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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.

Effect of porosity distribution on flexural and free vibrational behaviors of laminated composite shell using a novel sinusoidal HSDT

Addou Farouk Yahia, Bourada Fouad, Tounsi Abdeldjebbar, Bousahla Abdelmoumen Anis, Tounsi Abdelouahed, Benrahou Kouider Halim, Albalawi Hind

Archives of Civil and Mechanical Engineering

2024

Vol. 24, no. 2

art. no. e102, 2024

This work analyzes the impact of porosity on the static and dynamic behaviors of laminated composite shells using a novel high-order shear deformation theory. The employed model considers five unknown variables with a new sinusoidal shear function which provides precise distribution of transversal shear stresses through the thickness direction of the shell. The porosity can occur in the structure and can reduce their mechanical properties. For this purpose, three different porosity distributions in the thickness direction are considered in this investigation, the first model has the same percentage of the micro-void in the all thickness, the second one the percentage of the porosity is higher in the upper and lower surfaces contrary the third model the porosity percentage is maximum at the means axis. The governing differentials equations are derived using Hamilton’s principle and solved by Navier’s method. In the numerical results, transversal deflection, natural frequencies and axial and shear stresses are determined for laminated composite plates and shells with porosity, to verify the exactness and effectiveness of the new shell theory and to compare the results with those of the other solutions previously published.