Thermal post-bunkling analyses of functionally graded material rod

Abstract

The non-linear governing differential equations of immovably simply supported functionally graded material (FGM) rod subjected to thermal loads were derived. The thermal post-buckling behaviors of FGM rod made of ZrO2 and Ti-6A1-4Vwere analyzed by shooting method. Firstly, the thermal post-buckling equilibrium paths of the FGM rod with different gradient index in the uniform temperature field were plotted, and compared with the behaviors of the homogeneous rods made of ZrO2 and Ti-6A1-4V materials, respectively. For given value of end rotation angles, the influence of gradient index on the thermal post-buckling behaviors of FGM rod was discussed. Secondly, the thermal post-buckling characteristics of the FGM rod were analyzed when the temperature difference parameter is changed while the bottom temperature parameter remains constant, and when the bottom temperature parameter is changed while the temperature difference parameter remains constant, and compared with the characteristics of the two homogeneous material rods.

Thermomechanical buckling oftemperature-dependent FGM beams

“…Huang and Li [6] obtained an exact solution for mechanical buckling of FGM columns subjected to uniform axial loading based on various beam theories. Zhao et al [7] studied the post-buckling of simply supported rod made of functionally graded materials under uniform thermal loading and nonlinear temperature distribution across the beam thickness using the numerical shooting method. They found that, under the same temperature condition, the deformation of immovably simply supported FGM rod is smaller than those of the two homogenous material rods.…”

Nonlinear thermal dynamic buckling of FGM beams

“…Zhao et al [7] reformulated the non-linear governing equilibrium equations of an FGM beam to a new system of ordinary differential equations suitable for shooting method. Numerical results of this study reveal the unique and stable equilibrium path for simply supported FGM beams under uniform thermal loading.…”

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

“…Ma and Lee [11] obtained a closed-form solution for the non-linear static response of both clamped-clamped and pinned-pinned FGM beams subjected to in-plane thermal loads. Zhao et al [12] studied post-buckling deformations of immovable simply-supported (S-S) FGM EBBs subjected to a thermal load and presented thermal post-buckling equilibrium paths for di erent values of the material gradient parameter. The post-buckling of clamped FGM TBs was numerically studied by Li et al [13] with the shooting method.…”