A preliminary study of selected integration methods in XFEM

Resumo

In this paper, we conduct a preliminary study of some numerical integration strategies employed in the
modeling of weak discontinuity interfaces inside the context of XFEM, such that used as enrichment to model
interfaces bi-materials. The first integration strategy considered is the standard Gauss quadrature method. The
second uses sub-elements conformed to the discontinuity, which are generated by the Delaunay triangularization.
In this case, the Gauss points are applied to the triangular sub-elements and transformed into the quadrilateral
element domain. The third technique replaces the discontinuity by an equivalent polynomial that eliminates the
use of sub-elements applying directly the standard Gaussian quadrature. A numerical example is carried out in
order to draw the very first impressions of the integration strategies.