A general assessment index for non-probabilistic reliability of structures with bounded field and parametric uncertainties

This paper focuses on the reliability assessment of structures exhibiting both bounded field uncertainties and uncertain-but-bounded parameters in a non-probabilistic framework. Based on the bounded field model for spatially varying uncertainties and the multi-ellipsoid convex set description for uncertain parameters, the mathematical definition of a new reliability index is proposed to quantify the safety measures of a structure. The problem is defined as finding the maximal allowable range of uncertainties within the safety margin of the performance function in the normalized uncertain space. A gradient-based mathematical programming algorithm is used to seek the most probable failure realization of uncertainties and to obtain the non-probabilistic reliability index. The proposed index provides a general and unified formation of structural non-probabilistic reliability with uncertain-but-bounded field or parameters. Numerical examples, considering the reliability assessment of structural performance in stiffness, eigenfrequency, and buckling problems, are also given to illustrate the validity and applicability of the proposed method.