Lateral-Torsional Buckling of Nonuniformly Loaded Beam Using Differential Transformation Method

The paper presents the application of the differential transformation method (DTM) to the stability analysis of nonuniformly loaded beams under bending. The main advantage of the method is the possibility to obtain the semi-analytical solution for the critical loads of the beam undergoing lateral-torsional buckling. To determine the critical load, the system of two coupled ordinary differential equations with variable coefficients and parameters have to be solved. Numerical analyses were carried out for three different types of load functions: (i) Uniformly distributed load, (ii) linearly varying load and (iii) sinusoidally distributed load. The results were compared with the solutions computed by the finite element method (FEM) and those obtained by the authors using the variational iterative method (VIM). In each case, it was found that the difference with reference to the existing one does not exceed 3%, which testifies the effectiveness of the DTM used. Nevertheless, it should be emphasized that the number of terms of the approximation series used is fairly large and therefore the calculation of higher critical loads can be very time-consuming.