Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

Abstract

The Dynamic Finite Element (DFE) theory is applied to calculate the natural frequencies of Functionally Graded Material (FGM) beams. The formulation derived is based on Euler-Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness of the beam. Results from DFE are numerically validated against methods such as Classical Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM), as well as other data found in literature. Commercial software was used to further validate the proposed DFE formulation. The test cases showed that DFE results displayed excellent agreement to published results. When compared to the FEM method, DFE showed higher accuracy while requiring fewer elements to converge to the solution. Finally some general comments are made on possible future research paths for DFE method on FGM beams.