A topological derivative method for topology optimization

J. Norato, Martin P. Bendsøe, RB Haber, D Tortorelli

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.
    Original languageEnglish
    JournalStructural and Multidisciplinary Optimization
    Volume33
    Issue number4-5
    Pages (from-to)375-386
    ISSN1615-147X
    DOIs
    Publication statusPublished - 2007

    Cite this

    Norato, J. ; Bendsøe, Martin P. ; Haber, RB ; Tortorelli, D. / A topological derivative method for topology optimization. In: Structural and Multidisciplinary Optimization. 2007 ; Vol. 33, No. 4-5. pp. 375-386.
    @article{e619b479983e4ca2af48fa0b888b8672,
    title = "A topological derivative method for topology optimization",
    abstract = "We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.",
    author = "J. Norato and Bends{\o}e, {Martin P.} and RB Haber and D Tortorelli",
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    pages = "375--386",
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    A topological derivative method for topology optimization. / Norato, J.; Bendsøe, Martin P.; Haber, RB; Tortorelli, D.

    In: Structural and Multidisciplinary Optimization, Vol. 33, No. 4-5, 2007, p. 375-386.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - A topological derivative method for topology optimization

    AU - Norato, J.

    AU - Bendsøe, Martin P.

    AU - Haber, RB

    AU - Tortorelli, D

    PY - 2007

    Y1 - 2007

    N2 - We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.

    AB - We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.

    U2 - 10.1007/s00158-007-0094-6

    DO - 10.1007/s00158-007-0094-6

    M3 - Journal article

    VL - 33

    SP - 375

    EP - 386

    JO - Structural and Multidisciplinary Optimization

    JF - Structural and Multidisciplinary Optimization

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