【作者】 魏庆辉；

【导师】 张楠；

【作者基本信息】 北京交通大学 ， 桥梁与隧道工程， 2012， 硕士

【摘要】 近年来城市轨道交通和高速铁路发展迅速,由此引发的环境振动问题已经引起许多专家和学者的高度重视。现有研究表明：火车运行造成的地面振动幅值很小,可以把半无限土体近似为弹性半空间无限域用以研究运行火车产生的土体振动问题,本文建立了弹性半空间无限域的数值模型并对其相关动力、静力特性进行了分析。首先,利用映射无限元单元和有限元单元建立了参数可控的弹性半空间无限域静力分析模型；提出了适合求解映射无限元单元刚度矩阵显式表达式的无限元形函数；通过与已知集中荷载作用下半空间无限域的理论解作对比,得到与弹性半空间内部有限元区域相匹配的刚度比值系数取值范围,并分析了利用有限元单元和无限元单元建立的耦合数值模型数值解的准确性,进而利用此数值模型可以求得复杂受力下所关心区域的静力特征；通过与用ansys建立的有限元模型数值解作对比,验证了利用有限元单元和无限元单元建立的耦合数值分析模型的准确性和高效性。其次,利用衰减无限元单元和有限元单元建立弹性二维无限域动力数值分析模型,基于对火车行驶于铁轨的实际工程背景,本文利用平面应变单元处理弹性半空间无限域的建模问题,即建立了以平面应变单元为基础的二维动力分析数值模型。求得了不计波数的衰减无限元单元刚度矩阵和单元质量矩阵；修改了幅值衰减系数取值；研究了简谐荷载作用下所建二维数值模型的数值结果,并与ansys建立的有限元模型进行比较,验证了利用衰减无限元模拟无限元边界条件的有效性,为三维模型的建立和火车荷载的进一步精确模拟奠定了基础。更多还原

【Abstract】 The urban rail transit and high speed railway have developed rapidly in recent years, and the environmental vibration caused by them gets many experts and research schloars’attention. According to the current studies, the soil vibration magnitudes induced by moving trains are so small that it is possible to treat the soil as elastic body in the aspect of solving the soil vibration problems. The elastic semi-infinite space’s numerical model has been created in the paper with the dynamic and static features researched.Firstly, the numerical modal with a controllable parameter is created using mapping infinite elements and finite elements. The shape fuction which is suitable for making the explicit expressions of element stiffness matrix is proposed. Compared with the theoretical solutions in point load, the stiffness ratio coefficient suiting for the inside finite elements is got which can be used to get the concerned semi-infinte space’s numerical results in complex load and it also can be used to proved the simulations’ precision. Compared with the finite element model’s numerical solutions, the simulations’high efficiency and precision are proved.Secondly, using the decay infinite elements and finite elements the elstic2-D infinte area numerical simulation is proposed to research the dynamic characteristics. Base on the engineering back ground of trains moving on tracks, a2-D elstic infinite space dynamic model is proposed with plane starin elements. The stiffness matrix and mass matrix of the decay elements are proposed without considering the wave number. It has changed the amplitude attenuation coefficient. The elastic semi-infinite space’s dynamic characteristics are researched under harmonic load, and the effectiveness about using the decay infinite is got throught the compare between the coupling model solution and the finite model solution, which lay a solid foundation for the three-dimensional model and train load’s accurate simulation.更多还原