A n-order refined theory for bending and free vibration of functionally graded beams

In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton\'s principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.