渗流转角奇异问题的数值流形单元法

发布时间：2018-06-27 04:00

  本文选题：数值分析 + 数值流形法　； 参考：《岩石力学与工程学报》2017年S2期

【摘要】：在水利工程中的渗流计算中,大量存在着转角奇异性问题。一般有限元方法需要构建特殊的奇异形函数和单元属性来处理,存在不便利性,而且广泛使用的等参单元又忽视了奇异性问题。运用数值流形方法,提出了采用构造局部特殊片的方法来解决该奇异性问题。首先,将转角奇异的解析解构建为一个基函数,与常数项基函数一起形成奇异片覆盖函数,在奇异点影响到的星点上采用奇异片覆盖函数,其他星点采用常数片覆盖函数进行求解,计算结果逼近真解,并能很好地反映转角中的强奇异性。其次,给出这类问题的流形元离散列式,将经典正三角形流形元改进为正四边形,并介绍程序的编制步骤,和该特殊物理片的施加方法。再次,3个工程算例分别为坝基不透水帷幕有压渗流解析解对比、经典流速跌落试验对比以及堰下板桩有压渗流与已有计算流网对比,算例表明了该方法的有效性和正确性,为进一步分析奇异性对结构和复杂工程的影响打下基础。该方法也适用于其他基于单位分解插值的数值分析方法,也为其他场变量连续而偏导数不连续问题提供了思路。
[Abstract]:In the seepage calculation of hydraulic engineering, there are many problems of angle singularity. The general finite element method needs to construct special singular shape function and element attribute to deal with it, which is not convenient, and the widely used isoparametric element ignores the singularity problem. Using the numerical manifold method, the method of constructing local special plates is proposed to solve the singularity problem. First of all, the analytic solution of angular singularity is constructed as a basis function, and the singular sheet covering function is formed together with the constant term basis function, and the singular slice covering function is used on the star affected by the singular point. The other star points are solved by the constant sheet covering function, and the results approach the true solution, and can well reflect the strong singularity in the rotation angle. Secondly, the manifold element discrete formulation of this kind of problem is given. The classical regular triangle manifold element is improved to a regular quadrilateral, and the programming steps and the application method of the special physical slice are introduced. Thirdly, the three engineering examples are the comparison of the analytical solutions of the impervious curtain pressure seepage, the classical velocity drop test, and the pressure seepage under the Weir and the existing flow net. The results show the validity and correctness of the method. It lays a foundation for further analysis of the influence of singularity on structure and complex engineering. This method is also suitable for other numerical analysis methods based on unit decomposition and interpolation, and also provides a way for other field variables to be continuous and partial derivative discontinuous.
【作者单位】： 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室;中国科学院大学;北京工业大学建筑工程学院;
【基金】：国家自然科学基金资助项目(11572009,51538001) 国家重点基础研究发展计划(973)项目(2014CB047100)~~
【分类号】：TV139.1
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本文编号：2072582