Abstract
In this study, three-dimensional cracks in one-dimensional hexagonal piezoelectric quasicrystals are investigated. Based on the general solutions and Hankel transform, the fundamental solutions for unit point extended displacement discontinuities (including the phonon and phason displacement discontinuities and the electric potential discontinuity) are derived. The extended displacement discontinuity boundary integral equations for a planar crack of arbitrary shape in the periodic plane of one-dimensional hexagonal piezoelectric quasicrystals are established in terms of the extended displacement discontinuities. Using the boundary integral equation method, the singularities of near-crack border fields are obtained and the stress and electric displacement intensity factors are derived.
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