Theory and applications of shape optimization of singular points in continuum
| Project/Area Number |
16K05285
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Hiroshima Kokusai Gakuin University |
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Principal Investigator |
Ohtsuka Kohji 広島国際学院大学, 情報文化学部, 教授 (30141683)
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| Co-Investigator(Kenkyū-buntansha) |
高石 武史 武蔵野大学, 工学部, 教授 (00268666)
畔上 秀幸 名古屋大学, 情報学研究科, 教授 (70175876)
木村 正人 金沢大学, 数物科学系, 教授 (70263358)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 偏微分方程式境界値問題 / 変分法 / 特異点 / 形状最適化 / 有限要素法 / 破壊力学 / 界面問題 / 数理モデル / 偏微分方程式楕円型境界値問題 / 特異点集合 / 形状最適化問題 / 境界形状最適化 / 界面形状最適化 / 破壊問題 / 一般J積分 / 有限要素解析 / 偏微分方程式 |
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| Outline of Final Research Achievements |
The author devise a general J-integral(GJ-integral) as an amount of energy release rate in 3d-fracture mechanics and computational complexity including shape sensitivity analysis of continuum. We combine GJ-integral with the H1 gradient method by Professor Azegami (member of the project) to find the optimal shape. The formulation and solution of “shape optimization problem of singular points in boundary value problem” are derived. The shape optimization of singular points is the optimization of boundary shape including mixed boundary, crack shape, and interface at discontinuous coefficient with cost functions (energy, average compliance, mean square error, eigenvalue, etc.). Although functional shape sensitivity analysis is divided into terms including material derivatives and shape derivatives due to initial shapes, Professor Kimura (member of the project) has shown that terms including material derivatives disappear for shape sensitivity analysis in the minimum value problem.
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| Academic Significance and Societal Importance of the Research Achievements |
工学において，破壊力学，形状最適化，界面形状最適化は重要な問題であり，独立して研究されてきた．本研究によりこれらの分野を統合する偏微分方程式境界値問題の特異点集合形状最適化問題に関する理論が構成でき，有限要素法を使った数値計算も容易であることが示せた．一般J積分は筆者が考案したものであり，理論の拡張も主に筆者が行ってきたことから国内外において同様な研究はない．
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Report
(4 results)
Research Products
(90 results)
