Abstract
This paper presents a worst-case approach to robust optimization of plane frame structures under variation in uncertain parameters. The optimization procedure is first implemented without considering uncertainty, resulting in an optimal structure that may be unstable without bending stiffness. Based on such optimal solution, we then take variation in uncertain parameters into consideration and estimate the quantile response or trimmed mean of order statistics, where the quantile response is used as a relaxation of worst value of structural response. In order to obtain robust optimal solutions at various robustness levels, a multiobjective optimization problem is formulated and solved to simultaneously minimize the several order statistics or trimmed means with different orders. It is demonstrated in the numerical examples that the optimal distribution of cross-sectional areas of elements vary with the change of robustness level, and the convergence by using trimmed mean as estimation of quantile response is better than that of the simple order statistics.
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All the results in this research are obtained using homemade MATLAB codes. The source code and the research data can be available from the corresponding author with reasonable request.
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This research is partially supported by China Scholarship Council (File No. 201806050114).
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Shen, W., Ohsaki, M. & Yamakawa, M. Multiobjective robust shape and topology optimization of plane frames using order statistics. Struct Multidisc Optim 63, 75–94 (2021). https://doi.org/10.1007/s00158-020-02663-8
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DOI: https://doi.org/10.1007/s00158-020-02663-8