Modeling of the Lateral-Torsional Buckling of the Functionally Graded Material Open Section Thin-Walled Columns

A new torsion theory system for thin-walled structures, the Plate–Beam theory, was used to explore the lateral torsional buckling (LTB) performance of functionally graded material (FGM) thin-walled columns with open cross-section. The application details were presented using the T-section columns as the study carrier. The energy functional model was first determined, in the derivation process from which the warping constant, centroid and shear center were derived concomitantly. Afterward, the equilibrium differential equation model and the LTB critical load were formulated. The analytical process did not involve any sectorial coordinate operation. A numerical program was performed in parallel to evaluate the accuracy of theoretical equations. The section twist rotation and critical load error between the theoretical and numerical results were all lower than 2%. Especially, the warping displacement and warping normal stresses can be described with high precision. Based on the comprehensive theoretical analysis and numerical simulation, it was evident that the Plate–Beam theory was a reliable method for the FGM thin-walled member torsion performance study. The formulation process in this work provided a replicable direct reference for FGM members with other types of open sections.