Element Functions of Discrete Operator Difference Method

TIAN Zhong-xu; TANG Li-min; LIU Zheng-xing

Volume 23 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(6): 551-557

TIAN Zhong-xu, TANG Li-min, LIU Zheng-xing. Element Functions of Discrete Operator Difference Method[J]. Applied Mathematics and Mechanics, 2002, 23(6): 551-557.

Citation:

TIAN Zhong-xu, TANG Li-min, LIU Zheng-xing. Element Functions of Discrete Operator Difference Method[J]. Applied Mathematics and Mechanics, 2002, 23(6): 551-557.

Citation:

TIAN Zhong-xu, TANG Li-min, LIU Zheng-xing. Element Functions of Discrete Operator Difference Method[J]. Applied Mathematics and Mechanics, 2002, 23(6): 551-557.

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Element Functions of Discrete Operator Difference Method

1.
Center of CIMS & Robotics, Shanghai University, Shanghai 200072, P R China;
2.
Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, P R China;
3.
Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P R China

Received Date: 2000-07-07
Rev Recd Date: 2002-01-29
Publish Date: 2002-06-15

Abstract

Abstract

The discrete scheme called discrete operator difference for differential equations was given.Several difference elements for plate bending problems and plane problems were given.By investigating these elements,the ability of the discrete forms expressing to the element functions was talked about.In discrete operator difference method,the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not.According to this point,discrete operator difference method is a method with good performance.
- discrete operator difference method,
- element function,
- reproduce exactly

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References(6)

References

[1]	唐立民,张允真,吴金仙,等.关于连续体结构数值计算的微分算子的离散化方法(一)[J]. 大连工学院学报,1973,13(1):7-30.
[2]	唐立民,张允真,吴金仙,等. 关于连续体结构数值计算的微分算子的离散化方法(二)[J]. 大连工学院学报,1973,13(3):27-57.
[3]	李荣华,陈仲英. 微分方程广义差分法[M]. 长春:吉林大学出版社,1994.
[4]	陈仲英. 双调和方程广义差分法的变分原理和数值分析[J]. 高等学校计算数学学报,1993, 15(2):182-194.
[5]	田中旭,唐立民. 薄板弯曲问题的一种弱形式离散算子解法[J]. 计算力学学报,2000,17(2):163-169.
[6]	唐立民,齐朝辉,丁克伟,等. 弹性力学方程弱形式广义基本方程的建立和应用[J]. 大连理工大学学报,2001,41(1):1-8.

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