Implementacão não intrusiva do método dos elementos finitos generalizados com enriquecimento global-local para análises multi-domínio

Abstract

This master's thesis expands the non-intrusive implementation of the Generalized Finite Element Method with Global-Local enrichment (IGL-GFEMgl) for multi-domain analyses. In IGL-GFEMgl, the global problem is initially discretized using a coarse mesh, without considering localized phenomena, thereby minimizing user interference in the analysis model construction. The solution for this domain is obtained through the standard formulation of the Finite Element Method, which is applied in this work using Abaqus commercial software. Subsequently, as many mesoscales as necessary are defined, acting as intermediate scales between the global and local domains. The phenomena of interest, such as cracks, are effectively represented in the local scale. The association between each mesoscale and its respective local problem is carried out through the global-local enrichment of GFEMgl. The mesoscales coupling to the global problem is established through the transfer of displacements and generalized forces, characterizing the non-intrusive strategy known as Iterative Global-Local (IGL). Numerical simulations using GFEMgl are performed in the computational system INSANE (Interactive Structural ANalysis Environment - www.insane.dees.ufmg.br), a free software project developed at the Department of Structural Engineering at the Federal University of Minas Gerais. The ability to perform analyses with multiple local domains and the combination of solvers, aims to use algorithms developed in the academic environment to improve complex models solving through commercial software. Numerical examples are presented to demonstrate simulation's performance and to investigate the influence of the main parameters related to the proposed strategy. The results quality are evaluated based on the state of stresses and strains at critical points of the models, in addition to parameters of Linear Elastic Fracture Mechanics. The investigations indicate that the convergence process is not affected by the consideration of multiple local domains, as long as these do not result in a significant increase in the stiffness difference between the coupled scales. Additionally, the computational performance of the algorithm was evaluated, comparing simulations which the mesoscales processing were executed sequentially and in parallel.