A Novel Virtual Node Method for Polygonal Elements

TANG Xu-hai; WU Sheng-chuan; ZHENG Chao; ZHANG Jian-hai

doi:10.3879/j.issn.1000-0887.2009.10.003

Volume 30 Issue 10

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TANG Xu-hai, WU Sheng-chuan, ZHENG Chao, ZHANG Jian-hai. A Novel Virtual Node Method for Polygonal Elements[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1153-1164. doi: 10.3879/j.issn.1000-0887.2009.10.003

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A Novel Virtual Node Method for Polygonal Elements

doi: 10.3879/j.issn.1000-0887.2009.10.003

1.
State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China;

Received Date: 2008-12-22
Rev Recd Date: 2009-09-03
Publish Date: 2009-10-15

Abstract

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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References(18)

References

[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