复合材料Reissner板中与界面相交的裂纹奇异性分析

Singularity analysis for cracks terminating at the interface in orthotropic Reissner plates

基于切口尖端附近区域位移场的渐近展开,提出了分析复合材料板中与界面相交的切口应力奇异性的新方法。将位移场渐近展开式的典型项代入弹性板的基本方程,得到关于复合材料板中与界面相交的切口应力奇异性指数的一组非线性常微分方程的特征值;采用变量代换法,将非线性特征问题转化为线性特征问题,并用插值矩阵法求解获得了各向异性结合材料中与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律;最后将计算结果与现有结果进行对比。结果表明:两种结果吻合较好,表明本文方法是有效的。

Based on the asymptotic expansion of the generalized displacement fields at the notch tip, a characteristic analysis method for calculating the singularity orders of the V-notch terminating at the interface in the anisotropic plates is proposed. By introducing the generalized displacement functions in the asymptotic expansion into the fundament equations of the plate, the governing equations of the anisotropic plate are transformed into a set of nonlinear characteristic ordinary differential equations(ODEs) with the singularity orders. By adding the new functions, the established non-linear characteristic equations are transformed into a set of linear ones. Then the interpolating matrix method is introduced to solve the derivative ODEs. The relation between the stress singularity and the ply angle of the crack terminating at the interface of bonded dissimilar anisotropic materials can be easily obtained. The validity of the present method is confirmed by comparing with the existed results in the numerical examinations.