In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues.

在壳屈曲的分析建模中，已经非常关注具有至少两个相对边缘的封闭圆柱壳或圆柱板，其解被称为 Lévy 型解。然而，关于常用的非Lévy型圆柱板的解析解的报道很少，这主要归因于在规定边界条件下求解控制高阶偏微分方程的广泛公认的困难。为了解决这一差距，本研究在基于哈密顿系统的辛框架内提供了一些非 Lévy 型圆柱板的新解析屈曲解。圆柱板的屈曲首先在哈密顿系统中被公式化，以实现一个新的矩阵形式的控制方程。然后将具有非 Lévy 型边界条件的原始问题视为通过严格辛方法解决的两个精心设计的子问题的叠加。根据子问题与原问题的叠加等价，得到最终解。对于基准使用，针对具有不同面内尺寸比、不同面内尺寸与曲率半径比以及不同厚度与面内比的典型非 Lévy 型面板，提供了综合屈曲载荷和屈曲模式尺寸。本研究首次成功地将辛叠加方法扩展到圆柱板的屈曲分析，这可以为类似问题提供更多新的分析解决方案。