General solutions of plane elasticity of one-dimensional orthorhombic quasicrystals with piezoelectric effect

• We give constructively the general solution of the plane elasticity of 1D QCs with piezoelectric effect.
• The general solutions are very convenient to be used in the study of inhomogeneity and defect.
• They also play an important role in numerical simulations.
• They simplify the calculation and improve the efficiency of the computation.

By introducing four potential functions, the governing equations of plane problems in 1D orthorhombic quasicrystals with piezoelectric effect are composed of four second-order partial differential equations, in which the quasi-harmonic functions are the essential unknowns. The general solution of these equations is further established, and all expressions are expressed in terms of the potential functions. As an application of the general solution, the closed-form solutions are obtained for wedge problems or half-plane problems of 1D orthorhombic piezoelectric quasicrystals.