Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization

Kiyohiro Ikeda, Kazuo Murota, Akito Yanagimoto, Hirohisa Noguchi

研究成果: Article査読

10 被引用数 (Scopus)

抄録

In the nonlinear bifurcation analysis for large-scaled structures, the standard eigenanalysis of the tangent stiffness matrix yields important information, but, at the same time, demands a large amount of computational cost. The scaled corrector method was developed as a numerically efficient, eigenanalysis-free, bifurcation-analysis strategy, which exploits byproducts of the numerical iteration for path tracing. This method, however, has a problem in its accuracy, especially when eigenvalues are nearly or exactly coincidental. As a remedy for this, we propose a new bifurcation analysis method through the implementation of bifurcation mechanism of a symmetric structure into the scaled corrector method. The bifurcation mode is accurately approximated by decomposing a scaled corrector vector into a number of vectors by means of block-diagonalization method in group-theoretic bifurcation theory and, in turn, by choosing the predominant one among these vectors. In order to demonstrate the usefulness of this method, it is applied to the bifurcation analysis of reticulated regular-hexagonal truss domes to compute accurately the locations of double bifurcation points and nearly coincidental bifurcation points, and associated bifurcation modes.

本文言語English
ページ(範囲)1648-1661
ページ数14
ジャーナルComputer Methods in Applied Mechanics and Engineering
196
9-12
DOI
出版ステータスPublished - 2007 2月 1

ASJC Scopus subject areas

  • 計算力学
  • 材料力学
  • 機械工学
  • 物理学および天文学(全般)
  • コンピュータ サイエンスの応用

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