
A Hybrid Virtual Element Method for laminated composite plates
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The Hybrid Virtual Element Method (HVEM), recently proposed in the context of linear elasticity [1], is a discretization technique that allows for polygonal meshes. It is based on an energy projection and a divergence-free assumption for stresses. It is demonstrated to be equivalent to a mixed finite element formulation based on an Hellinger-Reissner variational formulation [2]. The resulting discretization is stabilization-free, exhibits a high rate of convergence and provides an accurate solution for coarse meshes. Its extension to material non-linearity demonstrates accuracy and reliability [3]. In the present study, the implementation of the formulation is discussed in the context of the analysis of linear elastic laminated composite plates. The proposal assumes cubic linked interpolation for transversal displacement and normal rotation along the boundary, and quadratic polynomial for tangential rotation. The assumed stresses satisfy equilibrium even in the presence of bulk loads. The polygonal plate elements are locking-free. The absence of spurious energy modes is tested numerically for various polygonal and distorted concave and convex geometries. Beam-like tests are analyzed for both thick and thin cases. The accuracy of the displacements and stresses (bending moments and shear stresses) is demonstrated. A numerical comparison of the proposed HVEM with other discretion techniques for different tests shows its higher performance, in particular for coarse meshes solution. REFERENCES [1] F.S. Liguori, A. Madeo, S. Marfia, E. Sacco. A hybrid virtual element formulation for 2D elasticity problems. Computer Methods in Applied Mechanics and Engineering, Vol. 426, 116970, 2024. [2] A. Madeo, F.S. Liguori, G. Zucco, S. Fiore. An efficient isostatic mixed shell element for coarse mesh solution. International Journal for Numerical Methods in Engineering, Vol. 122 (1), 82-121, 2021. [3] F.S. Liguori, A. Madeo, S. Marfia, G. Garcea, E. Sacco. A stabilization-free hybrid virtual element formulation for the accurate analysis of 2D elasto-plastic problems. Computer Methods in Applied Mechanics and Engineering, Vol. 431, 117281, 2024.