EI、Scopus 收录
中文核心期刊
Gao Xiaowei, Hu Jinxiu, Cui Miao. A MDBEM BASED ON ROW ELIMINATION-BACK-SUBSTITUTION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 361-368. DOI: 10.6052/0459-1879-2012-2-20120220
Citation: Gao Xiaowei, Hu Jinxiu, Cui Miao. A MDBEM BASED ON ROW ELIMINATION-BACK-SUBSTITUTION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 361-368. DOI: 10.6052/0459-1879-2012-2-20120220

A MDBEM BASED ON ROW ELIMINATION-BACK-SUBSTITUTION METHOD

Funds: The project was supported by the National Natural Science Foundation of China(10872050)and the Fundamental Research Funds for Centred Universities (DUT11ZD(G)01).
  • Received Date: March 31, 2011
  • Revised Date: May 28, 2011
  • A novel multi-domain boundary element method (MDBEM) analysis technique is presented to solve large-scale engineering problems. Firstly, the basic integral equations of each domain formulated in terms of internal, boundary and interface nodal variables are reduced to the algebraic equations in terms of interface nodal variables only by the three-step variable condensing technique. Then, a sparse system of equations formulated in terms of interface nodal quantities is assembled using the equilibrium equation and consistence condition at interface nodes. To solve the system of equations efficiently, this paper, for the first time, introduces a robust linear equation solution method, called the row elimination-back-substitution method (REBSM), to solve the non-symmetric sparse system of equations. REBSM performs both the elimination and back-substitution procedures when each row of the system is formed. When the last row is finished for assembling, the solutions of the system are obtained at the same time, without the need of the last back-substitution procedure. Since some repeated terms are incorporated, REBSM needs less storage than the Gaussian elimination method, has an improvement in computational speed by orders of magnitude, and provide BEM a robust equation solver for solving large engineering problems.
  • 1 Brebbia CA, Dominguez J. Boundary Elements: An Introductory Course. London: McGraw-Hill Book Co, 1992
    2 牛忠荣, 王秀喜, 周焕林. 三维边界元法中几乎奇异积分的正则化算法. 力学学报, 2004, 36(1): 49-56 (Niu Zhongrong, Wang Xiuxi, Zhou Huanlin. A regularization algorithm for nearly singular integral in 3D BEM. Acta Mechanica Sinica, 2004, 36(1): 49-56 (in Chinese))
    3 Gao XW, Davies TG. Boundary Element Programming in Mechanics. London: Cambridge University Press, 2002
    4 柴军瑞, 仵彦卿. 采用边界元法确定渗流自由面的一种改进方法. 陕西水力发电, 2000, 16(1): 11-13 (Chai Junrui, Wu Yanqing. A modified iterative approach for solving seepage free surface by BEM. Journal of Shanxi Water Power, 2000, 16(1): 11-13 (in Chinese))
    5 王燕昌, 郑静, 高效伟. 径向积分边界元法确定非均质土石坝渗流自由面. 计算力学学报, 2010, 27(6): 1011-1015 (Wang Yanchang, Zheng Jing, Gao Xiaowei. Radial integration boundary element method determining seepage free surface of non-homogeneous soil-stone dams. Chinese Journal of Computational Mechanics, 2010, 27(6): 1011-1015 (in Chinese))
    6王静, 高效伟. 基于单元子分法的结构多尺度边界单元法. 计算力学学报,2010, 27(2): 258-263 (Wang Jing, Gao Xiaowei. Structural multi-scale boundary element method based on element subdivision technique. Chinese Journal of Computational Mechanics, 2010, 27(2): 258-263 (in Chinese))
    7 秦飞, 岑章志, 杜庆华. 多裂纹扩展分析的边界元方法. 固体力学学报, 2002, 23 (4): 431-438 (Qin Fei, Cen Zhangzhi, Du Qinghua. Boundary element analysis of cracked bodies. Acta Mechanica Solida Sinica, 2002, 23 (4): 431-438 (in Chinese))
    8 Zhang CZ, Cui M, Wang J, et al. 3 D crack analysis in functionally graded materials. Engineering Fracture Mechanics, 2011, 78: 585-604   
    9 姚振汉, 刘永健. 三维弹性接触问题边界元法的一种误差直接估计. 燕山大学学报, 2004, 28(2): 95-98 (Yao Zhenhan, Liu Yongjian. A direct error estimation of BEM for 3D elastic contact problem. Journal of Yanshan University, 2004, 28(2): 95-98 (in Chinese))
    10 Wu TW. Boundary Element Acoustics: Fundamentals and Computer Codes. Southampton: Wit Pr/Computational Mechanics, 2001
    11 张有天, 王镭, 陈平. 边界元方法及其在工程中的应用. 北京:水利电力出版社, 1989 (Zhang Youtian, Wang Lei, Chen Ping. Boundary Element Method and It's Application in Engineering. Beijing: Water Conservancy and Electric Power Press, 1989 (in Chinese))   
    12 Kane JH, Kashava Kumar BL, Saigal S. An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis. Comput Meth Appl Mech Eng, 1990, 79: 219-244   
    13 Gao XW, Guo L, Zhang CZ, Three-step multi-domain BEM solver for nonhomogeneous material problems. Engineering Analysis with Boundary Elements, 2007, 31: 965-973
    14 高效伟, 杨恺. 功能梯度材料结构的热应力边界元分析. 力学学报, 2011, 43(1): 1-8 (Gao Xiaowei, Yang Kai. Thermal stress analysis of functionally graded material structures using boundary element method. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 1-8 (in Chinese))
    15 Strang G. Introduction to Linear Algebra. 3rd edn. Wellesley, Massachusetts: Wellesley-Cambridge Press, 2003. 74-76
    16 Saad Y. Iterative Methods for Sparse Linear Systems. SIAM, 2nd edn, 2003
    17 Gao XW. Source point isolation boundary element method for solving general anisotropic potential and elastic problems with varying material properties. Engineering Analysis with Boundary Elements, 2010, 34: 1049-1057   
    18 Gao XW. A boundary element method without internal cells for two-dimensional and three-dimensional elastoplastic problems. ASME Journal of Applied Mechanics, 2002, 69: 154-160   
    19 Press WH, Teukolsky SA, Vetterling WT, et al. Numerical Recipes in Fortran 77, 2nd edn. Cambridge: Cambridge University Press, 1992  
  • Related Articles

    [1]Yu Jiangfei, Zhou Zixuan, Peng Jiangpeng, Tang Tao, Yang Wangfeng, Yang Yixin, Wang Hongbo. OPTIMIZATION DESIGN OF COMBUSTION CHAMBER CONFIGURATION PARAMETERS FOR SCRAMJET ENGINES BASED ON SURROGATE MODELS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(11): 3359-3370. DOI: 10.6052/0459-1879-24-297
    [2]Zhang Jiangtao, Tan Yuanqiang, Ji Caiyuan, Xiao Xiangwu, Jiang Shengqiang. RESEARCH ON THE EFFECTS OF ROLLER-SPREADING PARAMETERS FOR NYLON POWDER SPREADABILITY IN ADDITIVE MANUFACTURING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2416-2426. DOI: 10.6052/0459-1879-21-240
    [3]Dai Han, Zhao Yanying. EQUAL-PEAK OPTIMIZATION OF DYNAMIC VIBRATION ABSORBER WITH NEGATIVE STIFFNESS AND DELAY FEEDBACK CONTROL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1720-1732. DOI: 10.6052/0459-1879-21-074
    [4]Sui Peng, Shen Yongjun, Yang Shaopu. PARAMETERS OPTIMIZATION OF A DYNAMIC VIBRATION ABSORBER WITH INERTER AND GROUNDED STIFFNESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1412-1422. DOI: 10.6052/0459-1879-21-058
    [5]Wu Mengzhen, Liu Yang, Xu Xianghong. SENSITIVITY ANALYSIS AND OPTIMIZATION ON PARAMETERS OF HIGH SPEEDPANTOGRAPH-CATENARY SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 75-83. DOI: 10.6052/0459-1879-20-207
    [6]Xing Zikang, Shen Yongjun, Li Xianghong. PERFORMANCE ANALYSIS OF GROUNDED THREE-ELEMENT DYNAMIC VIBRATION ABSORBER[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1466-1475. DOI: 10.6052/0459-1879-19-154
    [7]Zhaoyang Xing, Yongjun Shen, Haijun Xing, Shaopu Yang. PARAMETERS OPTIMIZATION OF A DYNAMIC VIBRATION ABSORBER WITH AMPLIFYING MECHANISM AND NEGATIVE STIFFNESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 894-903. DOI: 10.6052/0459-1879-18-375
    [8]Zhang Zhen, Li Jiachun. NEW SOURCE/SINK MODEL, FLOW SIMULATION AND PARAMETER OPTIMIZATION OF THE REGENERATOR FOR HIGH FREQUENCY PULSE TUBE REFRIGERATOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 421-430. DOI: 10.6052/0459-1879-16-287
    [9]Wu Zheng, Guo Mingmin, Xu Qian. STUDY ON OPTIMIZATION OF TRAFFIC FLOW VELOCITY-DENSITY MODELS FOR URBAN FREEWAY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, (4): 709-717. DOI: 10.6052/0459-1879-11-377
    [10]Weihong Zhang, Gaoming Dai, Fengwen Wang, Shiping Sun, Hicham Bassir. Topology optimization of material microstructures using strain energy-based prediction of effective elastic properties[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 77-89. DOI: 10.6052/0459-1879-2007-1-2006-086

Catalog

    Article Metrics

    Article views (1555) PDF downloads (804) Cited by()
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return