基于虚节点的多边形有限元法

唐旭海; 吴圣川; 郑超; 张建海

doi:10.3879/j.issn.1000-0887.2009.10.003

基于虚节点的多边形有限元法

doi: 10.3879/j.issn.1000-0887.2009.10.003

四川大学水力学与山区河流开发保护国家重点实验室,成都 610065; 2.合肥工业大学材料学院先进材料连接与计算中心,合肥 230009; 3.新加坡国立大学机械工程系工程科学计算研究中心,117576,新加坡

详细信息

作者简介:
唐旭海(1984- ),男,成都人,博士生(联系人.E-mail:X.H.Tang84@gmail.com).

中图分类号: O34
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- 被引次数: 0
出版历程
- 收稿日期: 2008-12-22
- 修回日期: 2009-09-03
- 刊出日期: 2009-10-15

A Novel Virtual Node Method for Polygonal Elements

State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China;

摘要

摘要: 虚节点法是一种新的基于单位分解理论的多边形有限元法．将虚节点法应用于求解弹性力学问题，并且通过大量数值实验测试虚节点法的计算效果．因为虚节点法具有多项式形式，所以有效地降低了传统多边形有限元法的积分误差．数值实验证明，在分片实验中虚节点法能得到比包括Wachspress法和mean value法在内的传统多边形有限元法更精确的数值结果．在收敛性试验中，虚节点法在相同节点数的条件下能取得比三角形一次单元更精确的数值结果．因为虚节点法能适应任意边数的多边形单元，所以对网格具有很强的适应性，在几何条件复杂、网格生成困难的问题中具有良好的应用价值．为了展示虚节点法潜在的应用价值，用虚节点法求解断裂力学应力强度因子和模拟裂纹扩展．同时，基于多边形单元的网格重划分技术和网格加密技术也应用于求解断裂力学应力强度因子和模拟裂纹扩展
- 虚节点法 /
- 多边形单元 /
- 单位分解法 /
- 裂纹扩展
Abstract: A novel polygonal finite element method (PFEM), which is based on partition of unity, was proposed and named as virtual node method (VNM). To test the perform ance of present method, intensive numerical examples were carried out for solid mechanic problems. With polynomial form, virtual node method achieves better results than that of traditional PFEM, including Wachspress method and mean value method in standard patch test Compared with standard triangular FEM, virtual node method can achieve better accuracy. With the ability to construct shape function on polygonal elements, virtual node method provides greater flexibility in mesh generation. Therefore, several fracture problems were studied to demonstrate poten tialim plemen tation. With the advantage of virtual node method, convenien trefinement and remeshing strategy are applied.
- virtual node method /
- polygonal finite elemen tmethod /
- partition of unity /
- crack propagation

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参考文献(18)

[1]	Wachspress E L. A Rational Finite Element Basis[M]. New York: Academic Press, 1975.
[2]	Tabarraei A,Sukumar N. Adaptive computations on conforming quadtree meshes[J]. Finite Elements in Analysis and Design, 2005, 41(7/8): 686-702. doi: 10.1016/j.finel.2004.08.002
[3]	Sukumar N, Malsch E A. Recent advances in the construction of polygonal finite element interpolants[J]. Archives of Computational Methods in Engineering, 2006,13(1): 129-163. doi: 10.1007/BF02905933
[4]	Floater M S. Mean value coordinates[J]. Computer Aided Geometric Design, 2003, 20(1): 19-27. doi: 10.1016/S0167-8396(03)00002-5
[5]	Melenk J M, Babuska I. The partition of unity finite element method: basic theory and applications[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1/4): 289-314. doi: 10.1016/S0045-7825(96)01087-0
[6]	Rajendran S, Zhang B R.A “FE-meshfree”QUAD4 element based on partition of unity[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 197(1/4): 128-147. doi: 10.1016/j.cma.2007.07.010
[7]	Liu G R, Gu Y T. A point interpolation method for two dimensional solid[J]. International Journal for Numerical Methods in Engineering, 2001, 50(4): 937-951. doi: 10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X
[8]	Zheng C,Tang X H, Zhang J H, et al. A novel mesh-free poly-cell Galerkin method[J]. Acta Mechanica Sinica, 2009,25(4): 517-527. doi: 10.1007/s10409-009-0239-5
[9]	Zheng C, Wu S C, Tang X H, et al. A meshfree poly-cell Galerkin (MPG) approach for problems of elasticity and fracture[J]. Computer Modelling in Engineering & Sciences, 2008, 38(2): 149-178.
[10]	Strang G, Fix G. An Analysis of the Finite Element Method[M]. Engle-wood Cliffs, New Jersey: Prentice-Hall, 1973.
[11]	Zienkiewicz O C, Taylor R L. The Finite Element Method[M]. 5th Ed. Oxford, UK: Butterworth Heinemann, 2000.
[12]	Mark S Shephard, Marcel K Georges. Automatic three-dimensional mesh generation by the finite octree technique[J]. International Journal for Numerical Methods in Engineering, 1991, 32(4): 709-749. doi: 10.1002/nme.1620320406
[13]	Timoshenko S P, Goodier J N. Theory of Elasticity[M]. 3rd Ed. New York: McGraw, 1970.
[14]	Roark R J, Young W C. Formulas for Stress and Strain[M]. New York: McGraw, 1975.
[15]	Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601-620. doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
[16]	Moes N, Dolbow J, Belyschko T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Method in Engineering, 1999, 46 (1): 131-150. doi: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[17]	Aliabadi M H, Rooke D P, Cartwright D J. Mixed-mode Bueckner weight functions using boundary element analysis[J]. International Journal of Fracture, 1987, 34(2): 131-147. doi: 10.1007/BF00019768
[18]	Bouchard P O, Bay F, Chastel Y, et al. Crack propagation modeling using an advanced remeshing technique[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 189(3): 723-742 doi: 10.1016/S0045-7825(99)00324-2