SH波作用下复合缺陷问题研究
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摘要
本文在线弹性力学范畴内,利用Green函数和二次“裂纹切割”相结合的方法研究了在SH波作用下无限弹性介质中圆形孔洞或圆形夹杂与其附近任意双直线型裂纹(复合缺陷)的相互作用问题。通过构造一个适合解答本文问题的Green函数,求出该函数为含有孔洞、夹杂和单裂纹时弹性空间内任意一点承受时间谐和出平面线源荷载作用时位移函数的基本解。然后采用“裂纹切割”方法建立问题的求解积分：即从缺陷(包括孔洞、夹杂和单裂纹)对SH波散射问题出发,沿第二个裂纹位置施加反向应力,即在欲出现裂纹的区域加置与缺陷和单裂纹对SH波散射产生应力相对应的大小相等、方向相反的出平面荷载,从而构造出第二个裂纹,并因而得到孔洞或夹杂与双裂纹同时存在条件下的位移与应力表达式,利用此表达式讨论了孔洞或夹杂周边的动应力集中问题。
利用Green函数、裂纹人工切割和多极坐标相结合的方法研究了在SH波作用下弹性介质半空间中多圆弹性夹杂和单直线型裂纹的相互作用问题。求解该问题的方法是构造一个适合解答本文问题的Green函数,该函数为含有多圆夹杂的弹性半空间上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解。然后采用“裂纹切割”方法建立问题的求解积分：即从缺陷对SH波散射问题出发,沿裂纹位置施加反向应力,即在欲出现裂纹的区域加置与缺陷和单裂纹对SH波散射产生应力相对应的大小相等、方向相反的出平面荷载,从而构造出一条裂纹,并因而得到多圆夹杂和单直线型裂纹共存条件下的位移与应力表达式,利用此表达式讨论夹杂周边的动应力集中情况。
本文所作的具体工作如下：
1.利用适用于孔洞问题的Green函数,采用二次“裂纹切割”的方法导出了圆形孔洞与双直线型裂纹相互作用的位移和应力表达式。并给出具体的算例,通过算例研究了SH波入射情况下无限弹性体中圆形孔洞与其附近任意双直线型裂纹作用时的孔洞周边动应力集中问题,讨论了入射波数、入射角度、两裂纹的长度比、裂纹位置等因素对此问题的影响情况。
2.研究了SH波入射情况下无限弹性体中圆形弹性夹杂与其附近任意双直线型裂纹的夹杂周边动应力集中分布问题。采用二次“裂纹切割”方法导出了圆形弹性夹杂与双裂纹相互作用的位移和应力表达式,研究了圆形夹杂周围的动应力集中情况,并利用具体的算例,讨论了入射波数、入射角度、两裂纹长度比、裂纹位置、基体和夹杂材料剪切模量比等因素对动应力问题的影响。
3.利用适用于此问题的Green函数,采用一次“裂纹切割”与多极坐标的相结合方法导出了多个圆形夹杂与单裂纹相互作用的位移和应力表达式。并利用具体的算例,研究了SH波入射情况下半空间弹性体内两个圆形弹性夹杂与单直线型裂纹的相互作用时,弹性夹杂周围的动应力集中情况,讨论了入射波数、入射角度、裂纹位置、两个夹杂之间相对位置、基体和夹杂材料性质组合形式等因素对动应力集中的影响。
By using Green's Function method and the method of crack-division, the interaction problems of combined defectiveness including circular cavity, inclusion with double cracks of any limited lengths near cavity or inclusion subjected by SH-wave were studied in the range of linear dynamic elasticity. Firstly a suitable Green's function, which is a fundamental solution of displacement field for an elastic space possessing circular cavity or inclusion with a linear crack while bearing out-of-plane harmonic line source force at any point is constructed for the present problem. Then using the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by circular cavity or inclusion with a linear crack are studied, reverse stresses are inflicted along the second crack, that is, out-of-plane harmonic line source forces which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH-wave scattering by cavity or inclusion with a linear crack are loaded at the region where cracks will appear, so the second crack can be made out. So the expression of displacement and stress is established while cavity or inclusion and double cracks are existent. Using the expression dynamic stress concentration near the cavity or inclusion is discussed.
By using Green's Function method and the method of crack-division and the method of multi-polar coordinate system, the interaction problem of multiple circular inclusions with an linear crack in half space by SH-wave is studied. Firstly a suitable Green's function, which is a fundamental solution of displacement field for half elastic space possessing multiple circular inclusions while bearing out-of-plane harmonic line source force at any point is constructed for the present problem. Then using the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by multiple circular inclusions is studied, reverse stresses are inflicted along the crack, that is, out-of-plane harmonic line source forces which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH-wave scattering by multiple inclusions are loaded at the region where crack will appear, so the crack can be made out. So the expression of displacement and stress was established while multiple inclusions and crack are existent. Employing the expression dynamic stress concentration near the inclusion was discussed.
The works in detail have covered three areas:
1. The problem of SH-wave scattering and dynamic stress concentration by circular cavity with double cracks of any limited lengths near the cavity is investigated. Using the Green's function which is suitable to the present problem, the expression of displacement and stress is established while the interaction of circular cavity with cracks is studied with crack-division technique. Dynamic stress concentration near the circular cavity is studied. An example and results are given. The influences of wave number, incident angles of SH-wave, and the geometrical location of the circular cavity and crack are discussed.
2. The problem of SH-wave scattering and dynamic stress concentration by circular inclusion with double cracks of any limited lengths near the inclusion is investigated. Using the Green's function which is suitable to the present problem, the expression of displacement and stress is established while the interaction of circular inclusion with cracks is studied with crack-division technique. Dynamic stress concentration near the circular inclusion is studied. An example and results are given. The influences of wave number, incident angles of SH-wave, the geometrical location of the circular cavity and crack and the combination of different media parameters are discussed.
3. The problem of SH-wave scattering and dynamic stress concentration by multiple circular inclusions with a linear crack near the inclusions are investigated. Using the Green's function which is suitable to the present problem, the expression of displacement and stress is established while the interaction of circular inclusions with crack is studied with crack-division technique. Dynamic stress concentration near the circular inclusion is studied. An example and results are given. The influences of wave number, incident angles of SH-wave, the geometrical location of the circular cavity and crack and the combination of different media parameters are discussed.
利用Green函数、裂纹人工切割和多极坐标相结合的方法研究了在SH波作用下弹性介质半空间中多圆弹性夹杂和单直线型裂纹的相互作用问题。求解该问题的方法是构造一个适合解答本文问题的Green函数,该函数为含有多圆夹杂的弹性半空间上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解。然后采用“裂纹切割”方法建立问题的求解积分：即从缺陷对SH波散射问题出发,沿裂纹位置施加反向应力,即在欲出现裂纹的区域加置与缺陷和单裂纹对SH波散射产生应力相对应的大小相等、方向相反的出平面荷载,从而构造出一条裂纹,并因而得到多圆夹杂和单直线型裂纹共存条件下的位移与应力表达式,利用此表达式讨论夹杂周边的动应力集中情况。
本文所作的具体工作如下：
1.利用适用于孔洞问题的Green函数,采用二次“裂纹切割”的方法导出了圆形孔洞与双直线型裂纹相互作用的位移和应力表达式。并给出具体的算例,通过算例研究了SH波入射情况下无限弹性体中圆形孔洞与其附近任意双直线型裂纹作用时的孔洞周边动应力集中问题,讨论了入射波数、入射角度、两裂纹的长度比、裂纹位置等因素对此问题的影响情况。
2.研究了SH波入射情况下无限弹性体中圆形弹性夹杂与其附近任意双直线型裂纹的夹杂周边动应力集中分布问题。采用二次“裂纹切割”方法导出了圆形弹性夹杂与双裂纹相互作用的位移和应力表达式,研究了圆形夹杂周围的动应力集中情况,并利用具体的算例,讨论了入射波数、入射角度、两裂纹长度比、裂纹位置、基体和夹杂材料剪切模量比等因素对动应力问题的影响。
3.利用适用于此问题的Green函数,采用一次“裂纹切割”与多极坐标的相结合方法导出了多个圆形夹杂与单裂纹相互作用的位移和应力表达式。并利用具体的算例,研究了SH波入射情况下半空间弹性体内两个圆形弹性夹杂与单直线型裂纹的相互作用时,弹性夹杂周围的动应力集中情况,讨论了入射波数、入射角度、裂纹位置、两个夹杂之间相对位置、基体和夹杂材料性质组合形式等因素对动应力集中的影响。
By using Green's Function method and the method of crack-division, the interaction problems of combined defectiveness including circular cavity, inclusion with double cracks of any limited lengths near cavity or inclusion subjected by SH-wave were studied in the range of linear dynamic elasticity. Firstly a suitable Green's function, which is a fundamental solution of displacement field for an elastic space possessing circular cavity or inclusion with a linear crack while bearing out-of-plane harmonic line source force at any point is constructed for the present problem. Then using the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by circular cavity or inclusion with a linear crack are studied, reverse stresses are inflicted along the second crack, that is, out-of-plane harmonic line source forces which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH-wave scattering by cavity or inclusion with a linear crack are loaded at the region where cracks will appear, so the second crack can be made out. So the expression of displacement and stress is established while cavity or inclusion and double cracks are existent. Using the expression dynamic stress concentration near the cavity or inclusion is discussed.
By using Green's Function method and the method of crack-division and the method of multi-polar coordinate system, the interaction problem of multiple circular inclusions with an linear crack in half space by SH-wave is studied. Firstly a suitable Green's function, which is a fundamental solution of displacement field for half elastic space possessing multiple circular inclusions while bearing out-of-plane harmonic line source force at any point is constructed for the present problem. Then using the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by multiple circular inclusions is studied, reverse stresses are inflicted along the crack, that is, out-of-plane harmonic line source forces which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH-wave scattering by multiple inclusions are loaded at the region where crack will appear, so the crack can be made out. So the expression of displacement and stress was established while multiple inclusions and crack are existent. Employing the expression dynamic stress concentration near the inclusion was discussed.
The works in detail have covered three areas:
1. The problem of SH-wave scattering and dynamic stress concentration by circular cavity with double cracks of any limited lengths near the cavity is investigated. Using the Green's function which is suitable to the present problem, the expression of displacement and stress is established while the interaction of circular cavity with cracks is studied with crack-division technique. Dynamic stress concentration near the circular cavity is studied. An example and results are given. The influences of wave number, incident angles of SH-wave, and the geometrical location of the circular cavity and crack are discussed.
2. The problem of SH-wave scattering and dynamic stress concentration by circular inclusion with double cracks of any limited lengths near the inclusion is investigated. Using the Green's function which is suitable to the present problem, the expression of displacement and stress is established while the interaction of circular inclusion with cracks is studied with crack-division technique. Dynamic stress concentration near the circular inclusion is studied. An example and results are given. The influences of wave number, incident angles of SH-wave, the geometrical location of the circular cavity and crack and the combination of different media parameters are discussed.
3. The problem of SH-wave scattering and dynamic stress concentration by multiple circular inclusions with a linear crack near the inclusions are investigated. Using the Green's function which is suitable to the present problem, the expression of displacement and stress is established while the interaction of circular inclusions with crack is studied with crack-division technique. Dynamic stress concentration near the circular inclusion is studied. An example and results are given. The influences of wave number, incident angles of SH-wave, the geometrical location of the circular cavity and crack and the combination of different media parameters are discussed.
引文
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