Buckling analysis of beams using higher-order theories and the Differential Transform Method

This study investigates the buckling behavior of beams using higher-order beam theory in conjunction with the Differential Transform Method. To validate the accuracy and effectiveness of the proposed approach, the buckling loads of a classical Euler beam are first determined and used as a benchmark. In calculating the critical load, the governing equations and boundary conditions of the beams are derived using the energy method. The critical loads of more complex beam models are then obtained using higher-order theories with the aid of the Differential Transform Method and compared with values reported in the literature for Euler and Timoshenko beams. The importance of the critical loads predicted by the higher-order theories is further illustrated through graphical representations.