含垂直极化方向穿透的共线半无限裂纹的狭长压电体的平面问题

Plane problem of piezoelectric strip with semi-infinite collinear cracks penetrating across the material and perpendicular to the poling direction

通过构造新的广义保角映射,利用广义复变函数方法研究了在电不可渗透边界条件下含有沿垂直于极化方向穿透的共线半无限裂纹的狭长压电体的平面问题,给出了裂纹尖端处的各场强度因子的解析解。此外,当狭长体高度和裂纹尺寸按一定的趋势变化时,还可以得到压电复合材料另外几种新构型的平面问题的解析解。通过数值算例分析得到了两裂纹之间的距离、狭长体的高度及裂纹面上的受载长度对场强度因子的影响规律。

Using the generalized complex variable method,the plane problem of the piezoelectric strip with semi-infinite collinear cracks penetrating across the material perpendicular to the poling direction is discussed by proposing a new generalized conformal mapping.With the assumption that the surface of the crack was electrically impermeable,the analytical solutions of the field intensity factors are presented.In addition,analytical solutions of some new defects can be derived as the height of the strip and the size of the crack change by a certain tendency.Finally,the influences of the distance of the two cracks,the height of the strip and the loaded crack length on the field intensity factors are obtained through some numerical examples.