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On filter boundary conditions in topology optimization

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Abstract

Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper we define three requirements that boundary conditions must fulfill in order to eliminate boundary effects. Previously suggested approaches are briefly reviewed in the light of these requirements. A new approach referred to as the “domain extension approach” is suggested. It effectively eliminates boundary effects and results in well performing designs. The approach is intuitive, simple and easy to implement.

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Acknowledgements

The authors wish to thank the TopOpt research group at the Technical University of Denmark, particularly Professor Ole Sigmund, for valuable discussions on the topic of this paper.

The authors acknowledge support from the Villum Foundation (the NextTop project) and DTU Mechanical Engineering.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Nils Koppels Alle, B. 404, DK-2800, Lyngby, Denmark

    Anders Clausen & Erik Andreassen

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  1. Anders Clausen
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  2. Erik Andreassen
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Correspondence to Anders Clausen.

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Clausen, A., Andreassen, E. On filter boundary conditions in topology optimization. Struct Multidisc Optim 56, 1147–1155 (2017). https://doi.org/10.1007/s00158-017-1709-1

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  • DOI: https://doi.org/10.1007/s00158-017-1709-1

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