An Efficient Shear Deformation Beam Theory Based on Neutral Surface Position for Bending and Free Vibration of Functionally Graded Beams#

In this article, an efficient shear deformation beam theory based on neutral surface position is developed for bending and frees vibration analysis of functionally graded beams. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded beam in which its material properties vary in the thickness direction is determined. Based on the present higher order shear deformation beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and vibration behavior of functionally graded beams.