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Level-set methods for structural topology optimization: a review

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Abstract

This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.

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Notes

  1. Some LSMs reverse the sign in (1) (e.g., Wang and Wang 2006b).

  2. Some implementations can be found on the internet: The codes of G. Allaire, V.J. Challis, N.P. van Dijk and M.Y. Wang.

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Acknowledgements

The authors would like to gratefully acknowledge the support of the National Science Foundation under grant EFRI-1038305 (second author) and the Dutch MicroNed programme (other authors). The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organization. We are grateful for the insights Professor Grégoire Allaire, Ecole Polytechnique, France, shared with us.

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Authors and Affiliations

  1. Uppsala University, Lägerhyddsvägen 1, Uppsala, Sweden

    N. P. van Dijk

  2. University of Colorado, Boulder, CO, 80309-0429, USA

    K. Maute

  3. Delft University of Technology, Mekelweg 2, 2628, CD Delft, The Netherlands

    M. Langelaar & F. van Keulen

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  1. N. P. van Dijk
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  2. K. Maute
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  3. M. Langelaar
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  4. F. van Keulen
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Correspondence to N. P. van Dijk.

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van Dijk, N.P., Maute, K., Langelaar, M. et al. Level-set methods for structural topology optimization: a review. Struct Multidisc Optim 48, 437–472 (2013). https://doi.org/10.1007/s00158-013-0912-y

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  • DOI: https://doi.org/10.1007/s00158-013-0912-y

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