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1 Journal of Applied Mathematics and Computational Mechanics

1 2024

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Buckling and bending analysis of porous fg beam using a simple integral QUASI-3D theory

Himeur Nabil, Menasria Abderrahmane, Bouhadra Abdelhakim, Mourad Chitour, Refrafi Salah, Guessoum Loubna, Ouchene Aya, Lebouazda Salima

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 4

30--41

This paper introduces a simplified approach to analyze the buckling and static bending of advanced composite beams, including functionally graded materials (FGMs), with various porosity distributions. This method uses a simple integral quasi-3D approach with a higher-order shear deformation theory, which offers several advantages: reduced complexity by requiring fewer unknowns and governing equations compared to other methods; improved accuracy by incorporating the effect of stretching across the beam’s thickness, leading to more accurate results; finally, accurate shear representation by satisfying the zero-traction boundary conditions on the beam’s surfaces without needing a shear correction factor; and it captures the parabolic distribution of the transverse shear strain and stress across the thickness. The virtual work principle is used to derive the governing equations, and the Navier solution is employed to find analytical solutions for buckling and static bending of various boundary conditions for FGM porous beams. The proposed method agrees well with the literature on FGMs and other advanced composite beams. Finally, numerical results showcase how material distribution (including power-law FGMs), geometry, and porosity affect the beam’s deflections, stresses, and critical buckling load.