Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory

In the present work, attention is focused on the prediction of thermal buckling and post-buckling behaviors of functionally graded materials (FGM) beams based on Euler-Bernoulli, Timoshenko and various higher-order shear deformation beam theories. Two ends of the beam are assumed to be clamped and in-plane boundary conditions are immovable. The beam is subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. The governing equations are developed relative to neutral plane and mid-plane of the beam. A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. New results of thermal buckling and post-buckling analysis of the beams are presented and discussed in details, the numerical analysis shows that, for the case of uniform temperature rise loading, the post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any arbitrary value of the power law index and any various displacement fields.