Green function and its application for a piezoelectric plate with various openings
Green function and its application for a piezoelectric plate with various openings
复制标题
DOI：
10.1007/s004190050210
复制
发表时间：
1999-03
影响因子：
2.8
通讯作者：
Q. Qin
中科院分区：
文献类型：
--
作者：
Q. Qin
对于二维压电板，利用Lekhnitskii的形式和保角变换技术，得到了一个满足沿着孔洞无牵引和精确电边界条件的绿色函数.对所用映射函数的临界点进行了数值研究，研究表明压电板上多边形孔到单位圆的变换是非单值的。一个简单的方法来处理这样的情况。基于本文提出的绿色函数，建立了裂纹面上未知位错的奇异积分方程组，用于研究裂纹与孔洞的相互作用。数值结果阐明裂纹方向对应力和电位移（SED）强度因子的影响，并说明所提出的配方的应用。
For a two-dimensional piezoelectric plate subjected to mechanical and electric load, a Green function satisfying traction free and exact electric boundary conditions along a hole is developed using Lekhnitskii's formalism and the technique of conformal mapping. The critical points for the mapping function used is investigated numerically, and the study indicates that the transformation of a polygonal hole in a piezoelectric plate into a unit circle is nonsingle-valued. A simple approach is presented to treat such a situation. Based on the Green function developed in this paper, a system of singular integral equations for the unknown dislocation defined on crack faces is presented to study the interaction between cracks and holes. Numerical results are presented to elucidate the effects of crack orientation on stress and electric displacement (SED) intensity factors and to illustrate the application of the proposed formulation.