Abstract
• 2D hexagonal quasicrystals planar crack with thermal effects analyzed numerically. • Green's functions are derived for uniform triangular and rectangular elements. • The EDD-BEM is proposed for planar crack analysis in infinite 2D hexagonal QC body. • Elliptical crack with different loadings are investigated and presented graphically. The extended displacement discontinuity (EDD) boundary element method is developed to analyze an arbitrarily shaped planar crack in two-dimensional (2D) hexagonal quasicrystals (QCs) with thermal effects. The EDDs include the phonon and phason displacement discontinuities and the temperature discontinuity on the crack face. Green's functions for uniformly distributed EDDs over triangular and rectangular elements for 2D hexagonal QCs are derived. Employing the proposed EDD boundary element method, a rectangular crack is analyzed to verify the Green's functions by discretizing the crack with rectangular and triangular elements. Furthermore, the elliptical crack problem for 2D hexagonal QCs is investigated. Normal, tangential, and thermal loads are applied on the crack face, and the numerical results are presented graphically.
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