In this paper, a novel discrete differential geometry-based numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed. In the proposed approach a plate is discretized using a finite number of rigid bars, lumped masses, and elastic rotational springs to simulate both bending and shear deformation responses, allowing the analysis of thick plates through the adoption of the Reddy’s third-order shear deformable plate theory. An interesting analogy between the proposed model and the central finite difference method for solving a set of partial differential equations is also highlighted, showing how the former can be seen as the physical model behind the mathematical representation of the latter. The numerical results presented show both the versatility and the accuracy of the proposed approach.

在本文中，开发了一种新的基于离散微分几何的数值程序，用于非均匀厚度矩形板的屈曲和振动分析。在建议的方法中，使用有限数量的刚性杆、集中质量和弹性旋转弹簧对板进行离散化，以模拟弯曲和剪切变形响应，允许通过采用 Reddy 的三阶剪切变形板对厚板进行分析理论。还强调了所提出的模型与求解一组偏微分方程的中心有限差分方法之间的一个有趣的类比，展示了前者如何被视为后者数学表示背后的物理模型。数值结果显示了所提出方法的通用性和准确性。