Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation)
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-derivative...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2015-09-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/81/830/81_15-00419/_pdf/-char/en |
| _version_ | 1828129322748084224 |
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| author | Fumio FUJII Kiyohiro IKEDA Masato TANAKA Masaki FUJIKAWA |
| author_facet | Fumio FUJII Kiyohiro IKEDA Masato TANAKA Masaki FUJIKAWA |
| author_sort | Fumio FUJII |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T16:17:30Z |
| format | Article |
| id | doaj.art-437a9a5724364b2d8d4bd9e3e690367c |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-11T16:17:30Z |
| publishDate | 2015-09-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-437a9a5724364b2d8d4bd9e3e690367c2022-12-22T04:14:27ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612015-09-018183015-0041915-0041910.1299/transjsme.15-00419transjsmeValidating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation)Fumio FUJII0Kiyohiro IKEDA1Masato TANAKA2Masaki FUJIKAWA3Department of Mechanical Engineering, Gifu UniversityDepartment of Civil Engineering, Tohoku UniversityToyota Central R&D Labs., Inc.Department of Mechanical Systems Engineering, University of the RyukyusFor 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.https://www.jstage.jst.go.jp/article/transjsme/81/830/81_15-00419/_pdf/-char/enasymptotic theoryhdnsingularitylimit pointasymmetric and symmetric bifurcation points |
| spellingShingle | Fumio FUJII Kiyohiro IKEDA Masato TANAKA Masaki FUJIKAWA Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation) Nihon Kikai Gakkai ronbunshu asymptotic theory hdn singularity limit point asymmetric and symmetric bifurcation points |
| title | Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation) |
| title_full | Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation) |
| title_fullStr | Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation) |
| title_full_unstemmed | Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation) |
| title_short | Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation) |
| title_sort | validating a 2 mode asymptotic expansion in computational bifurcation theory before introducing hdn for differential operation |
| topic | asymptotic theory hdn singularity limit point asymmetric and symmetric bifurcation points |
| url | https://www.jstage.jst.go.jp/article/transjsme/81/830/81_15-00419/_pdf/-char/en |
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