SH波作用下双相介质界面附近圆孔和裂纹的相互作用
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摘要
本文在弹性动力学范畴内,采用Green函数、复变函数和多极坐标方法研究了双向介质界面附近圆形孔洞及其附近任意方位有限长度裂纹对SH波的散射问题。
首要工作是构造适合本问题的Green函数,这也是本论文的关键技术问题。本文需要用到两个Green函数,一个是在含有圆孔和任意方位裂纹的弹性半空间表面的任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解。其中分别给出了在含圆孔的弹性半空间表面和内部的任意一点承受时间谐和的出平面线源荷载作用时的位移场,在圆孔附近采用裂纹“切割”方法构造出任意方位的裂纹,从而构造出适合本文问题的第一个Green函数。第二个Green函数为在完整的弹性半空间表面的任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解。
研究SH波对双相介质界面附近圆形孔洞和裂纹的散射问题,求解过程中将问题的模型视为“契合”问题:即可将所研究的问题沿其界面“剖分”为两个部分,其一为含有圆形孔洞和裂纹的弹性半空间,而另外一部分则可以是完整的弹性半空间。若在两个半无限空间的自由表面上,分别加置待定的出平面荷载,利用求出的Green函数写出界面上的连续条件,建立起确定待解外力系的第一类Fredholm积分方程组,采用直接离散的方法将定解积分方程组转化为线性代数方程组计算求解,从而可以得到双相介质界面附近圆形孔洞和裂纹对SH散射的位移场、应力场的解析表达式。针对具体算例,讨论了不同的入射波数、入射角度、圆孔到界面距离、裂纹与圆孔的距离、裂纹的角度、长度、双相介质等参数对界面附近圆孔周边动应力集中系数和裂纹尖端动应力强度因子的影响。
The problems of SH-wave scattering,which is caused by half-space circular cavity near the bimaterial interface and crack of arbitrary position,are studied in this paper beyond the field of elastodynamics,and the methods of Green's Function,complex variables function and multi-polar coordinates are used here.
First,a suitable Green's function is constructed,and this is the key technology of this problem.Two Green's functions are needed here:one is an essential solution of the displacement field for the elastic half-space possessing circular cavity and crack with arbitrary position while bearing out-of-plane harmonic line source loads at arbitrary point,and using this,displacement for the surface and internal of elastic half-space possessing circular cavity while bearing out-of-plane harmonic line source loads at arbitrary point can be obtained,the crack with arbitrary position is established by using the method of crack-division, then,the first Green' function for this problem is constructed.The second Green' function is an essential solution of the displacement field for the elastic whole space while bearing out-of-plane harmonic line source loads at arbitrary point.
The scattering of SH-wave by crack of arbitrary position and a circular cavity near the bimaterial interface is investigated,the problem can be regarded as harmony model:the bimaterial media is divided into two parts along the horizontal interface,one is an elastic half space with a circular cavity and a crack, and the other is a complete elastic whole space.The horizontal surfaces of the two parts are loaded with undetermined anti-plane forces in order to satisfy at the linking section.A series of Fredholm integral equations can be set up through continuity conditions.Then,the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite integral equations,the expressions of displacement field and stress field of scattering of SH-wave by crack and circular cavity near the bimaterial interface are given.Numerical examples are provided to show the influences of wave numbers,incident angle,the distance between the center of the circular cavity and horizontal surfaces,the distance between the center of the circular cavity and crack,the angle,length of crack,and parameter combinations of different media upon dynamic stress concentration factor(DSCF) and dynamic stress intensity factor(DSIF).
首要工作是构造适合本问题的Green函数,这也是本论文的关键技术问题。本文需要用到两个Green函数,一个是在含有圆孔和任意方位裂纹的弹性半空间表面的任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解。其中分别给出了在含圆孔的弹性半空间表面和内部的任意一点承受时间谐和的出平面线源荷载作用时的位移场,在圆孔附近采用裂纹“切割”方法构造出任意方位的裂纹,从而构造出适合本文问题的第一个Green函数。第二个Green函数为在完整的弹性半空间表面的任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解。
研究SH波对双相介质界面附近圆形孔洞和裂纹的散射问题,求解过程中将问题的模型视为“契合”问题:即可将所研究的问题沿其界面“剖分”为两个部分,其一为含有圆形孔洞和裂纹的弹性半空间,而另外一部分则可以是完整的弹性半空间。若在两个半无限空间的自由表面上,分别加置待定的出平面荷载,利用求出的Green函数写出界面上的连续条件,建立起确定待解外力系的第一类Fredholm积分方程组,采用直接离散的方法将定解积分方程组转化为线性代数方程组计算求解,从而可以得到双相介质界面附近圆形孔洞和裂纹对SH散射的位移场、应力场的解析表达式。针对具体算例,讨论了不同的入射波数、入射角度、圆孔到界面距离、裂纹与圆孔的距离、裂纹的角度、长度、双相介质等参数对界面附近圆孔周边动应力集中系数和裂纹尖端动应力强度因子的影响。
The problems of SH-wave scattering,which is caused by half-space circular cavity near the bimaterial interface and crack of arbitrary position,are studied in this paper beyond the field of elastodynamics,and the methods of Green's Function,complex variables function and multi-polar coordinates are used here.
First,a suitable Green's function is constructed,and this is the key technology of this problem.Two Green's functions are needed here:one is an essential solution of the displacement field for the elastic half-space possessing circular cavity and crack with arbitrary position while bearing out-of-plane harmonic line source loads at arbitrary point,and using this,displacement for the surface and internal of elastic half-space possessing circular cavity while bearing out-of-plane harmonic line source loads at arbitrary point can be obtained,the crack with arbitrary position is established by using the method of crack-division, then,the first Green' function for this problem is constructed.The second Green' function is an essential solution of the displacement field for the elastic whole space while bearing out-of-plane harmonic line source loads at arbitrary point.
The scattering of SH-wave by crack of arbitrary position and a circular cavity near the bimaterial interface is investigated,the problem can be regarded as harmony model:the bimaterial media is divided into two parts along the horizontal interface,one is an elastic half space with a circular cavity and a crack, and the other is a complete elastic whole space.The horizontal surfaces of the two parts are loaded with undetermined anti-plane forces in order to satisfy at the linking section.A series of Fredholm integral equations can be set up through continuity conditions.Then,the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite integral equations,the expressions of displacement field and stress field of scattering of SH-wave by crack and circular cavity near the bimaterial interface are given.Numerical examples are provided to show the influences of wave numbers,incident angle,the distance between the center of the circular cavity and horizontal surfaces,the distance between the center of the circular cavity and crack,the angle,length of crack,and parameter combinations of different media upon dynamic stress concentration factor(DSCF) and dynamic stress intensity factor(DSIF).
引文
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