形状最適化におけるミニマックス問題の数値解法　最大応力と最大変位の最小設計

• 下田 昌利

• 畔上 秀幸

• 桜井 俊明

書誌事項

タイトル別名

• Numerical Solution for Min-Max Problems in Shape Optimization. Minimum Design of Max. Stress and Max. Displacement.
• ケイジョウ サイテキカ ニ オケル ミニマックス モンダイ ノ スウチ カイホ

抄録

We describe a numerical shape optimization method of continua that minimizes maximum local measure such as stress and displacement. A solution to this min-max problem subject to volume constraint is proposed. To avoid impossibility of differentiation, local functionals are transposed to global integral functionals using the Kreisselmeier-Steinhauser function. With this function, a multiple leading problem is also transposed to a single loading problem. The shape gradient functions which are applied to the traction method are theoretically derived using the Lagrange multipliers and the material derivative method. Using the traction method, the optimum domain variation to decrease the objective functional is numerically and iteratively determined that maintaining the smoothness of the boundaries. The calculated results of 2D and 3D examples show the effectiveness and practical utility of the proposed method for min-max problems in shape designs.

収録刊行物

• 日本機械学会論文集Ａ編

  日本機械学会論文集Ａ編 63 (607), 610-617, 1997

  一般社団法人 日本機械学会

キーワード

• Optimum Design
• Finite-Element Method
• Shape Optimization
• Min-Max Problem
• Kreisselmeier-Steinhauser Function
• Traction Method
• Material Derivative Method
• Adjoint Method
• Multiple Loading

詳細情報

• CRID: 1390282679424681088
• NII論文ID: 120000973920
• NII論文ID: 110002374066
• NII書誌ID: AN0018742X
• DOI: 10.1299/kikaia.63.610
• ISSN: 18848338
• ISSN: 03875008
• HANDLE: 2237/7249
• NDL書誌ID: 4170506
• Web Site: https://nagoya.repo.nii.ac.jp/records/5642
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4170506
• Web Site: http://www.jstage.jst.go.jp/article/kikaia1979/63/607/63_607_610/_pdf
• 本文言語コード: ja
• データソース種別:
  • JaLC
  • IRDB
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可