Thermal postbuckling analysis of functionally graded tubes based on a refined beam model

This paper studies the thermal buckling and postbuckling of functionally graded tubes whose material properties are temperature-dependent based on a refined beam model. Firstly, the displacement field of the tubes is expanded in a Laurent series expansion form so that the shear stress on the inner and outer surfaces is vanished. Then, the nonlinear governing equations of the tubes are obtained by the generalized variational principle. Finally, the problem is solved by adopting a two-step perturbation technique. In order to valid the correctness of a present high-order beam model and calculation method, the analytical solution of Timoshenko beam model and Euler beam model for thermal postbuckling are presented. In numerical results, effects of transverse shear deformation, the volume fraction and inner radius on critical thermal buckling and postbukling are investigated.