This study presents an upgraded Ritz method capable of providing solutions to thin polygonal plates of regular and irregular shapes with various boundary conditions. The method presented herein is called the Boundary-Type Ritz (BTR) Method and it circumvents the complexity of the involved domains by transforming the encountered integrals to other forms that need to be evaluated only at corners. This leads to very fast computations with full preservation of the accuracy. The divergence theorem is implemented for this purpose. Following this method, the coordinates of the corners are solely needed to perform the integrations. The applicability of this method is proved in this paper by presenting various examples involving plates of different polygonal shapes with different boundary conditions. The results are compared to the counterpart FEM solutions and a very good agreement is observed.

本研究提出了一种升级的 Ritz 方法，能够为具有各种边界条件的规则和不规则形状的薄多边形板提供解决方案。此处介绍的方法称为边界型 Ritz (BTR) 方法，它通过将遇到的积分转换为仅需要在拐角处进行评估的其他形式来规避所涉及域的复杂性。这导致在完全保持准确性的情况下非常快速的计算。为此目的实施散度定理。按照这种方法，只需要角的坐标来执行积分。该方法的适用性在本文中通过展示涉及具有不同边界条件的不同多边形形状的板的各种例子来证明。