Static and Free Vibration Analysis of FGM Beam Based on Unified and Integrated of Timoshenko's Theory

Abstract In this paper, a higher-order element based on the unified and integrated approach of Timoshenko beam theory is developed. A two-node beam element with Hermitian functions of a 5th-degree polynomial (4 DOFs per node) called UI element is proposed to solve the problems of static and free vibration. In this proposed element, the Timoshenko beam theory is modified in such a way to prevent shear locking while taking account of the transverse shear effect. The static and free vibration analyses are used to obtain the displacements and natural frequencies of rectangular Functionally Graded Material (FGM) beam for hinged-roll, clamped-free and clamped-clamped boundary conditions and to study the effects of the power-law exponent (coupling of the anisotropic material) on the displacements and natural frequencies. Results of the present work are compared with the published data to learn the effectiveness of the proposed element and to verify the validity of the model theory. The numerical analysis shows that the coupling of axial-bending should be taken into consideration in static and vibration analysis of FGM. The comparison study confirms the accuracy and the efficiency of the proposed element for static and vibration analysis of FGM beam.