Implementação não intrusiva do método dos elementos finitos generalizados com enriquecimento global-local

Abstract

This work implements a non-intrusive coupling strategy for multiscale structural problems known as IGL-GFEMgl. In this approach, the problem is divided into three scales. The global scale is solved by standard Finite Element Method (FEM) and it does not evaluate any local feature. The mesoscale, which is an intermediary scale, and the local scale compose a second problem which is addressed by the global-local strategy applied to the Generalized Finite Element Method (GFEMgl). All the local features are properly modeled on the local problem. The compatibility between global and mesoscale solutions is assured by the Iterative Global-Local (IGL), a non-intrusive strategy for problem coupling. This work aims to bring methods and resources still under development in the academia, such as GFEMgl, closer to the industry reality. Regarding that, in the present implementation, the global scale, which often requires computational efficiency, is solved by Abaqus, a widespread software in the industry. On the other hand, meso and local scales are dealt by the INSANE platform (INteractive Structural ANalysis Environment), an open-source project develop by the Department of Structural Engineering of the Federal University of Minas Gerais. The implementation is validated by a set of static elastic linear problems. Then, some observations available in the related literature were explored. Finally, a set of simulations were evaluated in order to investigate some parameters of the IGL-GFEMgl. The results indicate that the size of the mesoscale impacts the convergence rate of the GLI algorithm. It was also shown that the dynamic relaxation overcomes a major limitation of the method. By the use of this technique, the initial stiffness gap between the scales no longer controls the convergence rate of the solution.