部分重叠覆盖的数值流形法是一种以独立覆盖为主的分析方式。为了在常规尺寸单元的数学网格中自动选取独立覆盖区域,应用图的着色方法将数学网格的单元分为若干个独立集。在此基础上,以独立覆盖区域最多为原则,选择用于定义独立覆盖的单元(其所有结点覆盖合并为一个覆盖),其余单元作为重叠区域以保持连续性,不属于独立覆盖单元的结点作为常规的结点覆盖。通过算例,揭示了重叠覆盖间的线性相关仅存在于数学网格边界上的结点覆盖,覆盖合并可以减少整体刚度矩阵零特征值的数目,甚至完全避免线性相关。
Abstract
Numerical manifold method with partially overlapping covers is an analysis mode mainly concerning independent covers. To automatically select independent cover regions in a mathematical mesh with general element size, the elements of the mathematical mesh are partitioned into a number of independent sets by graph colouring. Based on this, the elements for defining independent covers (i.e. the covers of all nodes of an element are merged into single one) are selected according to the principle of as many regions with independent covers as possible, and the rest of elements is defined as the overlapping cover regions for keeping the continuity, and the nodes which do not belong to the independent cover elements are defined as general nodal covers. Examples reveal that the linear dependencies between the overlapping covers exist only in the nodal covers on the mathematical mesh boundary, and cover merging could reduce the nullity of stiffness matrix or even avoid the linear dependencies.
关键词
数值流形法 /
广义有限元法 /
独立覆盖 /
自动选择 /
图着色 /
线性相关
Key words
numerical manifold method /
generalized finite element method /
independent covers /
automatic selection /
graph colouring /
linear dependencies
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1]石根华.数值流形方法与非连续变形分析[M]. 裴觉民译.北京: 清华大学出版社, 1997. (SHI Gen-hua. Numerical Manifold Method and Discontinuous Deformation Analysis [M].Translated by PEI Jue-ming. Beijing: Tsinghua University Press, 1997. (in Chinese))
[2] 祁勇峰,苏海东,崔建华. 部分重叠覆盖的数值流形方法初步研究[J]. raybet体育在线
院报,2013,30(1): 65-70. (QI Yong-feng, SU Hai-dong, CUI Jian-hua. Preliminary Study on Numerical Manifold Method with Partially Overlapping Covers[J]. Journal of Yangtze River Scientific Research Institute, 2013,30(1): 65-70.(in Chinese))
[3] 苏海东,祁勇峰. 部分重叠覆盖流形法的覆盖加密方法[J]. raybet体育在线
院报,2013,30(7): 95-100. (SU Hai-dong, QI Yong-feng. Cover Refinement for Numerical Manifold Method with Partially Overlapping Covers [J]. Journal of Yangtze River Scientific Research Institute, 2013,30(7): 95-100.(in Chinese))
[4] STROUBOULIS T,BABUSKKA I,COPPS K.The Design and Analysis of the Generalized Finite Element Method[J]. Computer Methods in Applied Mechanics and Engineering,2000,181(1-3):43-69.
[5] 李录贤,刘书静,张慧华,等. 广义有限元方法研究进展[J]. 应用力学学报,2009,26(1): 96-108. (LI Lu-xian, LIU Shu-jing, ZHANG Hui-hua, et al. Research Advances in Generalized Finite Element Method [J]. Chinese Journal of Applied Mechanics, 2009,26(1): 96-108. (in Chinese))
[6] 刘 欣,朱德懋. 基于单位分解的新型有限元方法研究[J]. 计算力学学报,2000,17(4):422-427.(LIU Xin, ZHU De-mao. Study on Partition of Unit FEM[J]. Chinese Journal of Computational Mechanics, 2000,17(4):422-427.(in Chinese))
[7] 林绍忠,祁勇峰,苏海东. 数值流形法中覆盖函数的改进形式及其应用[J]. raybet体育在线
院报,2006,23(6):55-58.(LIN Shao-zhong, QI Yong-feng, SU Hai-dong. Improved Local Cover Function of Numerical Manifold Method and its Application[J]. Journal of Yangtze River Scientific Research Institute, 2006,23(6):55-58. (in Chinese))
PDF(1029 KB)
