双相介质半空间椭圆形夹杂与直线裂纹对SH波的散射  

Scattering of SH-wave caused by an elliptical inclusion and a beeline crack in bi-material half space

作　　者：丁晓浩 齐辉[1] 赵元博[1] DING Xiao-hao Qi Hui ZHAO Yuan-bo(College of Aerospace and Civil Engineering,Harbin Engineering University,Harbin 150001, China)

机构地区：[1]哈尔滨工程大学航天与建筑工程学院,哈尔滨150001

出　　处：《振动与冲击》2017年第11期79-85,共7页Journal of Vibration and Shock

基　　金：黑龙江省自然科学基金(A201404)

摘　　要：利用Green函数法、复变函数法和保角映射法研究了双相介质半空间存在直线裂纹与椭圆形夹杂组成的复合缺陷对SH波的散射问题并给出了解析解。采用保角映射法将椭圆形夹杂外域映射为单位圆外域并利用镜像叠加原理构造了一个能自动满足直角域两个直线边界应力自由边界条件的散射位移场。利用裂纹"切割"技术构造区域I中的直线裂纹,并根据弹性叠加原理得出直角域中同时存在裂纹与椭圆形夹杂时的位移场和应力场。采用"契合"法在界面上添加未知的外力系以满足界面上的应力和位移连续性条件,根据连续性条件建立求解未知力系的定解积分方程组,并通过截断有限项求解。具体算例给出了不同参数条件下椭圆形夹杂的动应力集中系数分布情况,结果表明裂纹将对椭圆形夹杂的动应力集中系数的分布产生影响。The scattering problem of SH-wave by an elliptical inclusion in bi-material half space with beeline crack was investigated by using Green’s function and complex function method with conformal mapping method and the analytical solution was given. Firstly. the conformal mapping method, which was used to map the outside region of elliptical inclusion into circular region, and image method are employed here to construct the scattering wave function, which satisfies the condition of stress free on the straight boundaries. Secondly, with the aid of crack-division technique, the beeline crack was constructed and expression of displacement and stress field were given while both crack and elliptical inclusion exist. Finally, interface conjunction method was employed by adding unknown force system on the conjunction section to satisfy the continuity of displacement and stress. The integral equation to determine the unknown the force system was establish according to the continuity condition and solved by truncation method. The distribution of dynamic stress concentration factor（DSCF） on the edge of the elliptical inclusion were presented by some examples and results show that the crack was able to effect the distribution of DSCF.

关 键 词：双相介质半空间 椭圆形夹杂 直线裂纹 保角映射 动应力集中系数(DSCF) 

分 类 号：O343.1[理学—固体力学] P315.3[理学—力学]