A singular integral equation method is proposed to analyze the two-dimensional (2D) multiple cracks in anisotropic piezoelectric bimaterial. Using the Somigliana formula, a set of singular integral equations for the multiple crack problems are derived, in which the unknown functions are the derivatives of the generalized displacement discontinuities of the crack surfaces. Then, the exact analytical solution of the extended singular stresses and extended stress intensity factors near the crack tip is obtained. Singular integrals of the singular integral equations are computed by the Gauss–Chebyshev collocation method. Finally, numerical solutions of the extended stress intensity factors of some examples are presented and discussed.

提出了一种奇异积分方程方法来分析各向异性压电双材料中的二维 (2D) 多裂纹。利用Somigliana公式，推导出了一组多裂纹问题的奇异积分方程，其中未知函数是裂纹面广义位移不连续性的导数。然后，得到裂纹尖端附近扩展奇异应力和扩展应力强度因子的精确解析解。奇异积分方程的奇异积分由高斯-切比雪夫搭配法计算。最后，给出并讨论了一些例子的扩展应力强度因子的数值解。