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A short numerical study on the optimization methods influence on topology optimization

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Abstract

Structural topology optimization problems are commonly defined using continuous design variables combined with material interpolation schemes. One of the challenges for density based topology optimization observed in the review article (Sigmund and Maute Struct Multidiscip Optim 48(6):1031–1055 2013) is the slow convergence that is often encountered in practice, when an almost solid-and-void design is found. The purpose of this forum article is to present some preliminary observations on how designs evolves during the optimization process for different choices of optimization methods. Additionally, the authors want to open a discussion on how to properly define and identify the boundary translation that is often observed in practice. The authors hope that these preliminary observations can open for fruitful discussions and stimulate further investigations concerning slowly moving boundaries. Although the discussion is centered on density based methods it may be equally relevant to level-set and phase-field approaches.

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Notes

  1. In this manuscript the word solve (in the context of optimization problems) should be understood as finding a point numerically satisfying the KKT conditions within some prescribed tolerances.

  2. Number of optimization sub-problems solved.

  3. The KKT condition of IPOPT cannot be obtained with the interface used in these numerical examples, and thus cannot be presented in Fig. 9.

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Acknowledgements

We would like to thank Professor Krister Svanberg at KTH in Stockholm for providing the implementation of MMA. We also express our sincere thanks to the two reviewers and the editor for their honest comments and suggestions which lead to improvements of the article.

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Authors and Affiliations

  1. Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000, Roskilde, Denmark

    Susana Rojas-Labanda & Mathias Stolpe

  2. Department of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé, Building 404, 2800, Kgs. Lyngby, Denmark

    Ole Sigmund

Authors
  1. Susana Rojas-Labanda
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  2. Ole Sigmund
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  3. Mathias Stolpe
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Corresponding author

Correspondence to Susana Rojas-Labanda.

Additional information

This research is funded by the Villum Foundation through the research project Topology Optimization – the Next Generation (NextTop).

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Rojas-Labanda, S., Sigmund, O. & Stolpe, M. A short numerical study on the optimization methods influence on topology optimization. Struct Multidisc Optim 56, 1603–1612 (2017). https://doi.org/10.1007/s00158-017-1813-2

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  • DOI: https://doi.org/10.1007/s00158-017-1813-2

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