2019年
幾何学的特徴量に対する偏微分方程式系に基づく幾何学的特徴制約付きトポロジー最適化(積層造形における幾何学的特異点を考慮したオーバーハング制約法)
日本機械学会論文集
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- 巻
- 85
- 号
- 877
- 開始ページ
- 19
- 終了ページ
- 00129-19-00129
- 記述言語
- 日本語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1299/transjsme.19-00129
- 出版者・発行元
- 一般社団法人 日本機械学会
<p>This paper aims to develop a scheme for geometrical feature constraints in topology optimization for Additive Manufacturing (AM) without support structures based on the Partial Differential Equation (PDE) of geometrical shape features. To begin with, the basic concept of topology optimization and a level set-based topology optimization method are briefly described. Second, the PDE system for geometrical shape features is formulated. Here, aspects of the distribution of state variables are discussed using an analytical solution of the PDE. Based on the discussion, a function indicating the extended normal vector including geometrical singularity points is formulated. Third, geometrical requirements of product shape in AM without support structures – the so-called overhang constraint – are clarified in two-dimensions. A way of extending of the proposed concept to three-dimensional problems is also clarified. Additionally, geometrical singularities in the overhang constraint are discussed. Based on the PDE system and the clarified geometrical requirements, the overhang constraint including geometrical singularities is formulated. A topology optimization problem of the linear elastic problem is formulated considering the overhang constraint. A level set-based topology optimization algorithm is constructed where the Finite Element Method (FEM) is used to solve the governing equation of the linear elastic problem and the PDE, and to update the level set function. Finally, two-dimensional numerical examples are provided to confirm the validity and utility of the proposed method.</p>
- リンク情報
- ID情報
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- DOI : 10.1299/transjsme.19-00129
- CiNii Articles ID : 130007711795