An application of differential transformation to stability analysis of heavy columns

This paper uses a recently developed technique, known as the differential transformation, to determine the critical buckling load of axially compressed heavy columns of various support conditions. In solving the problem, it is shown that the differential transformation technique converts the governing differential equation into an algebraic recursive equation, which must be solved together with the differential transformation of the boundary conditions. Although a fairly large number of terms are required for convergence of the solution, the differential transformation method is nonetheless efficient and fairly easy to implement. The method is also shown to be very accurate when compared with a known analytical solution. The stability of heavy columns is further examined using approximate formulae currently available in the literature. In this case, the differential transformation method offers a reference for assessing the accuracy of the approximate buckling formulae