组合杂交有限元方法对等参双线性Q<sub>4</sub>-平板元的粗网格精度改进

谢小平; 周天孝

组合杂交有限元方法对等参双线性Q₄-平板元的粗网格精度改进

谢小平¹,
周天孝²

1.
四川大学数学学院, 成都 610064;
2.
中国航空计算技术研究所, 西安 710068

基金项目: 国家天元青年基金资助项目(TY10126027)

详细信息

作者简介:
谢小平(1970- ),男,四川德阳人,副教授,博士(E-mail:xiaopingxie@263.net).

中图分类号: O242.21
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- 被引次数: 0
出版历程
- 收稿日期: 2001-09-29
- 修回日期: 2003-06-20
- 刊出日期: 2003-12-15

Coarse-Mesh-Accuracy Improvement of Bilinear Q₄-Plane Element by the Combined Hybrid Finite Element Method

XIE Xiao-ping¹,
ZHOU Tian-xiao²

1.
Mathematical College, Sichuan University, Chengdu 610064, P. R. China;
2.
Aeronautical Computing Technique Research Institute, Xi'an 710068, P. R. China

摘要

摘要: 组合杂交有限元法具有增强低阶位移格式粗网格精度的内在机制.能量误差为零的组合杂交格式可获得改进的粗网络精度,而其中组合参数起着极其重要的作用.采用最简便的四边形位移\应力模式作为对协调双线性Q₄-平板元的改进:协调等参双线性位移插值和纯粹常应力模式.通过调整组合参数,得到了组合杂交元的优化型.数值试验表明这种参数＿调整型显著改进了协调Q₄-元,达到粗网格高精度.由于应力参数可在单元水平消去,这种组合杂交改进型的计算量与协调Q₄-元相当.
- 有限元 /
- 杂交方法 /
- 能量零误差 /
- 粗网格精度
Abstract: The combined hybrid finite element method is of an intrinsic mechanism of enhancing coarse-mesh-accuracy of lower order displacement schemes. It was confirmed that the combined hybrid scheme without energy error leads to enhancement of accuracy at coarse meshes, and that the combination parameter plays an important role in the enhancement. As an improvement of conforming bilinear Q₄-plane element, the combined hybrid method adopted the most convenient quadrilateral displacements-stress mode, i. e. the mode of compatible isoparametric bilinear displacements and pure constant stresses. By adjusting the combined parameter, the optimized version of the combined hybrid element was obtained and numerical tests indicated that this parameter-adjusted version behaves much better than Q₄-element and is of high accuracy at coarse meshes. Due to elimination of stress parameters at the elemental level, this combined hybrid version is of the same computational cost as that of Q₄-element.
- finite element /
- hybrid method /
- zero energy-error /
- coarse-mesh-accuracy

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参考文献(14)

[1]	ZHOU Tian-xiao.Finite element method based on combination of "saddle point" variational formulations[J].Science in China,Ser E,1997,27(1):75-87.
[2]	ZHOU Tian-xiao.Stabilized hybrid finite element methods based on combination of saddle point principles of elasticity problem[J].Math Co mput,2003,72(244):1655-1673.
[3]	ZHOU Tian-xiao,NIE Yu-feng.A combined hybrid approach to finite element schemes of high performance[J].Internat J Numer Methods Engrg,2001,51(2):181-202.
[4]	ZHOU Tian-xiao,XIE Xiao-ping.A combined hybrid finite element method for plate bending problems[J].J Comput Math,2003,21(3):347-356.
[5]	Allman D J.A compatibl,triangular element including vertex rotations for plane elasticity analysis[J].Comput Struct,1984,19(1):1-8.
[6]	Pian T H H,Sumihara K.Rational approach for assumed stress finite elements[J].Internat J Numer Methods Engrg,1984,20(9):1685-1695.
[7]	Piltner R,Taylor R L.A systematic construction of B-bar functions for linear and nonlinear mixedenhanced finite elements for plane elasticity problems[J].Internat J Numer Methods Eegrg,1999,44(5):615-639.
[8]	MacNeal R H,Harder R L.A proposed standard set of problems to test finite element accuracy[J].Finite Elements in Analysis and Design,1985,1(1):3-20.
[9]	Chen W-J,Cheung Y-K.Robust refined quadrilateral plane element[J].Internat J Numer Methods Engrg,1995,38(4):649-666.
[10]	Simo J C,Rifai M S.A class of assumed strain methods and the method of incompatible modes[J].Internat J Numer Methods Engrg,1990,29(8):1595-1638.
[11]	Pian T H H.Finite elements based on consistently assumed stresses and displacements[J].Finite Elements in Analysis and Design,1985,1(2):131-140.
[12]	CHIEN Wei-zang.Incompatible elements and generalized variational principle[A].In:Proceedings of Symposium on Finite Element Method[C].252.Beijing:Science Press; New York:Gorden and Breach,Science Publ,1982.
[13]	Brezzi F,Fortin M.Mixed and Hybrid Finite Element Methods[M].Berlin:Springer-Verlag,1992.
[14]	ZHOU Tian-xiao,XIE Xiao-ping.A unified analysis for stress/strain hybrid methods of high performance[J].Comput Methods Appl Meth Engrg,2002,191(41/42):4619-4640.