Propagação de trincas em meios elásticos lineares via método dos elementos finitos generalizados com estratégia global-local automatizada

Abstract

This master's thesis presents the automation of the global-local strategy under the Generalized Finite Element Method approach, evaluating its performance in the analysis of two-dimensional problems of Linear Elastic Frature Mechanics. The Generalized Finite Element Method is a numerical method established as an alternative to the Finite Element Method (MEF), being particularly efective for problems with non-smooth solutions. An automated strategy for building local problems,whose solution enriches the approximation of an unique global problem, is proposed, aiming to reduce user interference in the simulation of crack propagation. The implementation is carried out as an expansion of the INSANE (INteractive Structural ANALYSIS Environment) system, a free software project developed in the Department of Structural Engineering of the Federal University of Minas Gerais. New procedures were incorporated into the system, making possible the defnitionof adaptive local problems, able to follow the path described during the process of crack growth. The implementation was validated by the numerical simulation of problems with diferent geometries and loadings, seeking the correct extraction of stress intensity factors for crack opening modes I and II. The method performance was measured based on the results in strain energy, stress intensity factors and crack path. Inuences of the global-local analysis cycles, polynomial enrichment and meshtopology were considered. Additionally, the efect of the Stable Generalized Finite Element Method approach on the enrichment obtained from the local problem solution is evaluated.