Optimal shape analysis of a column structure under various loading conditions by using differential transform method (DTM)

The effects of loading on the optimal shape of an Euler-Bernoulli column is investigated by considering four loading conditions which are mainly classified as eccentric compressive and follower type. The governing equations obtained from the structural stability condition of the column are used as a constraint to determine the minimum value of the volume by applying Hamilton principle. In the preceding task, the analysis is presented in step-bystep manner. The calculations are carried out by using differential transform method (DTM) which is a seminumerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the non-linear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The optimal distribution of cross-sectional area along column-length is obtained. Then, the volume of such column is calculated and compared to that of the uniform column which is also stable under given loading. The results obtained revealed out that DTM is a quite powerful solution technique for optimal shape analysis of a column structure.