Thermal Buckling and Post-buckling Characteristics of Functionally Graded Material Rods with General Boundary Conditions

The present study focuses on thermal buckling and post-buckling analysis of functionally graded material (FGM) rods for various uniform temperature rises under different sets of boundary condition. Only chemical gradient FGMs are analyzed and power law functions are considered for material gradient along the thickness of the rod. The governing equations are developed relative to the neutral plane, and displacement fields are considered to be of first order to coincide with the Timoshenko beam theory. The set of highly nonlinear equations are solved using a commercial software package, ANSYS based on finite element method (FEM). To tackle the problem of spatial variation of material properties along the thickness of the FGM rod, the entire geometry is divided into finite number of layers, each layer being homogeneous and material properties are assigned to the layers from the power function making the spatial variation of any material property a piecewise function across the thickness of the whole geometry. Variation of critical buckling temperature and post-buckled configurations for different material gradient under different thermal loading and rod end conditions are observed and presented.