渗流问题的弱形式求积元分析

袁帅; 钟宏志

doi:10.11779/CJGE201502007

渗流问题的弱形式求积元分析 English Version

袁帅,
钟宏志

清华大学土木工程系,北京 100084

基金项目: 国家自然科学基金项目（51178247）

详细信息

作者简介:
袁帅（1984- ）,男,河北邯郸人,博士研究生,主要从事土力学数值方法的研究。E-mail: yuan_shuai@126.com。

中图分类号: TU47
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出版历程
- 收稿日期: 2014-06-13
- 发布日期: 2015-03-01

Seepage analysis using the weak form quadrature element method

Department of Civil Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 对于渗流问题的研究在很多领域有着广泛的应用,工程中通常采用有限元法对其进行数值求解,这往往需要耗费较大的计算资源从而限制了其计算规模。弱形式求积元法是一种简单和高效的数值方法,该方法基于问题弱形式描述,可对全域进行高阶近似,具有较快的收敛性,在结构分析领域已有广泛的应用。将弱形式求积元法应用于渗流问题的求解,分析了二维及三维渗流问题,包括承压渗流和无压渗流;对于无压渗流,采用变网格方法,使用积分点位置的多项式插值来近似表示自由面。求解了数值算例并得到了与解析解或者文献解一致的结果。结果表明：与有限元法相比,弱形式求积元法使用较少的自由度就可以得到收敛的结果,显示了弱形式求积元法在渗流分析中的有效性。
- 弱形式求积元法 /
- 渗流 /
- 混凝土坝 /
- 挡水板 /
- 渗流自由面
Abstract: Seepage analysis has found wide application in many areas. In practice, the conventional numerical tools such as the finite element method are mainly used in the seepage analysis, which often demand large computational resources and therefore impose restrictions on the problem scale. The weak form quadrature element method is a simple and efficient numerical tool which has been applied to structural analysis. Based on the weak form description of a problem, it has the characteristics of global approximation and enjoys rapid convergence. The method is used for simulation of two- and three-dimensional confined and unconfined seepage. For the unconfined seepage, the adaptive mesh method is employed, and the free surface is expressed by polynomial interpolation at integration points. The results are compared with those of other methods and good agreement is reached. It is shown that a relatively small number of degrees of freedom are needed to attain convergence by the quadrature element formulation as compared with those of the finite element method. The weak form quadrature element method is expected to be an effective numerical tool for seepage analysis.
- weak form quadrature element method /
- seepage /
- concrete dam /
- manger /
- free surface

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参考文献(16)

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