In this paper, an automated Ritz method is developed for the analysis of thin rectangular plates undergoing large deflection. The trial functions approximating the plate lateral and in-plane displacements are represented by simple polynomials. The nonlinear algebraic equations resulting from the application of the concept of minimum potential energy of the plate are cast in a matrix form. The developed matrix form equations are then implemented in a Mathematica code that allows the automation of the solution for an arbitrary number of the trial polynomials. The developed code is tested through several numerical examples involving rectangular plates with different aspect ratios and boundary conditions. The results of all examples demonstrate the efficiency and accuracy of the proposed method.

在本文中，开发了一种自动的Ritz方法来分析经受大挠曲的矩形薄板。用简单的多项式表示近似平板横向和平面位移的试验函数。应用板的最小势能概念得到的非线性代数方程以矩阵形式浇铸。然后在Mathematica代码中实现开发的矩阵形式方程，该代码允许针对任意数量的试验多项式自动求解。所开发的代码通过几个数值示例进行了测试，这些示例涉及具有不同长宽比和边界条件的矩形板。所有实例的结果证明了该方法的有效性和准确性。