Fundamental thermo‐electro‐elastic solutions for 1D hexagonal QC

Static general solutions, fundamental solutions, piezoelectric effect, 1D hexagonal quasicrystal,infinite/half-infinite spaces.This paper is concerned with the fundamental solutions, in the framework of thermo-electro-elasticity, for an infinite/half-infinite space of 1D hexagonal quasicrystals (QCs). To this end, three-dimensional static general solutions, in terms of 5quasi-harmonic functions, are derived with the help of rigorous operator theory and generalized Almansi’s theorem. Foran infinite/half-infinite space subjected to an external thermal load, corresponding problem is formulated by boundaryvalue problems. Appropriate potential functions are set by a trail-and-error technique. Green functions for the problemsin question are obtained explicitly in the closed forms. The present fundamental solutions can be employed to construct3D analysis for crack, indentation and dislocation problems. Furthermore, these solutions also serve as benchmarks forvarious numerical simulations.