Abstract
Despite a solid theoretical foundation and straightforward application to structural design problems, 3D topology optimization still suffers from a prohibitively high computational effort that hinders its widespread use in industrial design. One major contributor to this problem is the cost of solving the finite element equations during each iteration of the optimization loop. To alleviate this cost in large-scale topology optimization, the authors propose a projection-based reduced-order modeling approach using proper orthogonal decomposition for the construction of a reduced basis for the FE solution during the optimization, using a small number of previously obtained and stored solutions. This basis is then adaptively enriched and updated on-the-fly according to an error residual, until convergence of the main optimization loop. The method of moving asymptotes is used for the optimization. The techniques are validated using established 3D benchmark problems. The numerical results demonstrate the advantages and the improved performance of our proposed approach.
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Notes
Refining the basis by discarding the older less relevant information in favor of more recent information is a fairly standard strategy, also used by Gogu (2015)
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Acknowledgments
The first and third author formally acknowledge the contribution of their Masters student Mr. Jin Wentao, Huawei inc. to this work. The third and fourth author express their sincere gratitude to Mr. Tabrej Alam, Masters student at NIT Silchar for his help in testing the codes in its initial stages.
Funding
This multi-national research study was supported by the National Natural Science Foundation of China (Grant No. 11620101002 and Grant No. 11972166) and the Fundamental Research Funds for the Central Universities (Grant No. 310201911cx029).
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The source codes in this work are an evolution of the 88-line Matlab code, according to the proposed methodology, along with the definition of test cases, which allow to reproduce the numerical results presented in this paper. These codes could be made available on request by emailing the corresponding author.
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Xiao, M., Lu, D., Breitkopf, P. et al. On-the-fly model reduction for large-scale structural topology optimization using principal components analysis. Struct Multidisc Optim 62, 209–230 (2020). https://doi.org/10.1007/s00158-019-02485-3
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DOI: https://doi.org/10.1007/s00158-019-02485-3