Buckling capacity of functionally graded beams: A comparative study of different shear deformation beam theories

Abstract

This paper investigates the postbuckling response of simply supported functionally graded beams under axial loading using several beam theories; classical beam theory, CBT, Timoshenko beam theory, TBT and parabolic shear deformation beam theory, PSDBT. Hamilton’s principle is used to derive the governing equations which are solved by closed-form method. It is assumed that the Young’s modulus is varying continuously in the thickness direction according to power-law form while all other material properties are taken to be constant. The effects of the reinforcement distribution, the beam edge-to-thickness ratio and the phase contrast (ratio of the reinforcement Young’s modulus to the matrix Young’s modulus) on the postbuckling behavior and critical buckling load of functionally graded beam are studied. Results demonstrate the important contribution of the shear effect to both the buckling and postbuckling behaviors. Finally, the combinations of reinforcement distribution, beam edge-to-thickness ratio and phase contrast that correspond to the highest and the lowest buckling capacities are identified.