The influence of different projection operators in the Virtual Element Method applied to bi-dimensional elastic problem

Resumo

The Virtual Element Method (VEM) generalized the Finite Element Method (FEM) in terms of mesh discretization since any simple polygon can be used as elements in the mesh. By working with more general polygons, the shape functions are not always low-order polynomials, meaning that the VEM must compute these functions implicitly by using projection operators, which responsible to map functions from the virtual element space to polynomial spaces. The choice of different projection operators requires some adaptation of the VEM formulation but the general implementation pipeline still the same. In this way, this work shows those adjustments in the formulation and proposes to investigate how the choice of the operators influences the method convergence. For that, two numerical models are presented: a patch test in a unitary square and a static analysis regarding a zeta-profile (commonly used in pressure armors of risers). All the formulation is restricted to the Virtual Element Method linear two-dimensional case taking in consideration the Theory of Elasticity.