含椭圆孔压电材料的电弹场

THE ELECTRO-ELASTIC FIELDS OF PIEZOELECTRIC MATERIALS WITH AN ELLIPTIC HOLE

采用复变函数的方法,研究了含椭圆孔的压电材料在无限远处受力电荷载作用的平面问题。与已有文献不同,通过求解10元一次方程,得到了满足可导通和不可导通电边界条件,孔内和压电材料体内电弹场的通解。以PZT一4压电陶瓷为例,给出了孔内的电场、压电材料体内电弹场沿孔边和坐标轴向的分布情况。得出了以下新的结论:含椭圆孔压电材料的电弹场与边界条件、力电荷载的方向、椭圆孔的形状有关,但在水平方向的拉伸载荷和电位移的作用下,椭圆孔的形状对长半轴处的环向电位移和正应力的最大值没有影响。

Based on the complex potential approach, two-dimensional electromechanical analysis was performed on a transversely isotropic piezoelectric material containing an elliptic hole subjected to remote electromechanical loads. By solving ten-variable linear equations, the analytical solutions were given at both inside and outside the hole, which satisfied the permeable and impermeable electric boundary conditions. Taking PZT-4 ceramic as an exmple, the electric field in the hole was obtained, as well as the distributions of the electromechanical fields on the rim of the elliptic hole and along the axes. It is found that the electromechanical fields are related to the electric boundary conditions, the directions of electromechanical loads and the geometrical shape of the elliptic hole in principle, while the elliptical geometry has no influence on the hoop electric displacement and stress at the major semi-axis subjected to the remote horizontal loads of the tension and electric displacement.