General Solution for U-Shaped Bellows Overall-Bending Problems

Zhao Weiping; Guo ping; Huang Qian

Volume 21 Issue 4

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(4): 331-341

Zhao Weiping, Guo ping, Huang Qian. General Solution for U-Shaped Bellows Overall-Bending Problems[J]. Applied Mathematics and Mechanics, 2000, 21(4): 331-341.

Citation:

Zhao Weiping, Guo ping, Huang Qian. General Solution for U-Shaped Bellows Overall-Bending Problems[J]. Applied Mathematics and Mechanics, 2000, 21(4): 331-341.

Citation:

Zhao Weiping, Guo ping, Huang Qian. General Solution for U-Shaped Bellows Overall-Bending Problems[J]. Applied Mathematics and Mechanics, 2000, 21(4): 331-341.

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General Solution for U-Shaped Bellows Overall-Bending Problems

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University Shanghai 20072, P R China

Received Date: 1998-11-04
Rev Recd Date: 1999-10-15
Publish Date: 2000-04-15

Abstract

Abstract

The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zhu Weiping,et al.and the solution for ring plates.The results evaluated in this paper are compared with those on EJMA(standards of the expansion joint manufacturers association) and of the experiment given by Li Tingxin,et al.
- flexible shells,
- shells of revolution,
- circular ring shells,
- bellows,
- U-shaped bellows

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References(15)

References

[1]	钱伟长,郑思梁.半圆孤波纹管的计算——环壳一般解的应用[J].应用数学和力学,1981,2(1):97～111.
[2]	黄黔.用数值积分的初参数法解波纹管[J].应用数学和力学,1982,3(1):101～112.
[3]	钱伟长,吴明德.U型波纹管的非线性特性摄动法计算[J].应用数学和力学,1983,4(5):595～602.
[4]	黄黔.摄动初参数法解轴对称壳几何非线性问题[J].应用数学和力学,1986,7(6):533～543.
[5]	Narasimham S V,Paliwal D N,Upadhyaya A P.Stress analysis of V-shaped expansion joints under internal pressure[J].Int J Pres Ves & Piping,1997,71:35～45.
[6]	Hamada M,Nakagawa K,Miyata K,et al.Bending deformation of U-shaped bellows[J].Bulletin of JSME,1971,14(71):401～409.
[7]	Аксельрад　З　Л.　Гибкие　Оболочки[M].Москва:Наука,1976.
[8]	Axelrad E L.Theory of Flexible Shells[M].New York:Elsevier Science Publishing Company,Inc,1987.
[9]	Blazej Skoczen,Jacek Skrzypek.Application of the equivalent column concept to the stability of axially compressed bellows[J].Int J Mech Sci,1992,34(11):901～916.
[10]	Standards of the Expansion Joint Manufacturers Association(EJMA)[S].INC,Sixth Edition,1993,New York,USA.(美国膨胀节制造商协会标准,美国膨胀节制造商协会出版发行,约每5年更新版本一次——作者注)
[11]	黎廷新,李添祥,胡坚,等.膨胀节的各种位移应力[J].华南理工大学学报(自然科学版),1994,22(3):94～102.
[12]	朱卫平,黄黔,郭平.柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解[J].应用数学和力学,1999,20(9):889～895.
[13]	钱伟长,郑思梁.轴对称圆环壳的复变量方程和轴对称细环壳的一般解[J].清华大学学报,1979,19(1):27～47.
[14]	Zhu Weiping,Huang Qian,Guo Ping,Chien Weizang.General solution for C-shaped bellows overall-bending problems[A].In:Proc Thin-Walled Structure——Research and Development,2nd ICTWS[C].Singapore,1988; Oxford UK:Elsevier Science Ltd,1998,477～484.
[15]	钱伟长,郑思梁.轴对称圆环壳的一般解[J].应用数学和力学,1980,1(3):287～299.

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