Elastic buckling analysis of multistory functionally graded sway bending frame via finite element method

Current work presents buckling analysis of multistoryfunctionally graded sway bending frame subjected to uniformaxial compression by employing finite element method (FEM).The through-thickness gradation of functionally graded material(FGM) is modeled by conventional rule of mixture. The membersof the frame are ideal and assumed to be thin, consequentlyimperfections, shear deformations as well as extras rotations areneglected. The equivalent bending rigidity of members made upof FGM subjected to pure bending is calculated. The equilibriumequation of linear elastic buckling and deformation of buckledFGM member is calculated by considering total potential energyand using Euler-Lagrange equation. As a result, the local stiffnessmatrix is obtained by considering axial compression effect andignoring axial deformation. After constructing global stiffnessmatrix, neglecting constrained degrees of freedom andconsidering nontrivial solution, the characteristic equation iscalculated. First buckling loads and corresponding mode shapesare calculated by seeking first real positive roots of characteristicequation.