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
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摘要: 讨论了圆环壳在横向载荷作用下的整体弯曲问题,提出了中细柔性圆环壳的概念、基本方程和一般解。本文称粗细比(子午线曲率半径与子午线曲率中心到回转轴的距离之比)小于1/3的圆环壳为中细圆环壳;方程的推导基于E.L.Axelrad的柔性壳理论;所得的解含有处理边界问题所必须的积分常数并且在全域内处处收敛;本解能方便地用于有关波纹管的计算。全文共分4个部分:(Ⅰ)基本方程和一般解;(Ⅱ)Ω型波纹管的计算;(Ⅲ)C型波纹管的计算;(Ⅳ)U型波纹管的计算。Abstract: 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.
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[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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