A novel isogeometric analysis enriched element for accurate evaluation of singularities arising at the interface in V-notched one-dimensional hexagonal piezoelectric quasicrystals (PQCs) under anti-plane loading is developed. By taking the advantages of IGA and symplectic methodology, an enriched element centered at the notch tip is constructed by analytical symplectic eigensolutions. Explicit expressions of notch intensity factors and singular multi-physical fields within enriched element are obtained simultaneously. A comparison study between numerical predictions and analytical solutions is performed and excellent agreements are observed. Furthermore, the notch intensity factors for different V-notched PQC bi-material are presented and discussed in detail.

开发了一种新颖的等几何分析富集元素，用于准确评估反平面载荷下 V 型缺口一维六方压电准晶 (PQC) 界面处出现的奇异性。利用IGA和辛方法的优点，通过解析辛本征解构造了以凹口尖端为中心的富集元素。同时获得了富集元素内凹口强度因子和奇异多物理场的显式表达式。进行了数值预测和解析解之间的比较研究，并观察到了极好的一致性。此外，还详细介绍和讨论了不同 V 型缺口 PQC 双材料的缺口强度因子。