This paper presents the formulation of a novel axisymmetric plate element capable of capturing size effects observed in micro-scaled structures. To establish the element formulation, a size-dependent beam element is considered, and by axisymmetric expansion of the model, the stiffness and mass matrices and force vector for an axisymmetric plate element are derived. Comparing the results of this model with those from literature and the outcomes of COMSOL confirms that the present FE formulation can accurately predict the static and dynamic behavior of microplates as well as macro-scale plates. Furthermore, a convergence analysis is performed which indicates that this model can accurately predict the static deflection and natural frequency of circular plates utilizing very low number of elements and consequently with low values of computation cost. As an example of real-world application, the model is applied to analysis of microelectromechanical devices and its accuracy is confirmed.

本文提出了一种新型轴对称板单元的公式，该单元能够捕获在微尺度结构中观察到的尺寸效应。为了建立单元公式，考虑了尺寸相关的梁单元，并通过模型的轴对称展开，导出了轴对称板单元的刚度和质量矩阵以及力矢量。将该模型的结果与文献中的结果以及 COMSOL 的结果进行比较，证实当前的有限元公式可以准确预测微板以及宏观尺度板的静态和动态行为。此外，进行的收敛分析表明，该模型可以利用很少数量的单元准确预测圆板的静态挠度和固有频率，因此计算成本较低。作为实际应用的例子，该模型被应用于微机电器件的分析，并验证了其准确性。