Plane electroelastic problem is considered for a longitudinal crack in a transversely-isotropic piezoelectric half-space subject to remote electric field perpendicular to the flat surface of the half-space. The flat surface is fully covered by thin electrode and free of mechanical load. The Lekhnitskii’ generalized complex potentials are used for the solution representation. For a case of an internal crack, boundary conditions on the flat surface are satisfied analytically by use of the Cauchy integration technique. The least-square method is applied for satisfying boundary conditions on the crack surface. An edge crack is considered. Numerical investigations are carried out for a internal or an edge crack in dependency on crack orientation and location. The results showed that one of the most dangerous crack is parallel to the flat surface. A crack perpendicular to the flat surface does not cause any significant electroelastic field in a piezoelectric half-space. Location of a crack relative the flat surface influences on electromechanical coupling near its tips.

对于横向各向同性的压电半空间中的纵向裂纹，在垂直于半空间的平坦表面的远距离电场作用下，会产生平面电弹性问题。平坦的表面完全被薄电极覆盖，没有机械负载。Lekhnitskii的广义复势被用于解决方案表示。对于内部裂纹的情况，通过使用柯西积分技术可以解析地满足平面上的边界条件。最小二乘法用于满足裂纹表面的边界条件。考虑边缘裂纹。根据裂纹的方向和位置对内部或边缘裂纹进行了数值研究。结果表明，最危险的裂纹之一与平面平行。垂直于平面的裂纹不会在压电半空间中引起任何明显的电弹性场。裂纹相对于平面的位置会影响其尖端附近的机电耦合。