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...

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Published inKikai Gakkai ronbunshū = Transactions of the Japan Society of Mechanical Engineers Vol. 81; no. 830; p. 15-00419
Main Authors FUJII, Fumio, IKEDA, Kiyohiro, TANAKA, Masato, FUJIKAWA, Masaki
Format Journal Article
LanguageJapanese
Published The Japan Society of Mechanical Engineers 01.01.2015
Subjects
Asymmetric and symmetric bifurcation points
Asymptotic properties
Asymptotic theory
Bifurcation theory
Computation
Derivatives
HDN
Limit point
Mathematical analysis
Mathematical models
Mechanical engineers
Singularity
Stability
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Summary: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.
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ISSN:2187-9761
DOI:10.1299/transjsme.15-00419