A non-probabilistic robust reliability method for analysis and design optimization of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. Reliability issues stem rightly from the existence of all sorts of uncertainties. In reliability modeling, an appropriate way for dealing with uncertainties and a corresponding reasonable index system for measuring the reliability are essential. The main purpose of this paper is to present a generalized non-probabilistic reliability methodology for analysis and design of structures with bounded uncertainties. The input uncertain parameters are treated as interval variables, and the two representative convex-set models, hyper-rectangle model and hyper-ellipsoid model, are adopted to describe bounded uncertainties. A non-probabilistic reliability measuring system is developed, in which dimensionless non-probabilistic reliability indices are defined in different situations by adopting a similar way as the traditional probabilistic reliability method for structures. The measuring system of reliability is explained in detail and is illustrated schematically. Based on these, a non-probabilistic reliability methodology for structures with uncertain-but-bounded parameters is presented systematically. The fundamental problem of how to construct a convex-set model is briefly discussed by examples and numerical experiments. Four other numerical examples are provided to illustrate the effectiveness and feasibility of the presented method.