A Level Set-Based Topology Optimization Method Using the Boundary Element Method in Three Dimension

• SHICHI Shinichiro

  名古屋大学大学院工学研究科機械理工学専攻

• YAMADA Takayuki

  Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University

• SUZUKI Akihisa

  名古屋大学大学院工学研究科機械理工学専攻

• MATSUMOTO Toshiro

  Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University

• TAKAHASHI Toru

  Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University

Bibliographic Information

Other Title

• 三次元境界要素法を用いたレベルセット法に基づくトポロジー最適化

Abstract

Level set-based shape and topology optimization methods get attention as a new type of structural optimization. However, the structural optimization methods cannot treat explicitly a design dependent load, such as pressure load, because the finite elements for solving the equilibrium equation are fixed during the optimization process. On the other hand, Boundary Element Method (BEM) is only required boundary elements to solve a boundary value problem. Therefore, some complicated numerical techniques for re-meshing process are not required. This paper presents a level set-based topology optimization method using the BEM for three-dimensional problems. First, we briefly discuss BEM for three-dimensional elastic problems and the topology optimization method using the level set method and the Tikhonov regularization method. Second, the minimum mean compliance problem with volume constraint is formulated. Next, an optimization algorithm and numerical implementation for generating boundary elements based on the level set boundary expressions are shown. Finally, we show some three-dimensional numerical examples including design dependent load problem and discuss effectiveness and adequacy of proposed method.

Journal

• TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C

  TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C 78 (785), 228-239, 2012

  The Japan Society of Mechanical Engineers

Keywords

• Optimum Design
• Structural Analysis
• Boundary Element Method
• Topology Optimization
• Level Set Method
• Sensitivity Analysis

Details

• CRID: 1390282681363587456
• NII Article ID: 130002051287
• DOI: 10.1299/kikaic.78.228
• ISSN: 18848354
• ISSN: 03875024
• Web Site: http://www.jstage.jst.go.jp/article/kikaic/78/785/78_785_228/_pdf
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed