Thermomechanical buckling of temperature-dependent FGM beams

Abstract

Buckling of beams made of functionally graded materials (FGM) under thermomechanical loading is analyzed herein. Properties of the constituents are considered to be functions of temperature and thickness coordinate. The derivation of the equations is based on the Timoshenko beam theory, where the effect of shear is included. It is assumed that the mechanical and thermal nonhomogeneous properties of beam vary smoothly by distribution of the power law index across the thickness of the beam. The equilibrium and stability equations for an FGM beam are derived and the existence of bifurcation buckling is examined. The beam is assumed under three types of thermal loadings; namely, the uniform temperature rise, heat conduction across the thickness, and linear distribution across the thickness. Various types of boundary conditions are assumed for the beam with combination of roller, clamped, and simply-supported edges. In each case of boundary conditions and loading, closed form solutions for the critical buckling temperature of the beam is presented. The results are compared with the isotropic homogeneous beams, that are reported in the literature, by reducing the results of the functionally graded beam to the isotropic homogeneous beam.