2-D fracture mechanics problems by SGFEM

Abstract

In this paper, an extensive investigation is done on Stable Generalized Finite Element Method (SGFEM) performance through the analysis of 2-D fracture mechanics problems. Condition number, Stress Intensity Factors (SIFs), global and local measures of the energy norm are used to study SGFEM conditioning and accuracy. Computational time is also briefly discussed. The method is compared with the standard Generalized/eXtended Finite Element Method (G/XFEM). Numerical experiments corroborate and complement the knowledge available in the literature so far, and demonstrate SGFEM accuracy in 2-D cracked problems. Modified Heaviside Functions, combined with other enrichment functions, are also studied in the simulations. A simple and yet generic implementation for SGFEM is described, under the Object Oriented strategy, in a open source software. The implementation can be used in 2-D and 3-D problems, and it allows to generalize the implementation of any type of enrichment function under the SGFEM approach.