Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams

摘要

Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler-Bernoulli beam subjected to axial com-pressive load have been derived for clamped-clamped (C-C), simply supported-simply supported (S-S) and clamped-free (C-F) edges. However, no such relation is found for clamped-simply supported (C-S) beams. For C-S beams, the transcendental equation has been derived to find the critical buckling load for the FGM Timoshenko beam which is similar to that for a homogeneous Euler-Bernoulli beam. For the FGM beams Young's modulus, E, and Poisson's ratio, v, are assumed to vary through the thickness. The significance of this work is that for the C-C, S-S and C-F FGM Timoshenko beams, the critical buckling load can be easily found from that of the corresponding homogeneous Euler-Bernoulli beam and two constants whose values depend upon the through-the-thickness variations of ￡ and v. For the C-S FGM Timoshenko beam the transcendental equation for the determination of the critical buckling load is similar to that for the corresponding homogeneous Euler-Bernoulli beam.