三角形单元协调与非协调位移的能量正交关系

聂玉峰; 周天孝; 聂铁军

三角形单元协调与非协调位移的能量正交关系

1.
西北工业大学应用数学系, 西安 710072;
2.
中国航空计算技术研究所, 西安 710068

详细信息

作者简介:
聂玉峰(1968- ),男,讲师,正读博士学位.

中图分类号: O242.21
计量
- 文章访问数: 1929
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- 被引次数: 0
出版历程
- 收稿日期: 1997-04-28
- 修回日期: 1998-11-07
- 刊出日期: 1999-06-15

The Energy Orthogonal Relation Between Conforming and Non-Conforming Displacements of Triangular Element

1.
Applied Mathematics Department, Northwestern Polytechnical University, Xi'an 710072, P R China;
2.
Computing Technology Research Institute, CAE, Xi'an 710068, P R China

摘要

摘要: 基于组合稳定化变分原理,周天孝提出的组合杂交法是绝对收敛和稳定的,它给出了一种系统化的增强应力/应变方法,并建立了一簇低阶仿射等价的n-cube(n=2,3)单元。本文论证了单元上应力插值为线性,位移插值为协调线性部分和非协调二次部分之和的三角形组合杂交单元其协调部分与非协调部分的能量正交关系,进而得到此三角形单元刚度矩阵等同于协调的三角形线性元刚度矩阵,即非协调部分无应变增强特性。
- 组合稳定 /
- 能量正交 /
- 应变增强
Abstract: Based on the variational principle of combinative stability, combined hybrid methods posed by Zhou Tianxiao are absolutely convergent and stabilized. Zhou has advocated a systematic approach to enhanced stress/strain schemes and has designed a family of lower-order elements which are affine-equivalent to n-cube(n=2,3). The energy orthogonal relation between the conforming part and the non-conforming part of displacements interpolation functions in triangular element is given, in which the stress is interpolated by linear polynomials on each element, but the displacements are interpolated by the sum of conforming linear and non-conforming quadratic polynomials. Furthermore, this element is equivalent to the conforming triangular linear element, that is, the non-conforming parts have no contribution to enhanced strains.
- combinative stability /
- energy orthogonality /
- enhanced strain

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参考文献(7)

[1]	Zhou Tianxiao. Combined hybrid finite element method without requirement for Babuska-Brezzi Condition[J].Numerische Mathematik.(in Press)
[2]	Zhou Tianxiao. Finite element method based on combination of "saddle point" variational formulations[J].Science in China(Ser.E),1997,27(1):75～87.
[3]	周天孝.Wilson元的星星之火可否燎原[J].计算力学学报,1997,14(增刊):24～27.
[4]	钟万勰,纪峥.理性有限元[J].计算结构力学及其应用,1996,13(1):1～8.
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[7]	Reddy B D, Simo J C. Stability and convergence of a class of enhanced strain methods[J].SIAM J Numer Anal,1995,32(6):1705～1728.