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

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 5 quasi‐harmonic functions, are derived with the help of rigorous operator theory and generalized Almansi's theorem. For an infinite/half‐infinite space subjected to an external thermal load, corresponding problem is formulated by boundary value problems. Appropriate potential functions are set by a trail‐and‐error technique. Green functions for the problems in question are obtained explicitly in the closed forms. The present fundamental solutions can be employed to construct 3D analysis for crack, indentation and dislocation problems. Furthermore, these solutions also serve as benchmarks for various numerical simulations.