Topology Optimization Incorporating Level Set Boundary Expressions Using a Particle Method

• MANABE Masatoshi

  Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University

• YAMADA Takayuki

  名古屋大学大学院工学研究科機械理工学専攻

• IZUI Kazuhiro

  京都大学大学院工学研究科機械理工学専攻

• NISHIWAKI Shinji

  京都大学大学院工学研究科機械理工学専攻

Bibliographic Information

Other Title

• 粒子法を用いたレベルセット法による形状表現に基づくトポロジー最適化

Abstract

Topology optimization for structures has been applied to nonlinear structural problems, however conventional topology optimization methods for structures with geometrical nonlinearity encounter difficulties during nonlinear analysis using the FEM (Finite Element Method), due to the use of a mesh. In this study, we propose a new level set-based topology optimization method considering geometrical nonlinearity using a mesh-free/particle technique, for optimizing elastic structures that undergo large deformation. In the proposed method, the MPS (Moving Particle Semiimplicit) method, a particle method, is used for the response analysis, since it does not rely on a mesh for geometrically nonlinear analysis. In this paper, first, a topology optimization problem is formulated based on the level set method and a method for regularizing the optimization problem by the Tikhonov regularization method is explained. The reactiondiffusion equation that updates the level set function is then derived and an optimization algorithm, which uses the FEM to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function, is constructed. Next, the particle interaction model and the treatment of geometrical nonlinearity in the MPS method are shown, and the implementation of combining the level set-based topology optimization and the MPS methods is explained. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed method of topology optimization for geometrically nonlinear problems.

Journal

• TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A

  TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A 77 (784), 2054-2066, 2011

  The Japan Society of Mechanical Engineers

Keywords

• Optimum Design
• Structural Design
• Structural Analysis
• Nonlinear Problem
• Particle Method

Details

• CRID: 1390001204477446784
• NII Article ID: 130002050209
• DOI: 10.1299/kikaia.77.2054
• ISSN: 18848338
• ISSN: 03875008
• Web Site: http://www.jstage.jst.go.jp/article/kikaia/77/784/77_784_2054/_pdf
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed