ZHU Wei-ping, HUANG Qian. General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅰ)-Governing Equation and General Solution[J]. Applied Mathematics and Mechanics, 2002, 23(8): 790-797.
 Citation: ZHU Wei-ping, HUANG Qian. General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅰ)-Governing Equation and General Solution[J]. Applied Mathematics and Mechanics, 2002, 23(8): 790-797.

# General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅰ)-Governing Equation and General Solution

• Rev Recd Date: 2002-04-11
• Publish Date: 2002-08-15
• The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed.The derivation of the equations was based upon the theory of flexible shells generalized by E.L.Axelrad and the assumption of the moderately slender ratio less than 1/3(i.e.ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution).The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems.It can be used to calculate the stresses and displacements of the related bellows.The whole work is arranged into four parts: (Ⅰ)Governing equation and general solution;(Ⅱ)Calculation for Omega-shaped bellows;(Ⅲ)Calculation for C-shaped bellows;(Ⅳ)Calculation for U-shaped bellows.This paper is the first part.
•  [1] АксельрадЭЛ. ГибкиеОболочки[M]. Москва:Наука,1976. [2] Axelrad E L. Theory of Flexible Shells[M]. New York: Elsevier Science Publishing Company,Inc,1987. [3] 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. [4] 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. [5] 钱伟长. 半圆弧波纹管的计算——细环壳理论的应用[J]. 清华大学学报,1979,19(1):84-99. [6] 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. [7] CHEN Shan-lin. General solution of the bending of ring shells with equations in complex[A]. In: Yeh K Y Ed. Progress in Applied Mechanics[C]. Dordrecht: Martinus Nijhoff Publishers, 1987,181-192. [8] 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. [9] ZHU Wei-ping, HUANG Qian, GUO Ping, et al. General solution for C-shaped bellows overall-bending problems[A]. In: N E Shanmugam, J Y Kichard, V Thevendran Eds. Thin-Walled Structures-Research and Development,Proc 2nd ICTWS.1998,Singapore[C]. Oxford,UK:Elsevier Science Ltd,1998,477-484. [10] 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. [11] 朱卫平. 用初参数法解C型波纹管在子午面内整体弯曲[J]. 力学季刊,2000,21(3):311-315. [12] 钱伟长. 环壳方程级数解的收敛性问题及其有关收敛定理的研究[J].兰州大学学报,1979,(力学专号):1-38.

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