Discrete model analysis of optimal columns

The physical parameters of optimal discrete link-spring models, which maximize the buckling load, are reconstructed. The cases where the system is pinned or clamped at one end, and supported by linear spring at the other end, are analyzed. It is shown that the optimal system can be determined recursively by using a one parameter iterative loop. For the pinned-spring-supported boundary conditions there is a region where the optimal solution is not unique. This case is characterized in the paper for the continuous system and its discrete model representation.This study enlightens the results obtained by Tadjbakhsh and Keller in 1962. In particular, it allows evaluation of the strongest column in the transition from the clamped–free to the pinned–pinned boundary condition; and from the (unstable) pinned–free configuration to that associated with the pinned–pinned. We have restricted our study to the regular cases, where there are no internal vanishing cross-sectional areas in the column. It has been shown that for certain range of spring constant the optimal columns are regular in the sense that their cross-section area is positive.