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讨论了不可导通情况下三维横观各向刚性压电材料中受拉伸和电载荷作用的平片裂纹Ⅰ型断裂力学问题．使用自限部分概念，从二维线性压电理论出发，严格得到了一组以裂纹面位移间断和电势间断为未知变量的超奇异积分方程组；应用二维超奇异积分的主部分析法，从理论上分析得到了裂纹前沿应力和电势奇性指数以及应力和电位移奇性场，从而找到了以裂纹面位移间断和电势间断表示的应力和电位移强度因子、能量释放率表达式；为所得到的超奇异积分方程组建立了数值法，并用此计算了若干典型的平片裂纹问题，数值结果令人满意．
In this paper, the type I fracture mechanics problems of the flat plate crack subjected to tensile and electric loads in a three-dimensional transversely isotropic rigid piezoelectric material under non-conducting conditions are discussed. Based on the two-dimensional linear piezoelectric theory, a series of super-singular integral equations with displacement discontinuity and potential discontinuity as unknown variables were obtained strictly. Using the principal part analytic method of two-dimensional hyper-singular integral, From the theoretical analysis, crack front stress and potential singularity index and singularity field of electric stress and electric displacement are obtained. The stress and electric displacement intensity factor and energy release rate expression are obtained by the discontinuity and potential discontinuity of crack surface. The numerical examples are established for the super-singular integral equations obtained, and several typical flat-plate crack problems are calculated. The numerical results are satisfactory.