This paper presents an analytical study on thermal buckling of cylindrical shells with non-uniform thickness, which is common in engineering practice. Firstly, the shell thickness is assumed to be arbitrary in the axial direction. After solving the basic partial differential equations by the perturbation method, buckling temperature and modes in terms of thickness function and geometric sizes of the shell are obtained. Using the presented formulas, this paper deeply analyzes and discusses cosine distributed and stepwise thicknesses. For simple cosine distributed thickness, the classical Galerkin method is applied to derive buckling temperature factors, while stepwise thickness is verified by the finite difference method. Results from the Galerkin method and the finite difference method are in accordance with those by presented formulas in this paper. Furthermore, the influence of parameters in thickness functions and buckling modes on buckling temperature factors is discussed, and some interesting conclusions are drawn. The presented buckling temperature formulas can be applied to evaluate stability capacity of the cylinder used in thermal environment.

本文对厚度不均匀的圆柱壳的热屈曲进行了分析研究，这在工程实践中很常见。首先，假定壳厚度在轴向方向上是任意的。通过摄动法求解基本的偏微分方程后，获得了壳的厚度函数和几何尺寸方面的屈曲温度和模态。使用提出的公式，本文深入分析和讨论了余弦分布和逐步厚度。对于简单的余弦分布厚度，采用经典的Galerkin方法导出屈曲温度因子，而逐步厚度则通过有限差分法进行验证。Galerkin方法和有限差分方法的结果与本文给出的公式的结果一致。此外，讨论了厚度函数和屈曲模式中的参数对屈曲温度因子的影响，并得出了一些有趣的结论。提出的屈曲温度公式可用于评估在热环境中使用的气缸的稳定性。