Structural Engineering and Mechanics

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Analytical and finite element method for the bending analysis of the thick porous functionally graded sandwich plate including thickness stretching effect

  • Imad Benameur (Structures & Advances Materials Laboratory in Civil Engineering and Public Works, Faculty of Technology, Civil Engineering and Public Works Department, University of Sidi Bel Abbes) ;
  • Youcef Beldjelili (Structures & Advances Materials Laboratory in Civil Engineering and Public Works, Faculty of Technology, Civil Engineering and Public Works Department, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering and Public Works Department, University of Sidi Bel Abbes)
  • Received : 2021.09.11
  • Accepted : 2023.01.25
  • Published : 2023.03.10
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Abstract

This work presents a comparison between analytical and finite element analysis for bending of porous sandwich functionally graded material (FGM) plates. The plate is rectangular and simply supported under static sinusoidal loading. Material properties of FGM are assumed to vary continuously across the face sheets thickness according to a power-law function in terms of the volume fractions of the constituents while the core is homogeneous. Four types of porosity are considered. A refined higher-order shear with normal deformation theory is used. The number of unknowns in this theory is five, as against six or more in other shear and normal deformation theories. This theory assumes the nonlinear variation of transverse shear stresses and satisfies its nullity in the top and bottom surfaces of the plate without the use of a shear correction factor. The governing equations of equilibrium are derived from the virtual work principle. The Navier approach is used to solve equilibrium equations. The constitutive law of the porous FGM sandwich plate is implemented for a 3D finite element through a subroutine in FORTRAN (UMAT) in Abaqus software. Results show good agreement between the finite element model and the analytical method for some results, but the analytical method keeps giving symmetric results even with the thickness stretching effect and load applied to the top surface of the sandwich.

Keywords

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