Regularization solutions to shape and topology optimization problems of domains for elliptic boundary value problems
Project/Area Number |
20540113
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Nagoya University |
Principal Investigator |
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Project Period (FY) |
2008 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 応用数学 / 関数解析学 / 数理工学 / 設計工学 / 境界値問題 / 最適化 / 形状最適化 / 位相最適化 / 勾配法 |
Research Abstract |
Optimization problem of shape of domain in which an elastic body or a flow field is defined is called the shape optimization problem. Here, a deformation field of an elastic body for example is given as a solution of a boundary value problem of a partial differential equation (main problem). Cost functions are defined as functionals of the domain in which the main problem is defined and the solution of the main problem. In the present research, an admissible set of a design variable representing domain variation was defined. Based on the definition, an evaluation method of the shape derivatives of cost functions and a gradient method (H1 gradient method) for reshaping were presented. Moreover, it was confirmed that the domain sequence obtained by the method remains in the admissible set.
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Report
(7 results)
Research Products
(96 results)
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[Presentation] Shape Optimization Problem of Multi-body Systems2010
Author(s)
Kimihiro Umemura, Naoya Kondo, Taiki Aoyama, Hideyuki Azegami
Organizer
The Sixth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems (CJK-OSM 6)
Place of Presentation
Kyoto Garden Palace Hotel
Year and Date
2010-06-22
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[Presentation] リンク機構の形状最適化2010
Author(s)
近藤直也, 畔上秀幸
Organizer
日本応用数理学会2010年研究部会連合発表会
Place of Presentation
筑波大学 筑波キャンパス(つくば市)
Year and Date
2010-03-09
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[Presentation] 楽器のための形状最適化問題2008
Author(s)
中村有里, 新谷浩平, 青山大樹, 畔上秀幸
Organizer
日本応用数理学会2008 年度年会
Place of Presentation
東京大学柏キャンパス(柏市)
Year and Date
2008-09-17
Related Report
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[Presentation] 楽器のための形状最適化問題2008
Author(s)
中村有里, 新谷浩平, 青山大樹, 畔上秀幸
Organizer
日本応用数理学会2008年度年会
Place of Presentation
東京大学柏キャンパス
Year and Date
2008-09-17
Related Report
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[Presentation] Shape Identification of Forced Heat-Convection Fields2008
Author(s)
Eiji Katamine, Yoshiyuki Kawase, Hideyuki Azegami
Organizer
Eighth World Congress on Computational Mechanics (WCCM8) in conjunction with Fifth European Congress on Computational Methods in Applied Sciences and Engineering
Place of Presentation
Venice, Italy
Year and Date
2008-06-30
Related Report
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