Fundamental solutions for two-dimensional piezoelectric quasicrystals with polygonal holes

doi:10.1007/s10483-026-3356-6

Abstract

Abstract:

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.

Key words: piezoelectric quasicrystal (PQC), polygonal hole, the Stroh formalism, Green’s function, multifield coupling

2010 MSC Number:

O343.7

Tangrui LAI, Xiaoyu FU, Xiang MU, Liangliang ZHANG, Yang GAO. Fundamental solutions for two-dimensional piezoelectric quasicrystals with polygonal holes. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 623-638.

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Figures/Tables 14

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Table 1

λ values and the corresponding circumferential stresses tn1 for polygonal holes"

Hole	k	λ	$t n 1$
Triangular	2	0.5	$3.883 × 107$
Quadrilateral	3	0.33	$4.027 × 108$
Pentagonal	4	0.25	$2.349 × 108$

Table 1

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