Virtual Element Methods for plate bending problems

By Franco Brezzi, L. Donatella Marini. 2013

371 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f111cd968be79388a8c6b2eddb780a3025dc8d4a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. L. Beirão da Veiga
2. Gianmarco Manzini
3. Giuseppe Vacca
4. Alessandro Russo
5. Stefano Berrone
6. Paola Francesca Antonietti
7. Carlo Lovadina
8. Glaucio H. Paulino

In Mechanics of Materials

1. Gianmarco Manzini
2. L. Beirão da Veiga
3. Giuseppe Vacca
4. Alessandro Russo
5. Natarajan Sukumar
6. Glaucio H. Paulino
7. Carlo Lovadina
8. Stefano Berrone

Citations in the corpus

• Conforming and nonconforming virtual element methods for elliptic problems (2015, positive): “Concurrently, the VEM framework has been extended to the solution of plate-bending problems [14], linear elasticity problems in two and three spatial dimensions [6, 21], the Steklov eigenvalue problem [27], the simulation of discrete fracture networks [11], and the two-dimensional streamline…”
• A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, background): “The basic VEM introduced on the Poisson problem has then been extended to highly regular [11], non conforming [2] and discontinuous approximating spaces [16], to general elliptic [8] and mixed problems [6,7,14], as well as to Stokes [1], plate problems [15], linear and non linear elasticity [5, 10, ”
• Some basic formulations of the virtual element method (VEM) for finite deformations (2017, background): “[24, 26, 27, 28, 29, 25, 30, 31, 32, 33]), some attempts have been made for nonlinear [34, 35] and 3D [29] problems.”
• On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes (2013, methodology): “In this work, we focus on the recently-developed Virtual Element Method (VEM) that addresses some of the above-mentioned challenges facing finite element schemes [10, 11, 15].”
• Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, neutral): “See in particular, for Mimetic Finite Differences, [3], [13], [14], [17], [24], [26], [27], [25], and mostly [16], [49] (and the references therein), and [1], [2], [19], [10], [11], [18], [28], [29], [45], [46], [50], [53], [64] for Virtual Elements.”