On the imposition of the local boundary conditions in the G/XFEM-gl analysis

Resumo

The present work investigates the imposition of boundary conditions in the scope of the Generalized
Finite Element Method with Global-Local Enrichment (GFEMgl) in the analysis of a two-dimensional linear
elastic fracture mechanics problem. In the GFEMgl, the “global problem” is firstly solved with a course
discretization, and a “local problem” is defined in the region containing singularities, imposing the previously
obtained solution as boundary conditions. The solution of the local problem provides numerically obtained
enrichment functions capable of representing the singular features. Two aspects are analyzed here: the
application of Cauchy boundary conditions (displacements and stresses), as well as the influence of the local
domain size. As for the Cauchy boundary conditions, the problem is simulated using average stresses and
recovered stresses obtained by the ZZ-BD recovery procedure (based on the stragey of Zienkiewicz-Zhu to
recover a smooth stress field, but using a block-diagonal matrix in its formulation). The results are presented in
terms of the stress intensity factors and the strain energy of the enriched global problem. The numerical
simulations are performed in INSANE (INteractive Structural ANalysis Environment), an open-source software
developed in the Department of Structural Engineering at the Federal University of Minas Gerais.