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Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation)
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- FUJII Fumio
- Department of Mechanical Engineering, Gifu University
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- IKEDA Kiyohiro
- Department of Civil Engineering, Tohoku University
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- TANAKA Masato
- Toyota Central R&D Labs., Inc.
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- FUJIKAWA Masaki
- Department of Mechanical Systems Engineering, University of the Ryukyus
Bibliographic Information
- Other Title
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- 計算分岐理論における2-mode漸近展開の検証（微分演算ツールHDNの導入の前に）
Description
For error-free computation of high-derivatives of mathematical functions used in engineering applications, hyper-dual numbers (HDN) are receiving much attention in computational mechanics. Differently from classical finite differences, HDN provides a practically exact evaluation of higher-derivatives, such as the first and second derivatives of stiffness matrix with respect to nodal degrees-of-freedom (dof). As a preliminary step for introducing HDN in stability problems, the present paper formulates the theoretical basis of a 2-mode asymptotic bifurcation theory and examines its versatility on simple bench models. All obtained results in numerical examples well predict the stability behavior and agree with existing analytical solutions.
Journal
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- Transactions of the JSME (in Japanese)
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Transactions of the JSME (in Japanese) 81 (830), 15-00419-15-00419, 2015
The Japan Society of Mechanical Engineers
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Details 詳細情報について
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- CRID
- 1390001205514397056
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- NII Article ID
- 130005105241
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- ISSN
- 21879761
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- Text Lang
- ja
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
- OpenAIRE
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- Abstract License Flag
- Disallowed
