Green’s Function for Two-Dimensional Piezoelectric Quasicrystals Containing Elliptical Defects
摘要
Based on the linear elasticity theory of quasicrystals, this study addresses two defect problems in two-dimensional piezoelectric quasicrystals: rigid inclusions and holes. Using the Stroh formalism, Green’s function solutions are obtained for these defects under concentrated and uniformly distributed forces. Numerical examples are presented to analyze the mechanical behavior when loads are applied at various positions, including the center, outside, on the boundary, and at infinity of the elliptical defect. The study emphasizes the significant impact of the phonon line force on the distribution of key physical quantities. Results show that elliptical defects significantly disrupt multiple physical fields, leading to substantial variations in displacement and potential at the hole boundaries and pronounced stress concentrations. The stress in the phason field near the elliptical defect boundary exhibits complex variations under loading conditions, and the piezoelectric effect becomes more pronounced. These findings provide critical guidance for designing quasicrystal-based smart materials with controlled defect responses.