計算力学
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）
キーワード:
Asymptotic theory,
HDN,
Singularity,
Limit point,
Asymmetric and symmetric bifurcation points
2015 年 81 巻 830 号 p. 15-00419
詳細
2015 年 81 巻 830 号 p. 15-00419
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.
