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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