Non-intrusive implementation of the Generalized Finite Element Method with Global-Local Enrichment for multi-domain analysis

Resumo

This work proposes a non-intrusive implementation of the Generalized Finite Element Method with Global-Local enrichment (GFEMgl-IGL) for multi-domain analysis. In GFEMgl-IGL, the global problem is initially discretized with a coarse mesh and without considering localized phenomena. The solution of this domain is obtained through the standard formulation of the Finite Element Method, using the commercial software Abaqus in this work. Following, mesoscales, as many as necessary, are defined as intermediate problems between the global and local domains (where localized phenomena of interest, such as cracks, are effectively represented). The global-local enrichment of the GFEMgl determines the association of each mesoscale with the respective local problem. The coupling of mesoscales with the global problem is established through the transfer of displacements and generalized forces, defining the non-intrusive strategy denominated Iterative Global-Local (IGL). Numerical simulations via GFEMgl are executed in the computational system INSANE (INteractive Structural ANalysis Enviroment - www.insane.dees.ufmg.br). The combination of solvers indicated in the solution methodology focuses on endorsing the application of algorithms developed in the academy as instruments with the capacity to solve complex models utilizing commercial software. This work proposes the expansion of the implementation of the non-intrusive strategy in INSANE, enabling the consideration of multiple local domains. A numerical example is presented to show the simulation's performance and to investigate the influence of the main parameters related to the proposed strategy.