An interval iterative method for response bounds analysis of structures with spatially uncertain parameters. (1st July 2023) - Wu, Pengge; Ni, Bingyu; Jiang, Chao
Highlights: The spatially uncertain parameters are described by the interval field model with upper and lower bounds. An interval iterative method is proposed for static response analysis of structures with spatial uncertainties which can effectively avoid the overestimation existing in traditional interval analysis. The upper and lower bounds of the responses obtained by the proposed method could envelop the actual response bounds. Abstract: Parameters with spatial uncertainties are very common in practical engineering, which could have a significant effect on structural performances. Different from the framework of probability theory, the interval field model describes the spatial uncertainty with upper and lower bounds rather than the probability distribution function or other statistical characteristics. By introducing the interval field model into finite element analysis and solving the resulting interval finite element equilibrium equation, the upper and lower bounds of structural responses can then be obtained. This paper proposes an interval iterative method for static displacement response analysis of structures with spatial uncertainties, effectively improving the overestimation existing in traditional interval analysis due to dependency problems and obtaining a compact interval envelope of the exact response bounds. Firstly, the spatially uncertain parameters described by the interval field are represented by the interval Karhunen–Loève (K-L) expansion, based on which the interval finite element equilibrium equation is formulated. Secondly, the interval finite element problem is decomposed into several subproblems, and an interval iterative method is developed for an envelope solution of the structural response bounds. Finally, the accuracy and efficiency of the proposed method are verified by several numerical examples.