On robust design optimization of truss structures with bounded uncertainties

This paper investigates robust design optimization of truss structures with uncertain‐but‐bounded parameters and loads. The variations of the cross‐sectional areas, Young’s moduli and applied loads are treated with non‐probabilistic ellipsoid convex models. A robustness index for quantitatively measuring the maximal allowable magnitude of system variations is presented, and the design problem is then formulated as to maximize the minimum of the robustness indices for all the concerned design requirements under a given material volume constraint. For circumventing the difficulty associated with the max‐min type problem, an aggregate function technique is employed to construct a smooth objective function. The computational scheme for the sensitivity of the robustness index is derived on the basis of optimum sensitivity analysis. The optimization problem is then solved by using the GCMMA optimizer. Numerical examples illustrate the validity and effectiveness of the present formulation and solution techniques.