Robust fuzzy structural safety assessment using mathematical programming approach

This paper presents a robust safety assessment for engineering structures involving fuzzy uncertainties. Uncertain applied loads and yielding capacities of structural elements are modelled as fuzzy variables with associated membership functions representing possibility distributions. Anew computation-orientated methodology, namely the alpha-level collapse assessment (alpha-level CA) approach, is developed to provide structural safety profile by constructing membership function of the structural collapse load limit accommodating fuzzy uncertainties. The proposed method firstly utilizes the alpha-level strategy to transform the fuzzy limit analysis into a series of interval limit analyses. By implementing the concept of robust and optimistic optimizations, a mathematical programming (MP) scheme is proposed to explicitly capture the upper and lower bounds of the collapse load limit at each alpha-sublevel. Subsequently, the membership function of the collapse load limit is established by using the upper and lower bounds obtained from the series of alpha-sublevel calculations. The proposed alpha-level mathematical programming scheme preserves the quality of sharpness of the bounds of collapse load limit at each a-sublevel, which consequently provides a rigorous evaluation on the fuzzy profile of the safety of engineering structures against structural collapse. Numbers of numerical examples, motivated by real-world engineering applications, have been investigated to illustrate the accuracy, efficiency and applicability of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.