圆柱形缺陷与裂纹的动力反平面相互作用
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摘要
本文在线弹性力学范畴内,采用多极坐标方法、Green函数和裂纹切割相结合的方法分别研究了在SH波作用下弹性空间多个圆形夹杂与附近任意位置任意长度直线形裂纹的相互作用问题,和弹性半空间多个圆形孔洞与附近任意位置任意长度单条直线形裂纹的相互作用问题。首先,采用多极坐标方法构造了适合解决本文问题的Green函数,分别为含有多个圆形夹杂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的位移函数基本解,和含有多个圆形孔洞的弹性半空间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。然后采用裂纹切割方法构造裂纹,即在欲出现裂纹区域加置与缺陷对SH波产生应力相对应的大小相等、方向相反的出平面载荷,从而构造出裂纹,从而得到缺陷和裂纹同时存在时的位移、应力表达式。最后讨论了缺陷周围的动应力集中情况。本文所作的具体工作如下：
1.研究了含多个圆形夹杂的弹性空间对线源载荷散射时圆形夹杂周边的动应力集中问题。利用多极坐标方法求出了多圆夹杂相互作用的位移、应力表达式,研究了圆形夹杂周围的动应力集中情况,并利用具体的算例讨论了剪切模量比、入射波数、夹杂与点源的相对位置等因素对此问题的影响情况。
2.研究了SH波入射情况下弹性空间多圆夹杂与周围直线型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多圆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,并给出具体的算例,讨论了剪切模量比、入射波数、入射角度、夹杂与裂纹相对位置等因素对此问题的影响情况。
3.研究了SH波入射情况下半空间多圆孔洞与周围直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多圆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,并利用具体的算例,讨论了入射波数、入射角度、孔洞与裂纹相对位置、埋深等因素对此问题的影响情况。
In this paper, by using Green's Function method, the method of crack-division and the method of multi-polar coordinate system, the interaction problem of multiple circular inclusions with a linear crack in elastic space by SH-wave, and the interaction problem of multiple circular cavities with a linear crack in semi-space by SH-wave is studied. Firstly, the suitable Green's functions are constructed, which are the solution of displacement field for elastic space with multiple inclusions and the solution of displacement field for elastic semi-space with multiple circular shallow-buried cavities while bearing anti-plane harmonic line source force at any point separately. Then applying the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by defects(cavity or inclusion) 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 defects are loaded at the region where cracks whill appear, so cracks can be made out. So the expression of displacement and stress is established while defects and cracks exist at the same time. Using the expression dynamic stress concentration near the defects is discussed. The works in detail are as follows:
1. Green's Function is studied, which is the solution of displacement field for elastic space with multiple inclusions while bearing anti-plane harmonic line source force at any point. Applying the method of multi-polar coordinate system, the expression of displacement and stress is obtained. Then using the expressions, the dynamic stress concentration factor at the edge of the inclusion is discussed to the case of different parameters(.wave number, the radio of the shear modulus, the geometrical location of the circular inclusions and the line source).
2. The problem of SH-wave scattering by circular inclusions with a crack of any limited lengths near the inclusions in elastic space is investigated. By using Green's function which is suitable to this problem and the method of crack-division, the expression of displacement and stress is established. Then the dynamic stress concentration at the edge of the circular inclusion is discussed to the case of different parameters(the radio of the shear modulus, wave number, incident angles of SH-wave, and the geometrical location of the circular inclusions and the crack).
3. The problem of SH-wave scattering by circular cavities with a crack of any limited lengths near the inclusions in elastic semi-space is investigated. By using Green's function which is suitable to this problem and the method of crack-division, the expression of displacement and stress is established. Then the dynamic stress concentration at the edge of the circular cavities is discussed to the case of different parameters(wave number, incident angles of SH-wave, and the geometrical location of the circular inclusions and the crack, the embedded depth of the circular inclusions and the crack).
1.研究了含多个圆形夹杂的弹性空间对线源载荷散射时圆形夹杂周边的动应力集中问题。利用多极坐标方法求出了多圆夹杂相互作用的位移、应力表达式,研究了圆形夹杂周围的动应力集中情况,并利用具体的算例讨论了剪切模量比、入射波数、夹杂与点源的相对位置等因素对此问题的影响情况。
2.研究了SH波入射情况下弹性空间多圆夹杂与周围直线型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多圆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,并给出具体的算例,讨论了剪切模量比、入射波数、入射角度、夹杂与裂纹相对位置等因素对此问题的影响情况。
3.研究了SH波入射情况下半空间多圆孔洞与周围直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多圆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,并利用具体的算例,讨论了入射波数、入射角度、孔洞与裂纹相对位置、埋深等因素对此问题的影响情况。
In this paper, by using Green's Function method, the method of crack-division and the method of multi-polar coordinate system, the interaction problem of multiple circular inclusions with a linear crack in elastic space by SH-wave, and the interaction problem of multiple circular cavities with a linear crack in semi-space by SH-wave is studied. Firstly, the suitable Green's functions are constructed, which are the solution of displacement field for elastic space with multiple inclusions and the solution of displacement field for elastic semi-space with multiple circular shallow-buried cavities while bearing anti-plane harmonic line source force at any point separately. Then applying the method of crack-division, integration for solution is established:while the scattering problems of SH-wave by defects(cavity or inclusion) 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 defects are loaded at the region where cracks whill appear, so cracks can be made out. So the expression of displacement and stress is established while defects and cracks exist at the same time. Using the expression dynamic stress concentration near the defects is discussed. The works in detail are as follows:
1. Green's Function is studied, which is the solution of displacement field for elastic space with multiple inclusions while bearing anti-plane harmonic line source force at any point. Applying the method of multi-polar coordinate system, the expression of displacement and stress is obtained. Then using the expressions, the dynamic stress concentration factor at the edge of the inclusion is discussed to the case of different parameters(.wave number, the radio of the shear modulus, the geometrical location of the circular inclusions and the line source).
2. The problem of SH-wave scattering by circular inclusions with a crack of any limited lengths near the inclusions in elastic space is investigated. By using Green's function which is suitable to this problem and the method of crack-division, the expression of displacement and stress is established. Then the dynamic stress concentration at the edge of the circular inclusion is discussed to the case of different parameters(the radio of the shear modulus, wave number, incident angles of SH-wave, and the geometrical location of the circular inclusions and the crack).
3. The problem of SH-wave scattering by circular cavities with a crack of any limited lengths near the inclusions in elastic semi-space is investigated. By using Green's function which is suitable to this problem and the method of crack-division, the expression of displacement and stress is established. Then the dynamic stress concentration at the edge of the circular cavities is discussed to the case of different parameters(wave number, incident angles of SH-wave, and the geometrical location of the circular inclusions and the crack, the embedded depth of the circular inclusions and the crack).
引文
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