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Topology optimization using an explicit interface representation

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Abstract

We introduce the Deformable Simplicial Complex method to topology optimization as a way to represent the interface explicitly yet being able to handle topology changes. Topology changes are handled by a series of mesh operations, which also ensures a well-formed mesh. The same mesh is therefore used for both finite element calculations and shape representation. In addition, the approach unifies shape and topology optimization in a complementary optimization strategy. The shape is optimized on the basis of the gradient-based optimization algorithm MMA whereas holes are introduced using topological derivatives. The presented method is tested on two standard minimum compliance problems which demonstrates that it is both simple to apply, robust and efficient.

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Notes

  1. Presented at the 10th World Congress on Structural and Multidisciplinary Optimization in 2013.

  2. CHOLMOD is the default solver for sparse symmetric positive definite linear systems in MATLAB.

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Acknowledgments

The authors appreciate the support from the Villum Foundation through the grant: “NextTop”

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet, B.303B, 2800 Kgs., Lyngby, Denmark

    Asger Nyman Christiansen, Morten Nobel-Jørgensen & Jakob Andreas Bærentzen

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

    Niels Aage & Ole Sigmund

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  1. Asger Nyman Christiansen
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  2. Morten Nobel-Jørgensen
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  3. Niels Aage
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  4. Ole Sigmund
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  5. Jakob Andreas Bærentzen
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Correspondence to Asger Nyman Christiansen.

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Christiansen, A.N., Nobel-Jørgensen, M., Aage, N. et al. Topology optimization using an explicit interface representation. Struct Multidisc Optim 49, 387–399 (2014). https://doi.org/10.1007/s00158-013-0983-9

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  • DOI: https://doi.org/10.1007/s00158-013-0983-9

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