Plane Analysis for an Inclusion in 1D Hexagonal Quasicrystal Using the Hypersingular Integral Equation Method

  • Fei Lou
  • Ting Cao
  • Taiyan QinEmail author
  • Chunhui Xu


A model of a thin elastic inclusion embedded in an infinite 1D hexagonal quasicrystal is discussed. The atomic arrangements of the matrix and the inclusion are both periodic along the \(x_{1}\)-direction and quasiperiodic along the \(x_{2}\)-direction in the \(ox_{1}x_{2}\)-coordinate system. Using the hypersingular integral equation method, the inclusion problem is reduced to solving a set of hypersingular integral equations. Based on the exact analytical solution of the singular phonon and phason stresses near the inclusion front, a numerical method of the hypersingular integral equation is proposed using the finite-part integral method. Finally, the numerical solutions for the phonon and phason stress intensity factors of some examples are given.


Elastic inclusion 1D hexagonal quasicrystal Hypersingular integral equations 



The authors would like to express their special thanks to the National Natural Science Foundation of China (Project No. 11172320 and No. 11272341).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.College of ScienceChina Agricultural UniversityBeijingChina
  2. 2.College of EngineeringChina Agricultural UniversityBeijingChina

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