On buckling of axially functionally graded beams

Abstract

Abstract:In his study Aydogdu analyzed the vibration and buckling of axially functionally graded simply supported beams. By using pre-defined frequency and buckling loads he determined the Young's modulus in axial direction as a function of axial coordinate. In this study it is demonstrated that there is error in his calculation; moreover, corrected computation is presented and the right solution of the ODE is visualized. It is pointed out that the method used by Aydogdu is apparently not applicable for the solution of the problem at hand.

A note on semi-inverse method for buckling of axially functionally graded beams

“…which is the correct form of the faulty equation (15) in reference [1]. It was shown in reference [2] that the solution of differential equation of (1) is…”

“…From now on we concentrate on function (2). The domain of axial variable x is 0 x L. Introducing ¼ m L , we obtain that 0 x L ¼ m. It seems to be reasonable to introduce the new variable ¼ x L , for which we have 0 1, while the elasticity modulus EðxÞtakes the form…”

“…It was shown in reference [2] that the solution of differential equation of (1) is …”