基于六节点三角形单元优化虚单元法
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摘要
选取六节点三角形单元优化了虚单元法,弥补了三节点单元求解的自由面是折线的不足,同时解决了等参四边形单元难以寻找节点移动路径的问题.此外,在计算程序中引入节点相关次数矩阵,实现了对虚单元法的进一步优化,提高了计算效率和计算精度.与等效渗透系数法计算结果分别同电模拟试验解比较表明,本文方法在大网格单元划分下仍能得到准确且连续光滑的自由面曲线,计算精度没有因单元数量的减少而降低;在相同的精度条件下,计算效率较三节点单元提高.
Six-node triangular element is selected to optimize imaginary element method in this paper.It can not only make up for the shortcoming of polygonal line free surface as shown in the three-node triangular element approach,but also solve the problem that the moving path is difficult to seek in the equal parameter quadrilateral element approach.In addition,the node correlation-time-matrix is introduced to achieve the further optimization,which improves the efficiency and precision.A comparison with equivalent permeability coefficient method and electrical simulation test shows that even with large mesh division,the optimized method still obtains accurate,continuous and smooth free surface curve without losing calculating precision while reducing element number.Also,the optimized method has higher calculating efficiency than the three-node triangular element in the same accuracy.
Six-node triangular element is selected to optimize imaginary element method in this paper.It can not only make up for the shortcoming of polygonal line free surface as shown in the three-node triangular element approach,but also solve the problem that the moving path is difficult to seek in the equal parameter quadrilateral element approach.In addition,the node correlation-time-matrix is introduced to achieve the further optimization,which improves the efficiency and precision.A comparison with equivalent permeability coefficient method and electrical simulation test shows that even with large mesh division,the optimized method still obtains accurate,continuous and smooth free surface curve without losing calculating precision while reducing element number.Also,the optimized method has higher calculating efficiency than the three-node triangular element in the same accuracy.
引文
[1]毛昶熙,段祥宝,李祖贻,等.渗流数值计算与程序应用[M].南京:河海大学出版社,1999.
[2]ZIENKIEWIEZ 0 C,TAYLOR R L.The Finite Element Method[M].New York:Mcgraw-Hill,1991.
[3]李杰,严俊,蔡红,等.平原水库库区三维渗流分析方法及渗控措施研究[J].水力发电,2016,42(2):33-37.
[4]潘树来,王全凤,俞缙.利用初流量法分析有自由面渗流问题之改进[J].岩土工程学报,2012,34(2):202-209.
[5]朱军,刘光廷.改进的单元渗透矩阵调整法求解无压渗流场[J].水利学报,2001,8:49-52.
[6]陈昌禄,潘文彦,王晓章.求解渗流自由面的变单元法[J].岩土工程技术,2005,19(4),166-169.
[7]付延玲,周志芳,武永霞.改进复合单元渗透矩阵调整法求解自由面三维渗流场[J].岩土工程学报,2009,31(9):1434-1439.
[8]张巍,肖明.有自由面渗流分析的丢单元法的改进及其在地下工程中的应用[J].水利与建筑工程学报,2005,3(1):32-36.
[9]王均星,吴雅峰,白呈富.有自由面渗流分析的流行单元法[J].水电能源科学,2003,21(4):23-26.
[10]李连侠,廖华胜,刘达,等.渗流计算中求解自由面的自由面适应网格方法[J].四川大学学报(工程科学版),2006,38(5):76-81.
[11]RAFIEZADEH K,ATAIE-ASHTIANI B.Transient Free-surface seepage in three-dimensional general anisotropic media by BEM[J].Engineering Analysis with Boundary Elements,2014,46,51-66.
[12]吴梦喜,张雪勤.有自由面渗流分析的虚单元法[J].水利学报,1994,8:64-71.
[13]YU Xinjie,LI Zhenliu.Application of NEM in seepage analysis with A free surface[J].Mathematics and Computers in Simulation,2013,89:23-37.
[14]关明芳,陈洪凯.渗流自由面求解方法综述[J].重庆交通学院学报,2005,24(5):68-73.
[15]蒋胜银,李连侠,廖华胜,等.渗流自由面数值模拟方法比较[J].长江科学院院报,2011,28(7):37-42.
[16]张宜虎.采用等效渗透系数法搜索渗流自由面[J].工程地质学报,2004,12(02):187-192.
[2]ZIENKIEWIEZ 0 C,TAYLOR R L.The Finite Element Method[M].New York:Mcgraw-Hill,1991.
[3]李杰,严俊,蔡红,等.平原水库库区三维渗流分析方法及渗控措施研究[J].水力发电,2016,42(2):33-37.
[4]潘树来,王全凤,俞缙.利用初流量法分析有自由面渗流问题之改进[J].岩土工程学报,2012,34(2):202-209.
[5]朱军,刘光廷.改进的单元渗透矩阵调整法求解无压渗流场[J].水利学报,2001,8:49-52.
[6]陈昌禄,潘文彦,王晓章.求解渗流自由面的变单元法[J].岩土工程技术,2005,19(4),166-169.
[7]付延玲,周志芳,武永霞.改进复合单元渗透矩阵调整法求解自由面三维渗流场[J].岩土工程学报,2009,31(9):1434-1439.
[8]张巍,肖明.有自由面渗流分析的丢单元法的改进及其在地下工程中的应用[J].水利与建筑工程学报,2005,3(1):32-36.
[9]王均星,吴雅峰,白呈富.有自由面渗流分析的流行单元法[J].水电能源科学,2003,21(4):23-26.
[10]李连侠,廖华胜,刘达,等.渗流计算中求解自由面的自由面适应网格方法[J].四川大学学报(工程科学版),2006,38(5):76-81.
[11]RAFIEZADEH K,ATAIE-ASHTIANI B.Transient Free-surface seepage in three-dimensional general anisotropic media by BEM[J].Engineering Analysis with Boundary Elements,2014,46,51-66.
[12]吴梦喜,张雪勤.有自由面渗流分析的虚单元法[J].水利学报,1994,8:64-71.
[13]YU Xinjie,LI Zhenliu.Application of NEM in seepage analysis with A free surface[J].Mathematics and Computers in Simulation,2013,89:23-37.
[14]关明芳,陈洪凯.渗流自由面求解方法综述[J].重庆交通学院学报,2005,24(5):68-73.
[15]蒋胜银,李连侠,廖华胜,等.渗流自由面数值模拟方法比较[J].长江科学院院报,2011,28(7):37-42.
[16]张宜虎.采用等效渗透系数法搜索渗流自由面[J].工程地质学报,2004,12(02):187-192.