Buckling Analysis Behavior of Functionally Graded Beams

In this paper, the static-buckling behavior of functionally graded material (FGM) beams has been reported via the finite-element method. Two separate finite element formulations are developed, one based on Euler- Bernoulli theory and the other one on the Timoshenko beam theory. FGM beams have a smooth variation of material properties due to continuous (unbroken) change in micro-structural details. The variation of material properties is along the beam thickness and is assumed to trail a power-law of the volume fraction of the constituents, usually ceramic and metal. Principle of virtual work is used to obtain the finite element system of equations. The stiffness and the geometrical stiffness matrix of FGM beams are given in detail as they have not been presented before. The model has been evaluated and validated with benchmark results available in the literature and a good agreement was found. Finite element numerical results are presented in tabulated and graphical forms to figure out the effects of power-law index, slenderness ratio and boundary conditions on buckling analysis of FGM beams.