【作者】 刘清华；

【导师】 赵成刚；

【作者基本信息】 北京交通大学 ， 防灾减灾工程与防护工程， 2009， 硕士

【摘要】 在高层、高坝和核电站等重大复杂结构的动力反应分析中,波动能量向无限域地基的逸散影响是重要的。饱和多孔介质在自然界中普遍存在,如饱和土,它是由固体骨架和孔隙流体组成。当两者之间存在动力相互作用时,按饱和多孔介质分析比按单相固体介质分析更为科学、合理。由于饱和介质波动理论的复杂性及数学处理上的困难,有关饱和多孔介质动力响应研究的解析解仅局限于比较简单的边界情况。对于几何形状较复杂且存在近域介质非均匀和非线性的复杂情况,数值方法是有效的分析手段。在无限或半无限空间的饱和多孔介质动力有限元分析中,通常采用有限模型的数值方法进行分析。为反映无约束域能量辐射效应影响,需引入虚拟的人工边界条件。虚拟人工边界的处理方式和方法对模拟精度的影响较大。显式有限元结合局部人工边界的方法由于其时空解耦的特点,很适宜于上述复杂的近场波动问题的求解,获得学术界和工程界的重视。本文主要完成了以下工作:1.建立了饱和多孔介质的三维粘弹性人工边界以外行的球面波为研究对象,分析人工边界应力,得到应力的表达式,固相介质在人工边界的法向应力与其在边界处的位移和速度分别成线性关系,固相介质在边界的切向应力也与其切向位移和速度成线性关系;本文假设孔隙流体无粘性,不承受剪力,只在人工边界的法向存在应力,其只与流体的法向速度成正比。因此,对固相介质,可以在人工边界的法向、切向设置连续分布的弹簧和粘滞阻尼器;对孔隙流体,只在人工边界的法向设置连续分布的粘滞阻尼器。地震波输入可以通过在人工边界上施加等效荷载来实现。2.本文基于赵成刚教授的饱和多孔介质二维显式示有限元数值计算方法,建立了该理论的三维方法,并开发了实现该方法三维问题的有限元程序(PT-DEA)。数值模拟算例表明本文提出的饱和多孔介质三维粘弹性动力人工边界具有很好的精度和稳定性。本文边界与解析解、扩展有限元结果很接近,精度高于现有粘性边界、一、二阶透射边界。饱和多孔介质简谐动载动力响应分析表明,显式有限元结合粘弹性人工边界的解耦时域波动分析方法是有效的近场波动模拟方法。更多还原

【Abstract】 For the dynamic analysis of some important complex structures such as high-rise, high dam, nuclear power station and so on, the wave propagation from structure into infinite foundation should be considered.The saturated porous media is general existed in the nature, for example, the saturated soil, which is made up of solid skeleton and pore liquid fluid medium. If the dynamic interacting between the previous two part is concerned, using the saturated soil theory analyzing is more appropriate and scientific than using the single medium analyzing. As the complex of the saturated porous media theory and the difficulties of the disposing in mathematics, the analytic solution of saturated porous medium dynamic response is topical the simple boundary condition. To the complex geometry and the near field heterogeneous and nonlinear condition, numerical method is the effective mean. In the dynamic finite element analysis of saturated porous media in whole space or half-space, a finite model numerical method is usually selected for computing. To reflect unrestricted region energy radiation effect, it is necessary to input the supposed artificial boundary and computing method. The artificial boundary disposing means and computing means is largely influenced the computing accuracy. As the decoupling of time and position, explicit finite element combining local artificial method is proper to the previous complex near field wave-motion problem’s solving. The main studies in this dissertation are listed as follows:1. An approximate spring-dashpot three-dimensional artificial boundary conditions of saturated porous media are presented. It is shown that the normal and tangential wave stresses of the solid phase on the boundary are proportional to displacement and velocity, and the pore fluid has only normal wave stress which is proportional to it’s velocity on the artificial boundary. Therefore, the continuously distributed springs and dashpots can be set on the artificial boundaries in the normal and tangential directions to absorb the energy of outgoing waves. The wave motion input can be realized by applying equivalent loads on the artificial boundaries.2. According to the dynamic analysis of saturated porous media by using explicit finite element method proposed by professor chenggang zhao, this paper develops finite element method which could solve the three-dimensional problems, and develops finite element programme named PT-DEA.Numerical example indicate that the proposed three-dimensional viscous-spring artificial boundary enjoy good accuracy and good stability.Numerical example indicates that the accuracy and good stability of the proposed three-dimensional viscous-spring artificial boundary correspond with that of existing analytical, extended finite element solution and the second-order transmitting boundary.The analysis of the saturated porous medium dynamic response indicates that the combination method of the explicit finite element method and the three-dimensional viscous-spring boundary is effective.更多还原