General solutions for the semi-infinite space of two-dimensional (2D) piezoelectric quasicrystals (QCs) are acquired by means of the potential theory method and the generalized Almansi's theorem. Then based on the fundamental solutions of the concentrated loadings case, the frictionless contact problem in a semi-infinite of 2D hexagonal piezoelectric QCs is addressed by using the superposition principle and potential theory. Analytic solutions of fields quantities in terms of elementary functions for the phonon field, phason field and electric field are obtained under three different rigid indenters (flat-ended cylindrical, conical and spherical), which are convenient for numerical analysis. Numerical examples are given to display the relationship between the contact stiffness and the penetration depth through the change of the curves, and to demonstrate the distribution of the field components under the action of the flat-ended cylindrical. K E Y W O R D Scontact problem, fundamental solutions, potential theory, two-dimensional piezoelectric quasicrystals

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.

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