INTEGRAÇÃO NUMÉRICA NO CONTEXTO DO MÉTODO DOS ELEMENTOS FINITOS GENERALIZADOS THE NUMERICAL INTEGRATION IN GFEM ANALYSIS

Resumo

Structural problems involving variables with a quick change in a small scale of a certain do-
main requires a numerical approach which considers discontinuities, singularities and high gradients.

Fracture Mechanics problems are an example of this kind, considering its process of evaluation of crack
nucleation and propagation. Using the conventional Finite Element Method (FEM) for modelling this

type of situation may be time spending and not achieve great precision due to remeshing and inexact nu-
merical integration. An alternative approach is the Generalized Finite Element Method (GFEM), which

associates FEM with enrichment functions in local regions of the problem. In this paper it is evalu-
ated some strategies for GFEM numerical integration, allowing the representation of non-polynomial

enrichment functions – frequently seen in GFEM for crack modelling – to be more precise with less
processing time when compared to those results obtained with conventional Gauss quadrature rule. The

computational analysis is inserted on the open source software INSANE (Interactive Structural Analy-
sis Environment), developed by the Structural Engineering Department of Federal University of Minas

Gerais.