Abstract
This paper presents an efficient computational method for optimal structural design in the presence of uncertain Young’s modulus modeled using discretized random fields. To quantify and propagate the uncertainty, random matrix theory is employed to quantify uncertainty in the context of robust topology optimization (RTO) for the minimization of compliance. Random matrix theory employs statistical inference methods to model the matrix-variate probability distribution of the finite element stiffness matrix. This provides analytical expressions for the mean and the standard deviation of the compliance, a combination of which is minimized in RTO. The novel random matrix theory-based RTO is computationally efficient due to the intrusive nature of the method, and is flexible as its computational performance and robustness remain consistent regardless of the correlation lengths or the variance of the random field, as demonstrated through numerical cases. The random matrix RTO method is applied to several two-dimensional numerical problems where the random fields of the modulus are assigned with ranges of correlation lengths and variances to illustrate the versatility of the method. The performance of random matrix RTO is compared with Monte Carlo RTO and stochastic collocation RTO to explore the efficiency and accuracy of the method.
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Notes
In this paper, both the computational time per iteration and the total time are used as metrics for efficiency. The total time shows whether random matrix RTO provides a significant speed up in the overall optimization, while the time per iteration provides a consistent ratio of speed up when comparing amongst the algorithms.
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Acknowledgements
Financial support was provided by the University of Toronto Institute for Aerospace Studies and the Natural Sciences and Engineering Research Council Discovery Grant 2020-06029. The authors would also like to thank Krister Svanberg for supplying the MATLAB code for the MMA algorithm, and Dr. Daniel Pepler for his helpful input.
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Li, L., Steeves, C.A. Random matrix theory for robust topology optimization with material uncertainty. Struct Multidisc Optim 66, 240 (2023). https://doi.org/10.1007/s00158-023-03665-y
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DOI: https://doi.org/10.1007/s00158-023-03665-y