The thin plane plates are largely used in practice as single elements or as components of the thin-walled structures, and their behavior under compression is characterized by large post-buckling load-carrying capacity. Various semi-analytical solutions of the uniformly compressed simply supported plate with large deflections were formulated almost a century ago, mainly solving the fundamental equations governing the deformation of thin plates, or using classic energy methods. Due to several shortcomings, none of these solutions were introduced in the design codes of thin-walled members. This paper presents new semi-analytical solutions based on classic energy methods. The main innovation is brought by the considered displacement field which is far more accurate than the ones used by the previous formulations. The initial geometric imperfections are considered, and the proposed solutions are validated against numerical solutions and experimental data. The validation is also supported by a publicly available software application.

中文翻译：

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大挠度均压简支板的半解析解

薄平面板在实践中主要用作单个元件或薄壁结构的组成部分，它们在受压下的行为特点是具有较大的后屈曲承载能力。近一个世纪前，各种大挠度均压简支板的半解析解已经形成，主要是求解控制薄板变形的基本方程，或使用经典的能量方法。由于一些缺点，这些解决方案都没有被引入薄壁构件的设计规范中。本文提出了基于经典能量方法的新半解析解。主要的创新是由考虑的位移场带来的，它比以前的公式使用的要准确得多。考虑了初始几何缺陷，并根据数值解和实验数据验证了所提出的解决方案。公开可用的软件应用程序也支持验证。