Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method

A new approach based on combination of cell-center finite volume method (C-C FVM) and Timoshenko beam theory has been developed to analyze static and free vibration of functionally graded beams in this paper. The general dynamic equations for under uniformly load functionally graded beam (FGB) are derived using Hamilton’s principle, and the equations can be simplified for static bending or free vibration problem. Governing equations are discretized by C-C FVM in spatial space. In the analysis, three different kinds of shear correction factors are considered and material properties are assumed to vary continuously by power-law along the thickness. To validate the accuracy of the numerical method, the deflection and natural frequencies of FGB are studied. Good agreement is achieved between present results and literatures for different boundary conditions, shear correction factors, material distribution and span-depth ratios. Furthermore, the optimal shear correction factor is obtained by comparing three different kinds of shear correction factors and the no shear locking phenomenon in static analysis is presented.