Abstract This paper presents an analytical study on the buckling of cylindrical shells under arbitrarily distributed axial loads. It has three main innovation points. First, different from the previous studies, the axial loads need not be assumed to be specific forms beforehand and be simple ones such as cosine type, which are arbitrary in this paper (including continuous and discontinuous distributions). Second, combining the separation of variables and perturbation methods, it develops a novel general method to solve the fourth-order partial differential equations with unknown variable coefficients for cylindrical shells under distributed axial loads. Last, it derives the asymptotic formula of buckling loads with respect to shell geometry sizes and load functions for the first time. Using the presented formula, two continuous axial load distributions are analyzed first and the results show a good agreement with previous studies and those by the Bubnov-Galerkin method. Furthermore, one discontinuous axial load distribution is investigated. Comparative study on effects of load distribution parameters and types is also performed. The study has sufficient accuracy and significant engineering application value.

中文翻译：

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任意分布轴向载荷作用下圆柱壳屈曲的解析解

摘要 本文对任意分布轴向载荷作用下圆柱壳屈曲进行了分析研究。它具有三个主要创新点。首先，与以往的研究不同，轴向载荷不必事先假设为特定形式，而是简单的，如余弦型，本文中是任意的（包括连续和不连续分布）。其次，结合变量分离法和微扰法，提出了求解分布轴向载荷作用下圆柱壳变系数未知的四阶偏微分方程的新通用方法。最后，首次推导出了关于壳几何尺寸和载荷函数的屈曲载荷渐近公式。使用提出的公式，首先分析了两个连续的轴向载荷分布，结果显示与先前的研究和 Bubnov-Galerkin 方法的研究结果非常吻合。此外，研究了一种不连续的轴向载荷分布。还对负载分布参数和类型的影响进行了比较研究。该研究具有足够的准确性和显着的工程应用价值。