Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect

In this paper, a set of 3D general solutions to static problems of 1D hexagonal piezoelectric quasicrystals is obtained by introducing two displacement functions and utilizing the rigorous operator theory. All the physical quantities are expressed by five quasi-harmonic functions. Based on the general solutions and with the help of the superposition principle, fundamental solutions for infinite/half-infinite spaces are presented by trial-and-error technique. The general solutions can be conveniently used to solve the boundary value problems regarding dislocations, cracks and inhomogeneities. The fundamental solutions are of primary significance to development of numerical codes such as boundary element method. •3D general solutions to 1D hexagonal piezoelectric quasicrystals are expressed.•Infinite/half-infinite spaces subjected to concentrated loads are investigated.•Fundamental solutions are explicitly expressed in terms of elementary functions.