Locking and stabilization free Hybrid Virtual Elements for the coarse mesh analysis of elastic thick plates

Abstract

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.

A random-based benchmark is proposed for assessing numerically the absence of spurious modes in concave and convex distorted elements. The proposed HVEM for plate is validated in classical benchmark problems, demonstrating the superior accuracy of polygonal meshes compared to the quadrilateral ones, for an equivalent number of degrees of freedom. This result is relevant in all the applications where polygonal element shapes are necessary. In addition, it opens up the way to new modeling scenarios where polygonal meshes are preferred not only for their versatility but also for their enhanced accuracy.