Rational Finite Element Method for Elastic Bending of Reissner Plates

Sun Weiming; Yang Guangsong

Volume 20 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(2): 181-186

Sun Weiming, Yang Guangsong. Rational Finite Element Method for Elastic Bending of Reissner Plates[J]. Applied Mathematics and Mechanics, 1999, 20(2): 181-186.

Citation:

Sun Weiming, Yang Guangsong. Rational Finite Element Method for Elastic Bending of Reissner Plates[J]. Applied Mathematics and Mechanics, 1999, 20(2): 181-186.

Citation:

Sun Weiming, Yang Guangsong. Rational Finite Element Method for Elastic Bending of Reissner Plates[J]. Applied Mathematics and Mechanics, 1999, 20(2): 181-186.

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Rational Finite Element Method for Elastic Bending of Reissner Plates

Sun Weiming^1,2,
Yang Guangsong³

1.
Department of Steam, Gas and Nuclear Power Engineering, Naval Academy of Engineering, Wuhan 430033, P R China;
2.
Department of Astronautics, National University of Defence Technology, Changsha 410073, P R China;
3.
Mai box 7, Qinhe Building, Beijing 100085, P R China

Received Date: 1997-05-15
Rev Recd Date: 1997-08-24
Publish Date: 1999-02-15

Abstract

Abstract

In this paper,some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements.And therefore the rational FEM,which is perfect combination of the analytic methods and numeric methods,has been presented.This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures.What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.
- thick Reissner plates,
- elastic bending of thick plates,
- rational finite element method

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References(11)

References

[1]	蒋炜.有限单元-放松边界条件法解弹性理论平面问题[J].力学学报,1981,13(3):236～247
[2]	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
[3]	黄炎.弹性薄板理论[M].长沙:国防科技大学出版社,1992,31～39
[4]	孙卫明,杨光松.Reissner厚板弹性弯曲的一般解析解[J].应用数学和力学,1998,19(1):79～87
[5]	蒋炜.弹性理论平面问题中由应力函数积分位移分量的一般方法[J].上海力学,1980,1(1):23～37
[6]	钱伟长.广义变分原理[M].上海:知识出版社,1985,228～256
[7]	丁皓江,周卫宇,孙丽波.一种新型的平板弯曲单元[J].力学学报,1986,18(5):421～429
[8]	张福范.均布载荷下悬臂矩形板的弯曲[J].应用数学和力学,1980,1(3):349～362
[9]	吴良芝.结构有限元的修正解[J].固体力学学报,1981,2(4):457～467
[10]	浙江大学.平板分析中的有限元法译文集[C].1973:87～109
[11]	王家林.8点超参板壳单元的改进[J].吉林工业大学学报,1982,(1):1～11

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