This work presents a Virtual Element formulation (VE) for shear-deformable elastic plates. In particular, the Hybrid Virtual Element Method (HVEM) is adopted, which assumes a self-equilibrated stress interpolation and an energy-based projection, eliminating the need for stabilization terms. This choice, together with a cubic linked interpolation for displacement and rotations, makes the approach free from locking, even for very thin plates and highly distorted element geometries. These features enable the proposed VE to achieve high accuracy even for coarse meshes, yielding low errors when compared to analytical solutions and providing a smooth reconstruction of all the stress field components. Furthermore, low error in both the displacement and stress fields are obtained in the challenging case of single element polygonal discretization. The same performance are guaranteed in presence of bulk loads, thanks to a consistent treatment within the projection operation that a-priori assumes equilibrium for the stress field interpolation.

中文翻译：

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无锁定和稳定的 Hybrid Virtual Elements，用于弹性厚板的粗网格分析


这项工作提出了一种用于可剪切变形弹性板的虚拟元公式 （VE）。特别是，采用了混合虚拟元法 （HVEM），该方法假设自平衡应力插值和基于能量的投影，无需稳定性项。这种选择，再加上用于位移和旋转的三次联动插值，使该方法不受锁定，即使对于非常薄的板和高度变形的单元几何形状也是如此。这些特征使所提出的 VE 即使在粗网格下也能实现高精度，与解析解相比，误差较低，并提供了所有应力场分量的平滑重建。此外，在具有挑战性的单单元多边形离散化情况下，位移场和应力场的误差都很低。在存在大量载荷的情况下，可以保证相同的性能，这要归功于投影作中的一致处理，即先验假设应力场插值的平衡。