Post-Buckling Analysis of FGM Beams According to Different Shear Deformation Theories

Abstract

In this paper, the compact solution for post-buckling of beam made of functionally graded material under axial loading is introduced. The FGM beam ends are restrained from axial movement. The governing equations and the boundary conditions are derived using the principle of stationary potential energy and the governing equations are solved by closed-form method. The effects of material compositions, slenderness ratios and boundary conditions that lead to the considerable changes in buckling and post-buckling behaviors are investigated. The shear deformation effects on the critical buckling load is introduced using Euler-Bernoulli, Timoshenko, and some higher-order beam theories. Results of this analysis illustrate that classical and first-order theories underestimate the amplitude of buckling, while some higher-order theories yield very close results for the static post-buckling response.