U型波纹管及相关结构环向屈曲的有限元分析(Ⅱ）--半圆环壳的屈曲

环壳不仅是U型波纹管的一个组成部分，更是一类重要的结构，在航天、核能和海洋工程中有重要的应用，其屈曲是人们关注的问题之一，其中对半圆环壳的分析还较为少见。本文采用文7]的有限元法（考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理）计算了正Gauss曲率半圆环壳在均匀外压作用下的屈曲，将所得结果与已知的近似解进行了对比、并讨论了其中的差异。本文除了给出临界载荷和子午线的屈曲模态外，还给出了前屈曲弯曲应力分布，以便仔细了解屈曲问题。

Analysis of Circumferential Buckling of U-Shaped Bellows and Related Structures Part Ⅱ: Buckling of Semi-Toroidal Shells

Toroidal shells are important structure in space fligh t, nuclear plant and ocean engineering rather than a part of bellows. Their buckli ng has been interested for the resent three decades, however work for the semi- toroidal shells is still rare. In this paper, we use the finite element method o f Part I (treated as a linearized eigenvalue problem but the finite prebuckling rotations and the follower force effect of the pressure are considered) to calcu late the buckling of the semi-toroidal shells under uniform external pressure. The present results are compared with those of the available approximately analy tical solutions. In addition to the critical loads and the corresponding modes, the prebuckling bending stress distributions are also provided, which is conveni ent for studying the details of the buckling problem.