Finite Element Displacement Perturbation Method for Geometric Nonlinear Behaviors of Shells of Revolution Overall Bending in a Meridional Plane and Application to Bellows(Ⅰ)

ZHU Wei-ping; HUANG Qian

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(12): 1227-1240

ZHU Wei-ping, HUANG Qian. Finite Element Displacement Perturbation Method for Geometric Nonlinear Behaviors of Shells of Revolution Overall Bending in a Meridional Plane and Application to Bellows(Ⅰ)[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1227-1240.

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Finite Element Displacement Perturbation Method for Geometric Nonlinear Behaviors of Shells of Revolution Overall Bending in a Meridional Plane and Application to Bellows(Ⅰ)

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

Received Date: 2001-09-29
Rev Recd Date: 2002-05-20
Publish Date: 2002-12-15

Abstract

Abstract

In order to analyze bellows effectively and practically, the finite-element-displacement-per- turbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturbation that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's non- linear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered..
- shell of revolution,
- bellows,
- deflection by lateral force,
- geometrical non-linearity,
- perturbation technique,
- finite element method

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References(14)

References

[1]	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.
[2]	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.
[3]	钱伟长,郑思梁.半圆弧波纹管的计算-环壳一般解的应用[J].应用数学和力学,1981,2(1):97-111.
[4]	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.
[5]	朱卫平,郭平,黄黔.U型波纹管整体弯曲问题的一般解[J].应用数学和力学,2000,21(4):331-341.
[6]	Standards of the Expansion Joint Manufacturers Association (EJMA)[S].EJMA INC,Seventh Edition,New York,1998.
[7]	CHIEN Wei-zang.Large deflection of a circular clamped plate under uniform pressure[J].Chinese Journal of Physics,1947,7(2):102-113.
[8]	CHIEN Wei-zang.Asymptotic behavior of a thin clamped plate under uniform pressure at very large deflection[J].The Science Reports of National Tsing Hua University,1948,5(1):71-94.
[9]	黄黔.复合载荷作用下圆薄板的大挠度问题[J].应用数学和力学,1982,3(1):711-720.
[10]	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.
[11]	Cook R D.有限元分析的概念和应用(1981,第二版)[M].程耿东,何穷,张国荣译.北京:科学出版社,1989.
[12]	Sanders J L.Nonlinear theories for thin shells[J].Quart Applied Mathematics,1963,21(1):21-36.
[13]	欧阳鬯,马文华.弹性塑性有限元[M].湖南:湖南科技出版社,1983,377-400.
[14]	Skoczen B.Effect of shear deformation and relaxation of support conditions on elastic buckling of pressurized expansion bellows[J].Journal of Pressure Vessel Technology,Transaction of the ASME,1999,121(2):127-132.