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Large-deflection mathematical analysis of rectangular plates

机译：矩形板的大挠度数学分析

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摘要

A large-deflection mathematical analysis of rectangular plates under uniform lateral loading is presented in this paper. The analysis is based on solving two fourth-order, second-degree, partial differential Von Karman equations relating the lateral deflections to the applied load. This paper provides a mathematical procedure which benefits from the software and hardware computing capabilities that were unavailable when mathematical modeling was last attempted. The solution is presented in a simple form suitable for direct practical use and can be easily implemented in common spreadsheet packages. Plates with two boundary conditions, namely, simply supported edges and held edges, are considered. Comparisons are held against earlier exact and approximate solutions, including results of finite element analyses. The results show close agreement with other exact analysis methods. The solution is able to produce the same results as other exact solutions, but with a much simpler and a more practical approach.
机译：给出了矩形板在均匀横向荷载作用下的大挠度数学分析。该分析基于求解两个将侧向挠度与施加载荷相关的四阶，二阶偏微分冯卡曼方程。本文提供了一种数学程序，该程序得益于上次尝试进行数学建模时不可用的软件和硬件计算功能。该解决方案以适合直接实际使用的简单形式提供，并且可以在常见的电子表格程序包中轻松实现。考虑具有两个边界条件的板，即简单支撑的边和保持的边。比较是针对较早的精确和近似解，包括有限元分析的结果。结果表明与其他精确的分析方法非常吻合。该解决方案能够产生与其他精确解决方案相同的结果，但是使用的方法更加简单实用。

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