2018 Fiscal Year Final Research Report
Development of Elasto-Plastic Spectral Stochastic Finite Element Method based on Finite Deformation Theory
| Project/Area Number |
16K14300
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Structural engineering/Earthquake engineering/Maintenance management engineering
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| Research Institution | Oyama National College of Technology |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | スペクトル確率有限要素法 / NISP法 / 応力リターンマッピング / 微小変形問題 / 有限変形問題 / 確率弾塑性問題 / 確率弧長制御法 |
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| Outline of Final Research Achievements |
The stochastic finite element method (Intrusive SSFEM) is one of tools for efficiently solving models that probabilistically expresses objects whose parameters, such as structure, shape, material characteristics, boundary condition, etc., are not precisely known. In this study, the application of Intrusive SSFEM, which performs uncertainty analysis using response surface by polynomial chaos expansion, to stochastic elasto-plastic solid mechanics problem is considered. In particular, we have developed NISP-SFEM, which is a combination of Intrusive SSFEM and Non-Intrusive Spectral Projection Method(NISP method). As a result, we have found a solution to one of the major problems of nonlinear SSFEM, that it is possible to track the mean value accurately, but it is difficult to accurately track the stochastic fluctuation. Furthermore, the NISP-SFEM for plane strain and three-dimensional stochastic elastic-plastic problems with finite deformation has been developed.
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| Free Research Field |
応用力学, 計算力学
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| Academic Significance and Societal Importance of the Research Achievements |
材料特性，境界条件などが正確に分からない状況では，パラメータの不確かさを確率として表現した確率モデルを用いることが手法の１つとして考えられる．確率モデルを効率よく解くための手法としてスペクトル確率有限要素法(Intrusive SSFEM)があるが，確率弾塑性問題への適用はまだ発展途上である．2006年に有限変形確率弾塑性問題を扱った研究がAcharjee,Zabaras氏により発表されたが，確率的な変動を伴う中でのリターンマッピング法など，肝心となる箇所ついては明確にされておらず後追いが難しい状況であった．本研究は，有限変形確率弾塑性問題を扱いながら，応力の更新方法にも切り込んでいる．
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