本文選題：數(shù)值分析 + 數(shù)值流形法��； 參考：《巖石力學(xué)與工程學(xué)報(bào)》2017年S2期

【摘要】：在水利工程中的滲流計(jì)算中,大量存在著轉(zhuǎn)角奇異性問題。一般有限元方法需要構(gòu)建特殊的奇異形函數(shù)和單元屬性來處理,存在不便利性,而且廣泛使用的等參單元又忽視了奇異性問題。運(yùn)用數(shù)值流形方法,提出了采用構(gòu)造局部特殊片的方法來解決該奇異性問題。首先,將轉(zhuǎn)角奇異的解析解構(gòu)建為一個(gè)基函數(shù),與常數(shù)項(xiàng)基函數(shù)一起形成奇異片覆蓋函數(shù),在奇異點(diǎn)影響到的星點(diǎn)上采用奇異片覆蓋函數(shù),其他星點(diǎn)采用常數(shù)片覆蓋函數(shù)進(jìn)行求解,計(jì)算結(jié)果逼近真解,并能很好地反映轉(zhuǎn)角中的強(qiáng)奇異性。其次,給出這類問題的流形元離散列式,將經(jīng)典正三角形流形元改進(jìn)為正四邊形,并介紹程序的編制步驟,和該特殊物理片的施加方法。再次,3個(gè)工程算例分別為壩基不透水帷幕有壓滲流解析解對(duì)比、經(jīng)典流速跌落試驗(yàn)對(duì)比以及堰下板樁有壓滲流與已有計(jì)算流網(wǎng)對(duì)比,算例表明了該方法的有效性和正確性,為進(jìn)一步分析奇異性對(duì)結(jié)構(gòu)和復(fù)雜工程的影響打下基礎(chǔ)。該方法也適用于其他基于單位分解插值的數(shù)值分析方法,也為其他場變量連續(xù)而偏導(dǎo)數(shù)不連續(xù)問題提供了思路。
[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.
【作者單位】： 中國科學(xué)院武漢巖土力學(xué)研究所巖土力學(xué)與工程國家重點(diǎn)實(shí)驗(yàn)室;中國科學(xué)院大學(xué);北京工業(yè)大學(xué)建筑工程學(xué)院;
【基金】：國家自然科學(xué)基金資助項(xiàng)目(11572009,51538001) 國家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃(973)項(xiàng)目(2014CB047100)~~
【分類號(hào)】：TV139.1
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本文編號(hào)：2072582