. Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

Keywords

References

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  11. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  12. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  13. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  14. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  15. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  16. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2016, https://doi.org/10.12989/sem.2017.64.4.391
  17. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  18. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  19. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  20. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  21. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2016, https://doi.org/10.12989/gae.2018.15.1.711
  22. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2016, https://doi.org/10.12989/anr.2018.6.2.147
  23. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2016, https://doi.org/10.12989/scs.2019.30.1.013
  24. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  25. A novel refined shear deformation theory for the buckling analysis of thick isotropic plates vol.69, pp.3, 2019, https://doi.org/10.12989/sem.2019.69.3.335
  26. Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  27. A Novel Refined Plate Theory for Free Vibration Analyses of Single-Layered Graphene Sheets Lying on Winkler-Pasternak Elastic Foundations vol.58, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.58.151
  28. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2016, https://doi.org/10.12989/cac.2019.24.4.347
  29. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  30. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2016, https://doi.org/10.12989/was.2019.29.6.371
  31. Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory vol.62, pp.None, 2020, https://doi.org/10.4028/www.scientific.net/jnanor.62.108
  32. Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions vol.36, pp.6, 2016, https://doi.org/10.12989/scs.2020.36.6.689
  33. Quasi-3D Refined Theory for Functionally Graded Porous Plates: Vibration Analysis vol.24, pp.3, 2016, https://doi.org/10.1134/s1029959921030036
  34. Stress Distribution on the Cracked Sandwich Plate with Non Linear Thermal and Moisture Concentration vol.32, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/nhc.32.45
  35. Design and simulation analysis of Lattice bone plate based on finite element method vol.28, pp.13, 2021, https://doi.org/10.1080/15376494.2019.1665759
  36. Numerical investigation of thermal frequency responses of graded hybrid smart nanocomposite (CNT-SMA-Epoxy) structure vol.28, pp.21, 2021, https://doi.org/10.1080/15376494.2020.1725193