Keywords: thermal buckling, post-buckling, numerical analysis, functionally graded material, thin-walled, temperature distribution.

A beam model for thermal buckling analysis of thin-walled functionally graded (FG) open-section beams is presented. The Euler-Bernoulli-Navier bending theory and Vlasov torsion theory are employed. The finite element equilibrium equations are developed by updated Lagrangian formulation considering a non-linear displacement cross-section field that includes the effects of warping torsion and large rotations. Material properties are assumed to be graded across the wall thickness and considered as a function of temperature. Three cases of the temperature distribution across the thickness of the cross-section walls are considered, which are uniform, linear and nonlinear, and linear temperature distribution along the beam length. The numerical results for thin-walled FG beam with I-section and channel-section are obtained to investigate the effects of various values of power law index p, FGM configurations and different types of boundary conditions, clamped-clamped (CC), clamped-simply supported (CS), and simply supported (SS), on the critical buckling temperature and post-buckling behaviour. The accuracy and reliability of the beam model are tested by comparison with the results obtained by applying shell finite element models from established packages. It is shown that all of the mentioned effects affect the thermal buckling analysis of open-section beams.

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