Thien-Nhan Nguyen

This paper presents a static analysis of functionally graded porous (FGP) thin-walled beams based on higher-order shear deformation beam theory. The material properties are assumed to vary through the thickness of the thin-wall. Three porosity distribution models, namely uniform porosity distribution (UPD) and symmetric porosity distribution with stiffer (SPD-1) and softer at the surface (SPD-2), are considered. A mono-symmetrical thin-walled I-beam profile is analyzed under static loading conditions. The beam kinematics are formulated within the framework of higher-order thin-walled beam theory. The governing equations for the static problem are derived using Lagrange’s equations. Based on the Bézier approximation function, the Ritz method is employed to solve these equations. Additionally, the numerical results examine the effects of higher-order shear deformation, porosity coefficient, porosity distribution, and length-to-height ratio on the vertical displacement and twist angle of the beams. These outcomes aim to evaluate the model’s accuracy and establish benchmarks for future investigations.

This paper presents a novel shear deformation theory for analyzing porous microbeams’ bending, buckling, and free vibration resting on a foundation. The proposed shear function incorporating three kinetic variables satisfies zero-traction boundary conditions on the top and bottom surfaces of the beams and does not require a shear correction factor. The modified couple stress theory accounts for the size-dependent effects, and the governing equations are derived from Lagrange’s equation using the proposed shear function. Legendre–Ritz functions are developed to analyze the porous microbeams’ buckling, free vibration, and bending behaviors. The effects of material length scale parameter, porosity, span-to-height ratio, boundary condition, and foundation parameter on the mechanical responses of beams are investigated. Numerical results demonstrate the accuracy and efficiency of the proposed theory and can serve as benchmarks for future analysis of porous microbeams on elastic foundations.