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A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates

  • Sidhoum, Imene Ait (Laboratoire de mecanique applique, Universite des Sciences et Technologie d'ORAN Mouhamed Boudiaf) ;
  • Boutchicha, Djilali (Laboratoire de mecanique applique, Universite des Sciences et Technologie d'ORAN Mouhamed Boudiaf) ;
  • Benyoucef, Samir (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)
  • Received : 2017.09.11
  • Accepted : 2018.03.31
  • Published : 2018.09.25
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Abstract

An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.

Keywords

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