2013 Fiscal Year Final Research Report
Construction of the theory of variation applicable to shape optimization problems and fracture, whose application to problems in engineering.
| Project/Area Number |
23540258
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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 |
Global analysis
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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, 総合教育センター, 教授 (30141683)
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| Co-Investigator(Kenkyū-buntansha) |
AZEGAMI Hideyuki (70175876)
KIMURA Masato (70263358)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 変分法 / 形状最適化問題 / 特異性を持つ楕円型境界値問題 / 有限要素法 / 一般J積分 / 破壊現象 / 関数方程式 / 数理思考プログラミング |
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| Research Abstract |
The results of research are the following. (1) In theory of generalized J-integral (GJ-integral), there is the result called Main Theorem, that is, the variation of energies with respect to the perturbation of the singular points is expressed as GJ-integral. In this research, it is proved that Main Theorem hold in wide nonlinear problems with Professor Kimura. (2) Combining GJ-integral and H1-gradient method proposed by Professor Azegami, we could show that the shape optimization problems with singularities are solved theoretically and numerically. (3) It was shown that FreeFem++ developed by Professor F.Hecht at the Laboratory Jacques-Louis Lions in Paris VI University is the finite element solver for boundary value problems by mathematical thinking and programming.
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