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）

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タイトル別名
  • Validating a 2-mode asymptotic expansion in computational bifurcation theory (Before introducing HDN for differential operation)

説明

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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