摘要
本文在弹性动力学范畴内,采用复变函数法和Green函数法研究了SH波对多个脱胶界面圆形夹杂的散射问题。为解决这个问题,首先采用分区的思想构造出了在特定边界条件下的两个Green函数,即出平面线源荷载对半空间中多个界面圆形弹性夹杂的散射问题的解和出平面线源荷载对半空间中多个半圆形凹陷的散射问题的解。然后将整个空间沿界面分成下上两个区域,并分别构造出SH波入射时夹杂内的驻波和半圆弧的特定形式的散射波,利用“契合”时公共边界处位移和应力的连续性条件,建立含Green函数和未知外力系的积分方程组,采用数值方法对该积分方程组进行求解。最后以算例给出了夹杂周围的动应力集中系数的数值结果,分析了介质参数和入射波参数对动应力集中的影响情况。
另外,在研究出平面线源荷载对半空间中多个界面圆形弹性夹杂的散射问题的Green函数时,给出了具体算例,讨论了夹杂周围的动应力集中系数和水平表面位移幅值。又进一步利用Green函数,在界面上构造出直裂纹,研究了SH对脱胶夹杂及其边缘裂纹和脱胶夹杂及直线型裂纹两种情况下裂纹尖端的动应力强度因子。最后以算例讨论了入射波数对不同介质的动应力强度因子的数值结果。
In the elastic dynamics range, the scattering of multiple debonding interface cylindrical elastic inclusions by SH-wave is researched by complex variable method and the Green's Function method. To solve this problem, two specific Green's Functions under specific boundary are constructed firstly, which are the scattering of out-plane line source load by multiple cylindrical elastic inclusions in half space and the scattering of out-plane line source load by multiple semi-cylindrical canyons in half space. Then divide the whole space into two parts along the interface with the method of dividing the district. And a standing wave in each inclusion and the scattering waves in particular form by multiple semi-circular boundaries can be constructed seperately. Re-conjuct the two part along the interface together and establish integral equations about the Green'Fuctions and unknown funtions about external forces with the continuous condition of the displacement and stress around the common boundary. Use numerical method to solve the equations. In the end, as examples, numerical results of dynamic stress concentration factor around the inclusions and the influences of the incident wave on difference parameters of mediators are presented and discussed.
In addition, some examples are given and results of dynamic stress concentration factor around the inclusion and the ground vibration at the horizontal surface are presented and discussed after constructing the Green'Fuction of the scattering of out-plane line source load by multiple cylindrical elastic inclusions in half space. And do furher researth in the scatering of SH-wave by multiple debonding interface cylindrical elastic inclusions and linear cracks originating at the debonding tip near two-phase mediums, as well as the scatering of SH-wave by multiple debonding interface cylindrical elastic inclusions and III mode of interface cracks by using the Green'Fuction. In the end some results of dynamic stress intensify factor are discussed.
引文
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