Multi-scale shape optimization method for designing a macrostructure with periodic-microstructures using inverse homogenization method and H¹ gradient method

• KATO Takumi

  Graduate School of Advanced Science and Technology, Toyota Technological Institute

• FUJIOKA Minami

  Department of Advanced Science and Technology, Toyota Technological Institute

• SHIMODA Masatoshi

  Department of Advanced Science and Technology, Toyota Technological Institute

Bibliographic Information

Other Title

• 逆均質化法とH¹勾配法を用いた周期的ミクロ構造のマルチスケール形状最適化

Abstract

It is known that mechanical behavior of a composite structure is strongly influenced by not only the shape and properties of the macroscopic region but also the shape and properties of the micro region. In this study, we propose a multi-scale shape optimization method to design the shape of a periodic microstructure. The method consists of two-step optimization. At first, the material properties of a macrostructure are optimized using a size-optimization technique, where the components of the liner elastic tensor are set as the design variables. Objective function and the constraints are set according to design purpose. Next, the shapes of periodic-microstructures are determined to identity the material properties of the macrostructures obtained in the first step, where the inverse homogenization method and the H¹ gradient method are used. The shape optimization problem of a microstructure is formulated as a distributed-parameter optimization problem, in which the mass is set as an objective functional and the shape variation field is set as a design variable, as the constraints are the target macroscopic material properties and the homogenization equation. Through numerical calculation examples, we confirmed the effectiveness of the proposed method based on the inverse homogenization method and the H¹ gradient method.

Journal

• Transactions of the JSME (in Japanese)

  Transactions of the JSME (in Japanese) 85 (880), 19-00279-19-00279, 2019

  The Japan Society of Mechanical Engineers

Keywords

• Multi-scale optimization
• Homogenization
• Inverse homogenization method
• Shape optimization
• H¹ gradient method

Details

• CRID: 1390002184857066496
• NII Article ID: 130007772964
• DOI: 10.1299/transjsme.19-00279
• ISSN: 21879761
• Web Site: https://www.jstage.jst.go.jp/article/transjsme/85/880/85_19-00279/_pdf
• Text Lang: ja
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed