This paper presents a conforming thin plate bending element based on the Partition of Unity Finite Element Method (PUFEM) for the simulation of steady-state forced vibration. The issue of ensuring the continuity of displacement and slope between elements is addressed by the use of cubic Hermite-type Partition of Unity (PU) functions. With appropriate PU functions, the PUFEM allows the incorporation of the special enrichment functions into the finite elements to better cope with plate oscillations in a broad frequency band. The enrichment strategies consist of the sum of a power series up to a given order and a combination of progressive flexural wave solutions with polynomials. The applicability and the effectiveness of the PUFEM plate elements are first verified via the structural frequency response. Investigation is then carried out to analyze the role of polynomial enrichment orders and enriched plane wave distributions for achieving good computational performance in terms of accuracy and data reduction. Numerical results show that the PUFEM with high-order polynomials and hybrid wave-polynomial combinations can provide highly accurate prediction results by using reduced degrees of freedom and improved rate of convergence, as compared with the classical FEM.

中文翻译：

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统一有限元分区法对薄板弯曲振动建模

本文提出了一种基于统一有限元分区法（PUFEM）的一致薄板弯曲单元，用于模拟稳态受迫振动。确保单元之间位移和坡度连续性的问题通过使用三次 Hermite 型统一分区 (PU) 函数来解决。通过适当的 PU 函数，PUFEM 允许将特殊的富集函数合并到有限元中，以更好地应对宽频带中的板振荡。富集策略包括达到给定阶数的幂级数的总和以及渐进弯曲波解与多项式的组合。PUFEM板单元的适用性和有效性首先通过结构频率响应进行验证。然后进行调查以分析多项式富集阶数和富集平面波分布的作用，以在准确性和数据缩减方面实现良好的计算性能。数值结果表明，与经典有限元法相比，具有高阶多项式和混合波多项式组合的PUFEM可以通过降低自由度和提高收敛速度来提供高度准确的预测结果。