A New Higher Order Shear Deformation Model of Functionally Graded Beams Based on Neutral Surface Position

Abstract

This paper uses a new refined beam theory based on neutral surface position for the static and free vibration analysis of functionally graded material beams. The theory accounts for parabolic 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 with its material properties varying in the thickness direction is determined. Based on the present refined shear deformation beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

“…Li formulated an analytical solution to analyze the static and dynamic behaviours of FGM Timoshenko and Euler-Bernoulli beams [25]. Higher order theories were investigated to introduce more complex characteristics such as shear deformation and warping, a sample of research papers [26][27][28][29][30][31][32][33][34][35][36][37][38] are quoted here which provide a good introduction on the subject.…”

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

“…Li formulated an analytical solution to analyze the static and dynamic behaviours of FGM Timoshenko and Euler-Bernoulli beams [25]. Higher order theories were investigated to introduce more complex characteristics such as shear deformation and warping, a sample of research papers [26][27][28][29][30][31][32][33][34][35][36][37][38] are quoted here which provide a good introduction on the subject.…”