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A review on feature-mapping methods for structural optimization

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Abstract

In this review we identify a new category of methods for implementing and solving structural optimization problems that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is parameterized by a high-level geometric description and that features are mapped onto a non-body-fitted mesh for analysis. One motivation for using these methods is to gain better control over the geometry to, for example, facilitate imposing direct constraints on geometric features, while avoiding issues with re-meshing. The review starts by providing some key definitions and then examines the ingredients that these methods use to map geometric features onto a fixed mesh. One of these ingredients corresponds to the mechanism for mapping the geometry of a single feature onto a fixed analysis grid, from which an ersatz material or an immersed-boundary approach is used for the analysis. For the former case, which we refer to as the pseudo-density approach, a test problem is formulated to investigate aspects of the material interpolation, boundary smoothing, and numerical integration. We also review other ingredients of feature-mapping techniques, including approaches for combining features (which are required to perform topology optimization) and methods for imposing a minimum separation distance among features. A literature review of feature-mapping methods is provided for shape optimization, combined feature/free-form optimization, and topology optimization. Finally, we discuss potential future research directions for feature-mapping methods.

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Notes

  1. The latter work seems to be a more detailed journal version of the former, hence from hereon we only reference the latter.

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Acknowledgments

We thank Dr. Lukas Pflug from the Department of Mathematics at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany, for fruitful discussion and support.

The initiative for this review goes back to critical yet constructive comments by Prof. Kurt Maute, from the University of Colorado Boulder, USA.

We also thank Prof. Horea Ilies from the University of Connecticut, USA, for guidance and insight into some of the geometric aspects of this work.

The first author acknowledges support by Deutsche Forschungsgemeinschaft (DFG) in the framework of the collaborative research center CRC 814 (subproject C2). The third author thanks the support of the US National Science Foundation, award CMMI-1634563.

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Authors and Affiliations

  1. Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany

    Fabian Wein

  2. University of Aberdeen, Aberdeen, UK

    Peter D. Dunning

  3. University of Connecticut, Storrs, USA

    Julián A. Norato

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  1. Fabian Wein
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  2. Peter D. Dunning
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  3. Julián A. Norato
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Correspondence to Julián A. Norato.

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Replication of results

This review paper does not introduce any new methodology, and to replicate results of the different feature-mapping techniques discussed here, we refer the reader to the original works. The code to solve the simple test problems of Sections 3 and 4.4 is available by request from the authors.

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Wein, F., Dunning, P.D. & Norato, J.A. A review on feature-mapping methods for structural optimization. Struct Multidisc Optim 62, 1597–1638 (2020). https://doi.org/10.1007/s00158-020-02649-6

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