和界面接触的刚性线夹杂对SH波的散射

Scattering of SH wave by a rigid line terminating at the interface of a bi-material

利用积分变换方法,得出了两相材料中单位简谐力的格林函数。根据简谐集中力的格林函数得出了和界面接触的刚性线的散射场。利用无穷积分的性质,把和界面接触刚性线的散射场分解为奇异部分和有界部分。通过分解后的散射场建立了和界面接触刚性线在SH波作用下的Cauchy型奇异积分方程。根据所得奇异积分方程和刚性线的散射场得到了刚性线端点的奇异性阶数及奇性应力。应用刚性线端点的奇性应力定义了刚性线端点的应力奇异因子。对所得Cauchy型奇异积分方程的数值求解,可得刚性线端点的应力奇异因子。

In terms of integral transform methods, the Green function of harmonic force applied at two bound half planes is established. The scattered field of the rigid line is calculated by the obtained Green function. In virtue of the property of infinite integral, the scattered field is split into a singular part and a bounded part, by which the Cauchy type integral equation of the rigid line is obtained. The singular stress order at the terminating point and the singular stress at the neighborhood of the terminating point are determined by using the integral equation and the scattered field of the rigid line. The stress singularity factors at the rigid line tips are defined by the singular stress at the rigid line tips. The numerical solution of the integral equation yields the singular stress factors at the rigid line tips.