Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory

This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling of functionally graded beams. The present element has five nodes and ten degrees-of-freedom. Material properties vary continuously through the beam thickness according to the power-law form. Governing equations are derived with the aid of Lagrange's equations. Natural frequencies and buckling loads are calculated numerically for different end conditions, power-law indices, and span-to-depth ratios. Accuracy of the present element is demonstrated by comparisons with the available results.