Robust design of structures using convex models

Robust design aims to achieve a state of robustness so that the performance of a design is least sensitive to the variability of uncertain variables. In this paper, a novel method of robust design is proposed using the convex model with the help of the unsatisfactory degree functions. The robustness of the objective function is achieved by minimizing the worst value of unsatisfactory degree functions of the uncertainty parameters while the feasibility robustness is ensured by a sub-optimization conducting the worst-case analysis. The proposed model is a nested optimization and a decomposition technique is then employed to relieve computational burdens. The robust design of a 10-bar aluminium truss and a 25-bar steel truss under uncertain loads are carried out based on the proposed model as numerical examples.