Transient infinite elements for seepage problems in infinite media
Transient infinite elements for seepage problems in infinite media
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DOI：
10.1002/nag.1610170504
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发表时间：
1993-05
影响因子：
4
通讯作者：
Chong-bin Zhao;S. Valliappan
中科院分区：
文献类型：
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作者：
Chong-bin Zhao;S. Valliappan
本文提出了一种可用于模拟无限介质中瞬态渗流问题的时变无限元。详细推导了单元的水头分布函数，并建立了单元的性能矩阵。由于在构造单元水头分布函数的过程中同时使用了空间和时间变量，因此目前的无限大单元可称为瞬态单元。利用现有的无限单元来模拟系统的远场，可以严格地模拟无限介质中瞬态渗流问题的机理，因为单元的性质矩阵可以在分析中任何感兴趣的时刻求值。由于可以为无限大元素的性质矩阵编写显式表达式，因此它们可以很容易地求值，这可以通过在计算机程序中编写简单的子程序来实现。为了检验现有无限单元的准确性和效率，分别用有限单元和无限单元技术求解了半无限介质中的一维瞬态渗流问题和全平面中的二维瞬态渗流问题。结果表明，本文提出的无限元对于无限介质中瞬态渗流问题的数值模拟是非常有用的。
In this paper, a time-dependent infinite element which can be used to simulate transient seepage problems in infinite media is presented. The hydraulic head distribution function of the element has been derived in detail and the property matrices of the element have been well formulated. Since both space and time variables are used in the course of constructing the hydraulic head distribution function of the element, the present infinite element can be referred to as a transient one. Using the present infinite element to model the far field of a system, the mechanism of transient seepage problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis. Since explicit expressions can be written for the property matrices of the infinite element, they may be evaluated quite easily and this can be carried out by writing a simple subroutine in a computer program. In order to examine the accuracy and efficiency of the present infinite element, both a one-dimensional (ID) transient seepage problem in a semi-infinite medium and a 2D transient seepage problem in a full plane have been solved using the finite and infinite element technique. It has been demonstrated that the present infinite element is very useful for the numerical simulation of transient seepage problems in infinite media.