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Molding Direction Constraints in Structural Optimization via a Level-Set Method

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Variational Analysis and Aerospace Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 116))

Abstract

In the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not address the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature.

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Acknowledgements

The authors acknowledge fruitful discussions and helpful remarks from Marc Albertelli (Renault) and Charles Dapogny (Laboratoire Jean Kuntzmann, CNRS, Université de Grenoble). This work has been supported by the RODIN project (FUI AAP 13). G. Allaire is a member of the DEFI project at INRIA Saclay Ile-de-France.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées (CMAP), École Polytechnique, CNRS UMR 7641, Université Paris-Saclay, 91128, Palaiseau, France

    Grégoire Allaire

  2. Laboratoire J.L. Lions (UMR 7598), University Paris Diderot, Paris, France

    François Jouve

  3. SIMaP-Université de Grenoble INPG, Grenoble Cedex 1, France

    Georgios Michailidis

Authors
  1. Grégoire Allaire
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  2. François Jouve
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  3. Georgios Michailidis
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Corresponding author

Correspondence to Grégoire Allaire .

Editor information

Editors and Affiliations

  1. Department of Civil and Industrial Engineering, University of Pisa, Pisa, Italy

    Aldo Frediani

  2. Montpellier Institute Alexander Grothen, University of Montpellier, Montpellier, France

    Bijan Mohammadi

  3. LJLL-UPMC Boite, Paris, France

    Olivier Pironneau

  4. Department of Industrial and Civil Engineering, University of Pisa Aerospace Section, Pisa, Italy

    Vittorio Cipolla

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Allaire, G., Jouve, F., Michailidis, G. (2016). Molding Direction Constraints in Structural Optimization via a Level-Set Method. In: Frediani, A., Mohammadi, B., Pironneau, O., Cipolla, V. (eds) Variational Analysis and Aerospace Engineering. Springer Optimization and Its Applications, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-45680-5_1

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