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IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century


IASS Symposium 2016

SESSION: Deployable Structures

A perturbation procedure for prediction of bifurcation points on kinematic path

< Table of Contents for Deployable Structures
  • Proceedings Name: IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century
  • ISSN: (Electronic Version) 2518-6582
  • Session: Deployable Structures
  • Pages: 10
  • Title: A perturbation procedure for prediction of bifurcation points on kinematic path
  • Author(s): Toku Nishimura, Nana Shirai
  • Keywords: developable structure, rigid body displacement, kinematic bifurcation, perturbation method, singular value decomposition, eigenvalue problem
Abstract
Deployable structures are investigated in space engineering and others. If the structures change distinct shapes, a critical form has been existed in the movement. At the critical form, there may be a bifurcation point called kinematic bifurcation point. The bifurcation concerned with kinematics is identified by the change of the rank of compatibility matrix A or equilibrium matrix AT. Nishimura has proposed the strategy to predict critical points in the fundamental stability problems. A significant feature of this strategy is the application of a perturbation method to eigenvalue problem. The non-zero eigenvalues of ATA or AAT are equal to the signular values of A. Since ATA or AAT are symmetric matrices, the perturbation procedure is applicable to eigenvalue problem for ATA or AAT. In this pater, we present a methodology to predict the kinematic bifurcation points using a perturbation procedure. And we verify the availability of the methodology.

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