Bounds for uncertain structural problems with large-range interval parameters
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O R I G I NA L
Tonghui Wei · Feng Li Dan Yao
· Guangwei Meng · Wenjie Zuo ·
Bounds for uncertain structural problems with large-range interval parameters
Received: 21 August 2020 / Accepted: 9 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A novel bivariate interval function decomposition method is proposed and applied to predict the bounds of structural response with large-range interval parameters. When the existing interval methods solve large uncertainty problems, either the calculation accuracy is poor or better accuracy is often achieved at the cost of more computational effort. To overcome this drawback, the bivariate interval function decomposition (BIFD) is first constructed for the approximation of the original response function. The univariate and the bivariate points are substituted into the second-order Taylor expansion to derive BIFD; thus, the expression of BIFD contains only the one- and two-dimensional functions. Particularly, the response function is decomposed into the sum of multiple low-dimensional functions, and solving the bounds of multi-dimensional original response can be transformed into solving those of low-dimensional interval functions. Then, the sensitivity information of structural response with respect to uncertain parameters is utilized to save computational consumption. Finally, the precision and effectiveness of the method are validated by comparing it with the other six existing interval analysis methods through several numerical examples and engineering applications. Keywords Structural static analysis · Bivariate interval function decomposition · Large-range interval uncertain parameters · Taylor series
1 Introduction Structural static analysis usually based on deterministic modeling is a primary but key component of structural designing. However, their material properties, geometric dimensions, and boundary conditions are uncertain in practical engineering owing to multiple reasons, such as aggressive environmental factors and inevitable measurement errors [1–4]. Such parameter uncertainties will make structural response uncertain. Thus, the impacts of parameter uncertainty on structural response should be fully considered. Uncertainty analysis often employs probabilistic and non-probabilistic methods to determine the mechanical effects of uncertainty on structures. Generally, if the probability density function of uncertain parameters can be clarified, the probability model is the most effective solution. Nevertheless, the model is also encountered by a severe limitation: much information about uncertainty is needed to assess the statistical distribution of assumptions [5,6]. In comparison, the non-probabilistic model needs little information to clarify the bounds of parameters and thus is outstanding in uncertainty modeling. T. Wei · F. Li (B) · G. Meng · W. Zuo School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, Jilin, China E-mail: [email protected] D. Yao Changchun National Extreme Precision Optics
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