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

Plane Analysis for an Inclusion in 1D Hexagonal Quasicrystal Using the Hypersingular Integral... Abstract 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Solida Sinica" Springer Journals

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

, Volume 32 (2): 12 – Apr 1, 2019
12 pages

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Publisher
Springer Journals
Copyright
2019 The Chinese Society of Theoretical and Applied Mechanics
ISSN
0894-9166
eISSN
1860-2134
DOI
10.1007/s10338-018-0072-0
Publisher site
See Article on Publisher Site

### Abstract

Abstract 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.

### Journal

"Acta Mechanica Solida Sinica"Springer Journals

Published: Apr 1, 2019

Keywords: Theoretical and Applied Mechanics; Surfaces and Interfaces, Thin Films; Classical Mechanics