Thermo‐electric response in 2D hexagonal QC exhibiting piezoelectric effect

Abstract

Based on the theory of quasicrystal (QC) with piezoelectric effect, the general solutions of a two‐dimensional hexagonal QC under the thermo‐electric loadings are derived by using the strict operator theory and the generalized Almansi theorem. Based on the general solutions, two potential functions are introduced, and the basic solutions of QC are obtained according to the boundary conditions of the point source acting on the infinite body and the semi‐infinite body. Numerical examples are given to analyze the variations of temperature, displacement and stress of phonon field, electric field potential, and electric displacement.

Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

“…Hence, the investigation of thermo-electro-mechanical behaviors of QCs is of great practical interest. By using the rigorous operator theory and generalized Almansi’s theorem, the thermo-elastic or thermo-electro-elastic general solutions of 1D or 2D hexagonal QCs have been derived [27–30]. Based on these general solutions [27–30], several flat crack problems involving various crack geometries and different loading conditions were investigated using the generalized potential theory method, and the corresponding analytical solutions were obtained in terms of elementary functions [10–12].…”

“…By using the rigorous operator theory and generalized Almansi’s theorem, the thermo-elastic or thermo-electro-elastic general solutions of 1D or 2D hexagonal QCs have been derived [27–30]. Based on these general solutions [27–30], several flat crack problems involving various crack geometries and different loading conditions were investigated using the generalized potential theory method, and the corresponding analytical solutions were obtained in terms of elementary functions [10–12]. Using the displacement discontinuity boundary integral equation and the boundary element method, Zhao and his collaborators [14–18] studied an arbitrarily shaped flat crack in a thermo-elastic or thermo-electro-elastic hexagonal QC and obtained theoretical expressions for the coupled field variables and numerical solutions.…”