矩形压电体中反平面裂纹的电弹性场

基于线性压电理论,本文获得了含有中心反平面裂纹的矩形压电体中的奇异应力和电场。利用Fourier积分变换和Fourier正弦级数将电绝缘型裂纹问题化为对偶积分方程,并进一步归结为易于求解的第二类Fred-holm积分方程。获得了裂纹尖端应力、应变、电位移和电场的解析解,求得了裂纹尖端场的强度因子及能量释放率。分析了压电矩形体的几何尺寸对它们的影响。结果表明,对于电绝缘型裂纹,裂纹尖端附近的各个场变量都具有-1/2阶的奇异性,能量释放率与电荷载的方向及大小有关,并且有可能为负值。

Electroelastic Field for an Anti-Plane Crack in a Rectangular Piezoelectric Body

The singular stress and electric fields in a rectangular piezoelectric body containing a center anti-plane crack are obtained.Fourier transforms and Fourier sine series are used to reduce the mixed boundary value problems of the crack,which is assumed to be impermeable,to dual integral equations.The solution of the dual integral equations is then expressed in terms of Fredholm integral equations of the second kind.Expressions for stresses,strains,electric displacements and electric fields in the vicinity of the crack tip are derived.Also obtained are the field intensity factors and the energy release rates.Numerical results obtained show that the geometry of the rectangular body have significant influence on the field intensity actors and the energy release rates.All the field variables near the crack tip possess the inverse square root singularity,and the energy release rate can have negative values depending on the direction,the magnitude,and the type of the electrical loads.