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Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications

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Trends in PDE Constrained Optimization

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 165))

Abstract

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. The forward system is reformulated such that it involves the plastic multiplier and a complementarity condition. In order to derive necessary optimality conditions, a family of regularized optimal control problems is analyzed. C-stationarity type conditions are obtained by passing to the limit with the regularization. Numerical results are presented.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Technische Universität Chemnitz, 09126, Chemnitz, Germany

    Roland Herzog & Gerd Wachsmuth

  2. Faculty of Mathematics, Technical Universität Dortmund, Vogelpothsweg 87, 44227, Dortmund, Germany

    Christian Meyer

Authors
  1. Roland Herzog
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  2. Christian Meyer
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  3. Gerd Wachsmuth
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Corresponding author

Correspondence to Roland Herzog .

Editor information

Editors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

  2. Institut für Dynamik komplexer technisch, Max-Planck-Institut, Magdeburg, Germany

    Peter Benner

  3. Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Dortmund, Germany

    Sebastian Engell

  4. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

    Andreas Griewank

  5. Mathematisches Institut, Universität Basel, Basel, Switzerland

    Helmut Harbrecht

  6. Fachbereich Mathematik Optimierung und Approximation, Universität Hamburg, Hamburg, Germany

    Michael Hinze

  7. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

    Rolf Rannacher

  8. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Stefan Ulbrich

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Herzog, R., Meyer, C., Wachsmuth, G. (2014). Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications. In: Leugering, G., et al. Trends in PDE Constrained Optimization. International Series of Numerical Mathematics, vol 165. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05083-6_4

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