带有垂直于极化方向穿透的直裂纹的压电狭长体平面问题的解析解

Analytic Solutions to Plane Problem for Piezoelectric Strip with a Crack Penetrating Across the Material Perpendicular to the Poling Direction

通过构造新的广义保角映射,本文利用广义复变函数方法研究了裂纹面上受平面应力和面内电载荷共同作用的带有垂直于极化方向穿透的有限长直裂纹的压电狭长体的平面电弹性问题,给出了电不可渗透边界条件下裂纹尖端应力和电位移强度因子的解析解.结果表明,对于该问题应力场和电场是耦合的.若不考虑电场的作用,则可得到对应纯弹性材料的解析解.当压电狭长体的高度趋于无限大时,所得解析解可退化为已有结果.最后,通过数值算例说明了材料参数、裂纹长度和机电载荷对场强度因子的影响.

By introducing a new generalized conformal mapping and using the generalized complex variable function method, the plane electro/elastic problem of the piezoelectric strip with a straight crack penetrating across the material perpendicular to the poling direction was investigated under the in-plane stress and electric loads. The analytical solutions of the stress intensity factor and electric displacement intensity factor were derived under the assumption that the surface of the crack was electrically field and the electric field are coupled for this impermeable. It is concluded that the stress problem. The analytical solutions for a purely elastic material have been obtained in the absence of electric loading. When the height of the piezoelectric strip tends to infinity, the result is reduced to the well-known result. Finally, some numerical experiments have conducted to analyze the influences of the material constants, the crack length and the applied mechanical/electric loads on the field intensity factors.