Postbuckling Analysis of Functionally Graded Beams

This paper studies the geometrically non-linear bending behavior of functionally graded beams subjected to buckling loads using the finite element method. The computational model is based on an improved first-order shear deformation theory for beams with five independent variables. The abstract finite element formulation is derived by means of the principle of virtual work. High-order nodal-spectral interpolation functions were utilized to approximate the field variables which minimizes the locking problem. The incremental/iterative solution technique of Newton's type is implemented to solve the nonlinear equations. The model is verified with benchmark problems available in the literature. The objective is to investigate the effect of volume fraction variation in the response of functionally graded beams made of ceramics and metals. As expected, the results show that transverse deflections vary significantly depending on the ceramic and metal combination.