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Constrained Optimization and Optimal Control for Partial Differential Equations pp 245–256Cite as

Birkhäuser

Phase-field Approaches to Structural Topology Optimization

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Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 160))

Abstract

The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent approaches based on L2- and H-1-gradient flow dynamics are discussed. The resulting flows are given by Allen-Cahn and Cahn-Hilliard type dynamics coupled to a linear elasticity system. We finally compare numerical results obtained from the two different approaches.

Mathematics Subject Classification (2000). 74P15, 74P05, 74S03, 35K99.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Regensburg, D-93040, Regensburg, Germany

    Luise Blank & Harald Garcke

  2. Department of Mathematics, University of Sussex, Brighton, BN1 9RF, UK

    Lavinia Sarbu & Vanessa Styles

  3. Institut für Wissenschaftliches Rechnen, TU Dresden, D-01062, Dresden, Germany

    Tarin Srisupattarawanit & Axel Voigt

Authors
  1. Luise Blank
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  2. Harald Garcke
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  3. Lavinia Sarbu
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  4. Tarin Srisupattarawanit
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  5. Vanessa Styles
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  6. Axel Voigt
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Corresponding author

Correspondence to Luise Blank .

Editor information

Editors and Affiliations

  1. , Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, Erlangen, 91058, Germany

    Günter Leugering

  2. , Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Geschossbau 2, Dortmund, 44221, Germany

    Sebastian Engell

  3. , Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, Berlin, 12489, Germany

    Andreas Griewank

  4. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Michael Hinze

  5. , Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. , FB 4 - Department Mathematik, Universität Trier, Trier, 54286, Germany

    Volker Schulz

  7. Fakultät für Mathematik, M1, Lehrstuhl für Mathematische Optimierung, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85748, Germany

    Michael Ulbrich

  8. , Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Stefan Ulbrich

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Blank, L., Garcke, H., Sarbu, L., Srisupattarawanit, T., Styles, V., Voigt, A. (2012). Phase-field Approaches to Structural Topology Optimization. In: Leugering, G., et al. Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, vol 160. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0133-1_13

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