An efficient simple element for free vibration and buckling analysis of FG beam

Abstract

In this paper, a simple and efficient element is proposed for free vibration and buckling analysis of FGM beams. This element is formulating, based on Timoshenko beam theory. Assumption of constant shear strain in the element, reduces number of unknowns in addition to improving the efficiency of new element. The performance of the new element is evaluated with the help of several benchmark tests. First, the accuracy and convergence rate of the proposed element response in the analysis of free vibration and buckling of the beam are investigated separately by exponential variations of the modulus of elasticity and density in each of the beams' thickness and length. Subsequently, the element's ability to model material variations in both longitudinal and thickness directions of the beam will be measured simultaneously. For comparison, the answers of good elements of other researchers are available in each of the numerical tests. These tests will prove the high accuracy and rapid convergence rate of the proposed element.