Topology optimization of planar and plate structures using conformal mapping

S. Kitayama*, K. Yamazaki, H. Yamakawa

*この研究の対応する著者

    研究成果査読

    3 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ページ(範囲)125-133
    ページ数9
    ジャーナルStructural and Multidisciplinary Optimization
    29
    2
    DOI
    出版ステータスPublished - 2005 2

    ASJC Scopus subject areas

    • 工学(その他)
    • 材料力学
    • 計算力学
    • コンピュータ サイエンスの応用
    • 計算理論と計算数学

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