In terms of solving fracture mechanics problems of quasicrystals, the boundary element method known as Trefftz Method is used for the first time. In this paper, the collocation Trefftz method as an indirect Trefftz method has been demonstrated to be an excellent numerical method for the anti-plane fracture problems in quasicrystals plate, which can exactly satisfy the governing equations and approximately satisfy the boundary conditions. The algorithms of the collocation Trefftz method and the trial functions for the anti-plane fracture problems of piezoelectric quasicrystals are presented. The effects of the geometry size, the loadings and the materials properties on the fracture results are studied. For the materials with three dimensional constitutive relations, such as piezoelectric quasicrystals, the Trefftz method is an effective numerical method to solve the fracture problems.

在解决准晶断裂力学问题方面，首次采用边界元法Trefftz Method。本文证明了作为一种间接Trefftz方法的搭配Trefftz方法是一种很好的解决准晶板反平面断裂问题的数值方法，它可以精确满足控制方程，近似满足边界条件。提出了配置Trefftz法的算法和压电准晶反面断裂问题的试验函数。研究了几何尺寸、载荷和材料特性对断裂结果的影响。对于具有三维本构关系的材料，如压电准晶，