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Thickness control in structural optimization via a level set method

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Abstract

In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss different strategies and possible approximations to handle the geometric constraints. We implement our approach in two and three space dimensions for a model of linearized elasticity. As can be expected, the resulting optimized shapes are strongly dependent on the initial guesses and on the specific treatment of the constraints since, in particular, some topological changes may be prevented by those constraints.

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Acknowledgments

The authors acknowledge fruitful discussions and helpful remarks from Marc Albertelli (Renault) and Charles Dapogny (LJLL Paris VI - Renault). 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. CMAP (UMR CNRS 7641), Ecole Polytechnique, 91128, Palaiseau, France

    G. Allaire & G. Michailidis

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

    F. Jouve

  3. Renault DREAM-DELT’A, Guyancourt, France

    G. Michailidis

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  1. G. Allaire
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  2. F. Jouve
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  3. G. Michailidis
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Correspondence to G. Allaire.

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Allaire, G., Jouve, F. & Michailidis, G. Thickness control in structural optimization via a level set method. Struct Multidisc Optim 53, 1349–1382 (2016). https://doi.org/10.1007/s00158-016-1453-y

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  • DOI: https://doi.org/10.1007/s00158-016-1453-y

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