Yangjun Luo, Zhan Kang

[Steve Yenisch]

Paper: www.mae.ufl.edu/nkim/ISSMO/ZhanKangPaper.pdf

Reliability-based optimization of structures using probability and convex set mixed models
Yangjun Luo, Zhan Kang
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

ABSTRACT
In certain circumstances of the safety assessment and the reliability-based design optimization of structures, the probability and convex set mixed models may be suitably used for the uncertainty description. Based on the probabilistic and convex set mixed model, this paper presents a mathematical definition of reliability index for measuring the safety of structures. The optimization problem is then mathematically formulated and converted into more tractable one. Moreover, the double-loop optimization problem is transformed into an approximate single-loop minimization problem using the linearization-based technique, which further facilitates efficient solution of the design problem. Numerical examples demonstrate the validity of the proposed formulation as well as the efficiency of the presented numerical techniques.
Keywords: structural optimization; reliability; probability; convex set; mixed model

[haftka]

If I understand the formulation right, this is a worst-case design for the bounded variables that are not random. Is that right?

If this is the case, why do the bounds have to be convex? Won't the approach work even if they are not convex?

[kangzhan]

Actually, this approach accounts for design problems involving both stochastic and bounded uncertainties. The reliability of the structural is defined as the safely probability when the bouned variables take the worst-case values. We consider the ellipsoidal convex model as a differentiable and smooth descrition of the variation bounds. Therefore convex models are used in this study.