TWO-DIMENSIONAL ELASTIC LINEAR PROBLEMS USING THE VIR- TUAL ELEMENT METHOD

Resumo

Virtual Element Method (VEM) is a relatively new method for solving partial differential equations,
which proposes to generalize the classical Finite Element Method (FEM) with respect to the mesh discretization.
In the two-dimensional case, any simple polygon can be used as discretization element and, as a result, the shape
function are not strictly polynomials. The method main characteristic is to compute those functions implicitly,
without the necessity of knowing their explicit form, giving it great versatility when treating complex geometries.
The VEM presents a dense mathematical formulation, and it was originally developed for the Poisson equation. In
recent years, a considerable number of works has applied the method for different engineering problems usually
treated using finite element models. For example, VEM formulations were adapted to different rheology problems,
contact problems and topological optimization. However, the usage of the Virtual Element Method is not so popular
when compared to the Finite Element Method or the Extended Finite Element Method. The main goal of this paper
is to present the Virtual Element Method applied to linear elasticity problems in two-dimensions by focusing on
its implementation, aiming to contribute for the popularization of the method. The results obtained with VEM are
compared with the results from a Finite Element Method commercial software, showing good agreement and the
great potential of the method in engineering problems.