U型波纹管大挠度变形的积分方程描述及其迭代算法

Integral Equation Description and Iteration Procedure of Large Deflection for U-Shaped Bellows

采用格林函数法，导出了U型波纹管圆环壳部分和截头扁锥壳部分的非线性积分方程，其中的四个未知参数由圆环壳和截头扁锥壳的连接条件确定。联合应用梯度法和积分方程迭代法建立了U型波纹管大挠度分析的迭代算法，开发了相应的程序系统。数值结果表明，本文方法具有较高的精度，压缩角对峰值应力和刚度影响十分显著，应作为波纹管设计的重要参数。

The non-linear integral equations of circular ring shells and truncated shallow conical shells of U-shaped bellows are derived using the Green function method, and the conjunction conditions between circular ring shells and truncated shallow conical shells are applied to determine the four unknown parameters. The iteration procedure is suggested for large deflection analysis of U-shaped bellows by means of the integral equation iteration in conjunction with the Gradient method, and the corresponding program system is developed. Numerical results indicate that the present method is of high precision. The influence of compressed angle on peak stresses and rigidity is noticeable, and the compressed angle should be taken as an important design parameter for U-shaped bellows.