VIRTUAL ELEMENT METHOD PRE-PROCESSOR SOFTWARE

Resumo

The Virtual Element Method (VEM) is a relatively recent method where it is possible to have non-
polynomial functions inside the virtual elements (virtual elements are the equivalent of finite elements for VEM),

while requiring them to behave like polynomials only at the frontier of the virtual elements. The “virtual” term
comes from the fact that the shape functions are computed implicitly using an optimal set of degrees of freedom
leading to a stiffness matrix that heavily depends on the choice of the degrees of freedom.
Geometry parameters like coordinate of vertices, polygonal diameter and area are fundamental quantities
in VEM because they are related to the choice of the degrees of freedom and, consequently, the stiffness matrix
calculation. In this work, a graphical user interface to VEM focused on the two-dimensional case is developed in
order to ease input data and guarantee VEM performance by ensuring the optimal choice of the degrees of freedom.
The interface is responsible to generate the geometry from a set of coordinates, calculate the area, centroid, and
polygonal diameter.
As the main goal of the interface is to make the use o VEM less abstract, a set of requirements were defined
for the graphic tool development. Among them, two are crucial: the interface must be user-friendly, guaranteeing
that user with no prior experience of the method can use it, and data input must be simple. To keep data input
simple, a text file with the coordinates of vertices are used. And to guarantee that the graphic tool is user friendly,
C# programing language is employed in a very intuitive and clear construction.
Throughout the article, the requirements and the interface are shown, explaining the choices made during

the project phase related to programming language and libraries. To exemplify its use, a simple case of a two-
dimensional problem using VEM is done. More specifically, the computation of a local stiffness of a polygon with

more than 4 sides is shown.