Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness

The present work deals with geometrically non-linear post-buckling load-deflection behavior of functionally graded material (FGM) Timoshenko beam under in-plane thermal loading. Thermal loading is applied by providing non-uniform temperature rise across the beam thickness at steady-state condition. FGM is modeled by considering continuous distribution of metal and ceramic constituents across the thickness using power law variation of volume fraction. The effect of geometric non-linearity at large post-buckled configuration is incorporated using von Kármán type non-linear strain-displacement relationship. The governing equations are obtained using the minimum potential energy principle. The system of non-linear algebraic equations is solved using Broyden's algorithm. Four different FGMs are considered. A comparative study for post-buckling load-deflection behavior in non-dimensional form is presented for different volume fraction exponents and also for different FGMs, each for different length-thickness ratios.