On buckling optimization under uncertain loading combinations

This paper proposes a technique to optimize structural components for buckl ing when the applied loads are partially unknown or unpredictable. As oppos ed to the traditional buckling optimization situation where the loading con figuration is specified, the load ratios are assumed uncertain and are inco rporated as variables in the optimization problem formulation. As a result, the optimal designs obtained are insensitive to load variations within an admissible convex set. Additionally, in order to generalize the results and therefore provide a systematic solution procedure, a theorem concerning ti le shape of the stability boundary of structures whose buckling loads are t he solution of linear eigenproblems is stated and proven.