Static analysis of functionally graded porous thin-walled I-beams based on higher order shear deformation beam theory

Abstract

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.