Análise de problemas bidimensionais pelo método dos elementos finitos generalizados estável (MEFGE)

Abstract

The present work aims to evaluate the performance of the Stable Generalized Finite Element Method (SGFEM), a new approach that derives from a simple modication of enrichment functions used in Generalized Finite Element Method (GFEM), in the linear analysis of two-dimensional problems with plan loading. For this, the expansion of the INSANE (INteractive Structural ANalysis Environment) system, an open source project developed at the Structural Engineering Department of the Federal University of Minas Gerais, is carried out in such a manner that incorporates to this environment a component that provides the required analysis in a generic way, regardless of the nature of the enrichment function chosen and under the approach of SGFEM. This implementation is validated by numerical experiments with dierent problems, involving enrichment functions with distinct features. Among these, there are polynomial functions, singular functions, that describe the solution around a crack in mode I of opening, and jump functions, that incorporate the geometric discontinuity. In each one of these problems, the performance of SGFEM is compared to GFEM. In this way, interesting parameters for both methods are evaluated, such as rates of convergence, solution error, and rates of growth for the scaled condition number. The performance of these methods in the presence of blending elements is also studied