Boundary value problems of holomorphic vector functions in 1D QCs

Yang Gao*, Ying Tao Zhao, Bao Sheng Zhao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

By means of the generalized Stroh formalism, two-dimensional (2D) problems of one-dimensional (1D) quasicrystals (QCs) elasticity are turned into the boundary value problems of holomorphic vector functions in a given region. If the conformal mapping from an ellipse to a circle is known, a general method for solving the boundary value problems of holomorphic vector functions can be presented. To illustrate its utility, by using the necessary and sufficient condition of boundary value problems of holomorphic vector functions, we consider two basic 2D problems in 1D QCs, that is, an elliptic hole and a rigid line inclusion subjected to uniform loading at infinity. For the crack problem, the intensity factors of phonon and phason fields are determined, and the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystals and QCs are figured out. Moreover, the same procedure can be used to deal with the elastic problems for 2D and three-dimensional (3D) QCs.

Original languageEnglish
Pages (from-to)56-61
Number of pages6
JournalPhysica B: Condensed Matter
Volume394
Issue number1
DOIs
Publication statusPublished - 1 May 2007

Keywords

  • 1D QCs
  • Boundary value problems
  • Holomorphic vector functions
  • The generalized Stroh formalism

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Gao, Y., Zhao, Y. T., & Zhao, B. S. (2007). Boundary value problems of holomorphic vector functions in 1D QCs. Physica B: Condensed Matter, 394(1), 56-61. https://doi.org/10.1016/j.physb.2007.02.007