渗流转角奇异问题的数值流形单元法

doi:10.13722/j.cnki.jrme.2017.0057

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Abstract

In seepage calculation of hydraulic engineering，there are a large number of singularity problems at turning point. It is inconvenience that the general finite element method needs to construct special singularity shape function and element property to deal with the singularity problem，which used to be ignored when the isoparametric element was widely used. In this paper，a new method by constructing a local special patch is proposed to solve this singularity problem by using numerical manifold method. Firstly，the singularity covering function is formed together by the constant term basis function and a new basis function constructed by the analytic solution at turning point. The singularity covering function is used on the star points affected by the singularity point，at the same time，the constant patch covering function is used on the other star points，and the calculation result approximates the real solution and can well reflect the strong singularity in the corner. Secondly，the discrete formula of the numerical manifold method about this kind of problem is given，and the classical regular triangle of manifold element is improved to square，as well as，the procedure of the program and the application method of the special physical patch are introduced. Thirdly，three engineering examples are

respectively confined seepage of dam foundation with impervious curtain contrast with the analystic solution，the comparison of the classical flow velocity drop test，and the confined seepage of weir with sheet pile compared with flow net which had been calculated，those show the effectiveness and correctness of the method，and provide a basis for further analysis of the effects of singularity on the structure and complex engineering. Finally，The proposed method is also applicable to other numerical analysis methods based on the partition of unity method of interpolation，and also provides an approach for those problems with continuous field and discontinuous partial derivatives.

Key words： numerical analysis numerical manifold method seepage turning point singularity

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	Articles by authors
	FENG Qiang1
	2
	ZHENG Hong1
	2
	3

Cite this article:

FENG Qiang1,2,ZHENG Hong1, et al. Turning point singularity problem in seepage by numerical manifold method[J]. , 2017, 36(S2): 3892-3901.

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https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2017.0057 OR https://rockmech.whrsm.ac.cn/EN/Y2017/V36/IS2/3892

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