Estimadores de erro a posteriori e estratégias adaptativas para o método dos elementos finitos generalizados com enriquecimento global-local aplicado a problemas da mecânica da fratura

Abstract

The Generalized Finite Element Method with global-local enrichments (GFEMgl) has been consolidated, in recent years, as an important tool for solving problems containing discontinuities and singularities. The formulation is based on a two-scale decomposition of the solution: a coarse scale (global), capable of representing the smooth component of the solution, and a fine scale (local), where the special features of the problem are inserted. Despite the advances in the application of this numerical method, there is a lack of studies concerning approximation errors. Therefore, the present work proposes, for the first time, a posteriori error estimators and adaptive procedures for the GFEMgl, considering two-dimensional Linear Elastic Fracture Mechanics problems. Error measures are formulated in the two solution scales (local and global problems) based on the energy norm and, additionally, a goal-oriented error estimator specially designed for the stress intensity factors. These measures are employed in adaptive procedures to improve the approximate solution and reduce the dependence on the user of the computational platform. The numerical simulations are performed in INSANE (INteractive Structural ANalysis Environment), a free software project developed at the Department of Structural Engineering of the Federal University of Minas Gerais.