Topology optimization of planar and plate structures using conformal mapping

S. Kitayama, K. Yamazaki, H. Yamakawa

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    This paper proposes a new method to determine the optimum topology of planar and plate structures using conformal mapping. First it is proved that two invariants of stresses, which are the sum and difference of principal stresses, satisfy the Laplace equation. Additionally, it is proved that two invariants of bending moments are the sum and difference of principal bending moments, and is proved that they satisfy the Laplace equation under certain condition. Finally, we show that corresponding relationships between fluid mechanics and electromagnetism are valid to the theory of planar elasticity and plate bending. From these considerations, a convenient design method to optimize topologies of planar and plate structures for complicate design domains is proposed using conformal mapping. Several numerical examples of optimum topologies are treated by the proposed method. Through numerical results the effectiveness and validity of proposed method are discussed quantitatively and qualitatively.

    Original languageEnglish
    Pages (from-to)125-133
    Number of pages9
    JournalStructural and Multidisciplinary Optimization
    Volume29
    Issue number2
    DOIs
    Publication statusPublished - 2005 Feb

    Fingerprint

    Plate Structures
    Conformal mapping
    Topology Optimization
    Conformal Mapping
    Shape optimization
    Laplace equation
    Topology
    Bending moments
    Laplace's equation
    Moment
    Electromagnetism
    Plate Bending
    Invariant
    Fluid Mechanics
    Fluid mechanics
    Design Method
    Elasticity
    Optimise
    Valid
    Numerical Examples

    Keywords

    • Conformal mapping
    • Invariant of bending moments
    • Invariant of stresses
    • Optimum topology
    • Structural optimization

    ASJC Scopus subject areas

    • Engineering (miscellaneous)
    • Mechanics of Materials
    • Computational Mechanics
    • Computer Science Applications
    • Computational Theory and Mathematics

    Cite this

    Topology optimization of planar and plate structures using conformal mapping. / Kitayama, S.; Yamazaki, K.; Yamakawa, H.

    In: Structural and Multidisciplinary Optimization, Vol. 29, No. 2, 02.2005, p. 125-133.

    Research output: Contribution to journalArticle

    Kitayama, S. ; Yamazaki, K. ; Yamakawa, H. / Topology optimization of planar and plate structures using conformal mapping. In: Structural and Multidisciplinary Optimization. 2005 ; Vol. 29, No. 2. pp. 125-133.
    @article{cdad0e96cdd447218e5bb3efdfde7eb5,
    title = "Topology optimization of planar and plate structures using conformal mapping",
    abstract = "This paper proposes a new method to determine the optimum topology of planar and plate structures using conformal mapping. First it is proved that two invariants of stresses, which are the sum and difference of principal stresses, satisfy the Laplace equation. Additionally, it is proved that two invariants of bending moments are the sum and difference of principal bending moments, and is proved that they satisfy the Laplace equation under certain condition. Finally, we show that corresponding relationships between fluid mechanics and electromagnetism are valid to the theory of planar elasticity and plate bending. From these considerations, a convenient design method to optimize topologies of planar and plate structures for complicate design domains is proposed using conformal mapping. Several numerical examples of optimum topologies are treated by the proposed method. Through numerical results the effectiveness and validity of proposed method are discussed quantitatively and qualitatively.",
    keywords = "Conformal mapping, Invariant of bending moments, Invariant of stresses, Optimum topology, Structural optimization",
    author = "S. Kitayama and K. Yamazaki and H. Yamakawa",
    year = "2005",
    month = "2",
    doi = "10.1007/s00158-004-0477-x",
    language = "English",
    volume = "29",
    pages = "125--133",
    journal = "Structural and Multidisciplinary Optimization",
    issn = "1615-147X",
    publisher = "Springer Verlag",
    number = "2",

    }

    TY - JOUR

    T1 - Topology optimization of planar and plate structures using conformal mapping

    AU - Kitayama, S.

    AU - Yamazaki, K.

    AU - Yamakawa, H.

    PY - 2005/2

    Y1 - 2005/2

    N2 - This paper proposes a new method to determine the optimum topology of planar and plate structures using conformal mapping. First it is proved that two invariants of stresses, which are the sum and difference of principal stresses, satisfy the Laplace equation. Additionally, it is proved that two invariants of bending moments are the sum and difference of principal bending moments, and is proved that they satisfy the Laplace equation under certain condition. Finally, we show that corresponding relationships between fluid mechanics and electromagnetism are valid to the theory of planar elasticity and plate bending. From these considerations, a convenient design method to optimize topologies of planar and plate structures for complicate design domains is proposed using conformal mapping. Several numerical examples of optimum topologies are treated by the proposed method. Through numerical results the effectiveness and validity of proposed method are discussed quantitatively and qualitatively.

    AB - This paper proposes a new method to determine the optimum topology of planar and plate structures using conformal mapping. First it is proved that two invariants of stresses, which are the sum and difference of principal stresses, satisfy the Laplace equation. Additionally, it is proved that two invariants of bending moments are the sum and difference of principal bending moments, and is proved that they satisfy the Laplace equation under certain condition. Finally, we show that corresponding relationships between fluid mechanics and electromagnetism are valid to the theory of planar elasticity and plate bending. From these considerations, a convenient design method to optimize topologies of planar and plate structures for complicate design domains is proposed using conformal mapping. Several numerical examples of optimum topologies are treated by the proposed method. Through numerical results the effectiveness and validity of proposed method are discussed quantitatively and qualitatively.

    KW - Conformal mapping

    KW - Invariant of bending moments

    KW - Invariant of stresses

    KW - Optimum topology

    KW - Structural optimization

    UR - http://www.scopus.com/inward/record.url?scp=17444433004&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=17444433004&partnerID=8YFLogxK

    U2 - 10.1007/s00158-004-0477-x

    DO - 10.1007/s00158-004-0477-x

    M3 - Article

    AN - SCOPUS:17444433004

    VL - 29

    SP - 125

    EP - 133

    JO - Structural and Multidisciplinary Optimization

    JF - Structural and Multidisciplinary Optimization

    SN - 1615-147X

    IS - 2

    ER -