用初参数法解C型波纹管在子午面内整体弯曲

波纹管是一种呈波纹状的管形薄壁结构,作为弹性敏感元件、密封元件和位移补偿器,在现代工业、国防和民用设备中的应用日益广泛.波纹管的计算,特别是在非轴对称受力和变形方面亟待完善.本文讨论了C型波纹管在子午面内整体弯曲的应力分布和端面角位移.从柔性圆环壳在子午面内整体弯曲的复变量方程出发,化边值问题为初值问题,用S.Gill法,得到了该波纹管的数值解,适用于0＜α＜1的范围.通过3个例子,将本文的数值解和已有的细环壳一般解(解析解)作了比较.结果表明,两者基本一致,并且,当环壳较细(α较小)时,两种计算结果更为接近.

Numerical Solution for C-Shaped Bellows Overall Bending in a Meridian Plane by Initial Parameter Method

Bellows, a kind of wrinkled tube-like thin-walled structure, being widely used in equipment as elastic-sensitive element, seal and expansion joint, is usually concerned for its complex in calculation, specially in that of non-axial-symmetric problems. In this paper the stressess and angular rotation of C-shaped bellows under pure bending moments in a meridian plane are discussed. The governing differential equations are formulated on the theory of flexible toroidal shells with 0 < a < 1 and the initial parameter method with S. Gill's formulae is used. As a result, the boundary value problem.of the bellows is reduced into the initial value problem and the numerical solution is obtained. Three examples are calculated. It shows that the results given by the present numerical solutions are approximately coincide with those of the general analytical solutions based on a simplified theory of slender toroidal shells(a<1) ,and with smaller a of the shell, the both results agree better.