Buckling load optimization for heavy elastic columns: a perturbation approach

This paper discusses the problem of achieving the weight distribution of a column, along its height, that optimizes the buckling load of the column, taking into consideration the column self-weight. The field equations of optimality and stability were generated through variational principles and solved by applying the method of perturbation. Results obtained have shown that for the optimal buckling load of a plane-tapered column, the distribution of the cross-sectional area along the column axis follows a perturbed parabolic law. The optimal column has a buckling load which is 21.58% larger than that of the corresponding uniform column with the same volume and height.