SH波作用下孔洞、夹杂与直线形裂纹的相互作用
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摘要
本文在线弹性力学范畴内,采用Green函数和裂纹切割相结合的方法研究了在SH波作用下圆形孔洞、基体中圆形夹杂或半圆形凹陷地形与其附近任意直裂纹的相互作用问题。首先构造了一个适合解答本文问题的Green函数,该函数为含有孔洞、基体夹杂时弹性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,或含有半圆形凹陷地形时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(包括孔洞、基体夹杂、半圆形凹陷地形)对SH波散射问题出发,沿裂纹位置施加反向应力,即在欲出现裂纹区域加置与缺陷对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,从而构造出裂纹,并因而得到缺陷和裂纹同时存在条件下的位移与应力表达式,利用此表达式讨论缺陷周围的动应力集中情况,讨论裂纹尖端动应力强度因子的变化。本文所作的具体工作如下:
1.以完整的弹性空间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为Green函数,利用一个具体例子分析了裂纹构造方法。讨论了Green函数的连续、奇异等性状。
2.研究了SH波入射情况下圆形孔洞与周围直线形裂纹的动应力集中问题。利用适用于此问题的Green函数,采用裂纹切割方法导出了圆形孔洞与裂纹相互作用的位移、应力表达式,研究了圆形孔洞周围的动应力集中情况,研究了裂纹尖端的动应力强度因子,并给出具体的算例,讨论了入射波数、入射角度、裂纹位置等因素对此问题的影响情况。
3.研究了SH波入射情况下圆形夹杂与周围直线形裂纹的动应力集中问题。利用适用于此问题的Green函数,采用裂纹切割方法导出圆形夹杂与裂纹相互作用的位移、应力表达式,研究了圆形夹杂周围的动应力集中情况,研究了裂纹尖端的动应力强度因子,并利用具体的算例,讨论了入射波数、
Using Green's Function method and the method of crack-division, the interaction problems of circular cavity, inclusion or a cylindrical canyon with cracks of any limited lengths near gap or inclusion by SH-wave are studied in this paper in the field of linearly elastic dynamic mechanics. Firstly a suitable Green's function, which is a fundamental solution of displacement field for an elastic space possessing circular cavity or inclusion while bearing out-of-plane harmonic line source force at any point, or for an elastic half space possessing a cylindrical canyon 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 gap or inclusion (include circular cavity ,inclusion or a cylindrical canyon) are studied, reverse stresses are inflicted along the cracks, 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 gap or inclusion are loaded at the region where cracks will appear, so cracks can be made out. So the expression of displacement and stress is established while gap(or inclusion)and cracks are existent. Using the expression dynamic stress concentration near the gap (or inclusion) and the variety of dynamic stress intensity factor at crack tip are discussed. The works in detail are as follows:1 .The Green's function is a fundamental solution of displacement field for anelastic space possessing circular cavity or inclusion while bearing out-of-plane. harmonic line source force at any point. Using one example crack-divisiontechnique is analyzed. The continuity, singularity and some other characteristicsof the Green's function are discussed.2.The problem of SH-wave scattering and dynamic stress concentration by circular cavity with cracks of any limited lengths near the gap 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, and dynamic stress intensity factor at crack tip is discussed. Some examples 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.3. The problem of SH-wave scattering and dynamic stress concentration by
circular inclusion with 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, and dynamic stress intensity factor at crack tip is discussed. Some examples 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.4. The problem of SH-wave scattering and dynamic stress concentration by a cylindrical canyon with cracks of any limited lengths near the gap 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 the cylindrical canyon with cracks is studied with crack-division technique. Dynamic stress concentration near the cylindrical canyon is studied, and dynamic stress intensity factor at crack tip is discussed. Some examples and results are given. The influences of wave number, incident angles of SH-wave, and the geometrical location of the cylindrical canyon and crack are discussed.
1.以完整的弹性空间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为Green函数,利用一个具体例子分析了裂纹构造方法。讨论了Green函数的连续、奇异等性状。
2.研究了SH波入射情况下圆形孔洞与周围直线形裂纹的动应力集中问题。利用适用于此问题的Green函数,采用裂纹切割方法导出了圆形孔洞与裂纹相互作用的位移、应力表达式,研究了圆形孔洞周围的动应力集中情况,研究了裂纹尖端的动应力强度因子,并给出具体的算例,讨论了入射波数、入射角度、裂纹位置等因素对此问题的影响情况。
3.研究了SH波入射情况下圆形夹杂与周围直线形裂纹的动应力集中问题。利用适用于此问题的Green函数,采用裂纹切割方法导出圆形夹杂与裂纹相互作用的位移、应力表达式,研究了圆形夹杂周围的动应力集中情况,研究了裂纹尖端的动应力强度因子,并利用具体的算例,讨论了入射波数、
Using Green's Function method and the method of crack-division, the interaction problems of circular cavity, inclusion or a cylindrical canyon with cracks of any limited lengths near gap or inclusion by SH-wave are studied in this paper in the field of linearly elastic dynamic mechanics. Firstly a suitable Green's function, which is a fundamental solution of displacement field for an elastic space possessing circular cavity or inclusion while bearing out-of-plane harmonic line source force at any point, or for an elastic half space possessing a cylindrical canyon 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 gap or inclusion (include circular cavity ,inclusion or a cylindrical canyon) are studied, reverse stresses are inflicted along the cracks, 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 gap or inclusion are loaded at the region where cracks will appear, so cracks can be made out. So the expression of displacement and stress is established while gap(or inclusion)and cracks are existent. Using the expression dynamic stress concentration near the gap (or inclusion) and the variety of dynamic stress intensity factor at crack tip are discussed. The works in detail are as follows:1 .The Green's function is a fundamental solution of displacement field for anelastic space possessing circular cavity or inclusion while bearing out-of-plane. harmonic line source force at any point. Using one example crack-divisiontechnique is analyzed. The continuity, singularity and some other characteristicsof the Green's function are discussed.2.The problem of SH-wave scattering and dynamic stress concentration by circular cavity with cracks of any limited lengths near the gap 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, and dynamic stress intensity factor at crack tip is discussed. Some examples 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.3. The problem of SH-wave scattering and dynamic stress concentration by
circular inclusion with 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, and dynamic stress intensity factor at crack tip is discussed. Some examples 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.4. The problem of SH-wave scattering and dynamic stress concentration by a cylindrical canyon with cracks of any limited lengths near the gap 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 the cylindrical canyon with cracks is studied with crack-division technique. Dynamic stress concentration near the cylindrical canyon is studied, and dynamic stress intensity factor at crack tip is discussed. Some examples and results are given. The influences of wave number, incident angles of SH-wave, and the geometrical location of the cylindrical canyon and crack are discussed.
引文
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