Applied Mathematics and Mechanics >
Fundamental solutions for two-dimensional piezoelectric quasicrystals with polygonal holes
Received date: 2025-09-15
Revised date: 2025-12-22
Online published: 2026-03-02
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12272402 and 12102458), the Chinese Universities Scientific Fund (No. 2025TC014), and the China Agricultural University Education Foundation (No. 1101-240001)
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This paper investigates the mechanical behavior of two-dimensional (2D) piezoelectric quasicrystals (PQCs) containing polygonal holes under external forces. Based on the linear elastic theory of quasicrystals (QCs), the analytical solutions for the stress and displacement fields are derived with the Stroh formalism, Green’s function method, and polygonal mapping functions. Numerical simulations are performed to study the effects of hole geometry and corner sharpness on the stress distribution. The results show that the polygonal hole shapes significantly influence the generalized hoop stress, with sharper corners leading to stronger stress concentration and enhanced piezoelectric coupling effects. The stress concentrations at hole corners reach their maximum values at specific sharpness parameters, depending on the polygon type. The results contribute to a deeper understanding of the defect-induced mechanical behavior in 2D PQCs, and provide theoretical guidance for their structural design and optimization.
Tangrui LAI , Xiaoyu FU , Xiang MU , Liangliang ZHANG , Yang GAO . Fundamental solutions for two-dimensional piezoelectric quasicrystals with polygonal holes[J]. Applied Mathematics and Mechanics, 2026 , 47(3) : 623 -638 . DOI: 10.1007/s10483-026-3356-6
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