On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters

This paper investigates the formulation and numerical solution of reliability-based optimization of structures exhibiting grouped uncertain-but-bounded variations. Based on the multi-ellipsoid convex model description for grouped uncertain-but-bounded parameters, the mathematical definition of a non-probabilistic reliability index is presented for quantified measure of the safety margin. The optimal design is then formulated as a nested optimization problem. A method based on concerned performance is proposed for regularization of the reliability index constraints. The expensive computation of the non-probabilistic reliability index and its derivative is thus avoided. Numerical examples are given to illustrate the validity and efficiency of the present method.

► We propose an optimization formulation of structures with bounded uncertainties. ► A non-probabilistic reliability index is defined based on multi-ellipsoid convex model. ► This provides a quantified measure of safety margin. ► The optimal design is stated as a nested optimization problem. ► Concerned performance method enables regularization of reliability constraints.