Theories of strain analysis from shape fabrics: A perspective using hyperbolic geometry

HANDLE オープンアクセス

この論文をさがす

抄録

A parameter space is proposed for unifying the theories of two-dimensional strain analysis, where strain markers are approximated by ellipses with a prescribed area. It is shown that the theories are unified by hyperbolic geometry, the oldest and simple non-Euclidean geometry. The hyperboloid model of the geometry is used for this purpose. Ellipses normalized by their areas are represented by points on the unit hyperboloid, the curved surface in a non-Euclidean space. Dissimilarity between ellipses is defined by the distance between the points that represent the ellipses. The merit of introducing the geometry comes from the fact that this distance equals the doubled natural strain needed to transform one ellipse to another. Thus, the introduction is natural and convenient for strain and error analyses. Equal-area and gnomonic projections of the hyperboloid are introduced for the Rf/phi and kinematic vorticity analyses, respectively. In our formulation, the strain ellipse optimal for a set of Rf/phi data is obtained as the centroid of the points corresponding to the data on the hyperboloid, and the dispersion of the points shows the uncertainty of the optimal strain. By means of a bootstrap method, the confidence region of the strain is drawn upon the surface, and equal-area projection from the surface to a Euclidean plane shows the dispersion of the points and the size of the confidence region. In addition, our formulation provides a new graphical technique for kinematic vorticity analysis using the gnomonic projection. The technique yields the optimal kinematic vorticity number with its uncertainty.

収録刊行物

キーワード

詳細情報 詳細情報について

  • CRID
    1050282676917042432
  • NII論文ID
    120002561285
  • NII書誌ID
    AA00259438
  • ISSN
    01918141
  • HANDLE
    2433/130691
  • 本文言語コード
    en
  • 資料種別
    journal article
  • データソース種別
    • IRDB
    • CiNii Articles

問題の指摘

ページトップへ