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A simple quasi-3D theory for static stability analysis of imperfect FG beam

Menasria A., Slimani R., Bouhadra A., Refrafi S., Chitour M., Ali Rachedi M., Himeur N., Zerari K.

Archives of Mechanics

2025

Vol. 77, nr 3

263--287

This study introduces a simplified approach to assess the buckling and static bending of advanced composite beams, including those composed of functionally graded materials (FGMs) with various porosity models. The technique utilizes a straightforward integral quasi-3D approach based on the advanced shear deformation theory. This approach offers several advantages: it simplifies the analysis by reducing the number of unknowns and equations required, improves accuracy by considering the stretch effect across the entire depth of the beam, resulting in more reliable results, and accurately represents shear by satisfying the zero-traction boundary conditions on the beam’s surfaces without the need for a shear correction factor. Additionally, it captures the parabolic pattern of transverse shear strain and stress throughout the depth of the beam. The governing equations are obtained by applying the concept of virtual work, and the Navier solution is employed to calculate analytical solutions for the buckling and static bending of FGM porous beams under different boundary conditions. The approach is in line with and builds upon existing research on FGMs and other sophisticated composite beams, further enhancing its validity and reliability. Finally, computational analyses demonstrate how the distribution of materials, such as power-law functionally graded materials (FGMs), geometry, and porosity, affect the deflections, stresses, and critical buckling load of the beam.

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.