【作者】 赵嘉喜；

【导师】 齐辉；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2008， 博士

【摘要】 本文在弹性动力学范畴内,采用复变函数法和Green函数法研究了出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射问题;采用Green函数法和“契合”方法研究了界面附近半圆形脱胶的圆柱形弹性夹杂对SH波的散射问题以及SH波作用下界面附近含有半圆形脱胶的圆柱形弹性夹杂和界面裂纹的相互作用问题。研究出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射问题。首先,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上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,取该位移函数作为Green函数。然后,采用分区的思想,分别构造出夹杂内的驻波和夹杂外的散射波,满足公共边界处位移和应力的连续性条件,建立起求解该问题的无穷代数方程组。最后,给出了动应力集中系数和水平地面位移幅值的数值结果,并进行了讨论。研究SH波对双相介质界面附近含有半圆形脱胶的圆形弹性夹杂的散射问题。首先,沿界面将整个空间分成上下两部分。在下半空间,采用本文中所构造的Green函数,并采用“契合”的方法在上下空间连接时满足界面处连续性条件,构造出半圆形脱胶裂纹,进而求出应力和位移的表达式。最后作为算例,给出了动应力集中系数的数值结果,分析了介质参数和入射波参数对动应力集中的影响情况。研究SH波对双相介质界面附近含有半圆形脱胶的圆形弹性夹杂的散射问题的远场解。利用Hankel函数在宗量充分大时的渐近表达式,可以得到该问题的散射波远场位移模式和散射截面,分析了不同参数对远场解的影响结果。研究SH波对双相介质界面附近含有半圆形脱胶及其边缘直线型裂纹的圆柱形弹性夹杂的散射问题。沿界面将整个空间分成上下两部分。采用“契合”的方法和构造裂纹技术将上下空间连接,构造出半圆形脱胶裂纹和直线型裂纹。然后,给出了直线型裂纹的动应力强度因子的数值结果,并进行了讨论。研究SH波作用下双相介质界面附近含有半圆形脱胶的圆形弹性夹杂和直线型裂纹的相互作用,该问题中的界面裂纹与脱胶边缘脱离。采用Green函数法、复变函数法、“契合”方法以及构造裂纹技术,将问题归结为求解界面裂纹尖端的Ⅲ型动应力强度因子的问题,并对得到的数值结果进行了讨论。更多还原

【Abstract】 In the elastic dynamics range, the scattering of out-plane line source load by a semi-cylindrical hill of cylindrical elastic inclusion in half space is studied by complex variable method and the Green’s Function method; By the Green’s Function method and the "conjunction" method, the scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve, the interaction of an interface cylindrical elastic inclusion with semicircular disconnected curve and linear cracks impacted by SH-wave are investigated.The scattering of out-plane line source load by a semi-cylindrical hill of cylindrical elastic inclusion in half space is studied by complex variable method and the Green’s Function method. Firstly, in the elastic half space with the semi-cylindrical hill of cylindrical inclusion, the arbitrary displacement field while bearing out-plane harmonic line source load at horizontal surface is given as the Green’s function. Then, with the method of dividing the district, a standing wave in the inclusion and the scattering wave outside can be constructed seperately. In order to satisfy the continuous condition of the displacement and stress around the common boundary condition, a series of infinite algebraic equations can be obtained to settle this problem. In the end, as examples, numerical results of dynamic stress concentration factor and the ground vibration in the horizontal surface are presented and discussed.The scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve near two-phase mediums is researched. Firstly, we can divide the space into up-and-down parts along the interface. In the lower half space, with the suitable Green’s function constructed above, the semicircular disconnected curve can be constructed when the two parts are bonded which is continuous in the interface impacted by SH-wave by the "conjunction" method. And the expressions of displacement field and stress field are obtained under this situation. Finally, some examples and results of dynamic stress concentration factor are given and the influences by the difference parameters of mediators and the incident wave are discussed.The far field solution of SH-wave impacted by a cylindrical elastic inclusion with a semicircular disconnected curve near bi-media material interface. Based on the progressive expression of the Hankel function with the large enough independent variable, The displacement mode of scattered wave at far field and scattering cross-section are given. The influences to the far field solution by different parameters are discussed.The scattering of SH-wave by an interface cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks originating at the curve near two-phase mediums is investigated. Along the interface, the whole space is divided into two parts. With the "conjunction" method and the method of crack-constitution, the semicircular disconnected curve and the linear cracks are constructed when the two parts are bonded along the interface. Some examples and results of dynamic stress intensify factor are given with discussions.The interaction of an interface cylindrical elastic inclusion with semicircular disconnected curve and linear cracks impacted by SH-wave is investigated. In this problem, the linear cracks and the disconnected curve is not connected. By the Green’s Function method, complex variable method, the "conjunction" method and the method of crack-constitution, the subject is inverted into the solution of the dynamic stress intensityⅢmode of the interface cracks. And some results of dynamic stress intensify factor are discussed.更多还原