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

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