Mixed Dimensional Coupling in GFEM Global-Local

Resumo

The global-local Generalized Finite Element Method (GFEM) is use here to solve mixed dimensional
structure problems. Considered as an instance of the Partition of Unity Method (PUM), the GFEM uses enrichment
functions that, multiplied with the Partition of Unity (PU) functions, augment the space of problem solving. These
enrichment functions are chosen according to the problem analyzed, but they can also be numerically obtained from
the results of the analysis of a local problem, the so-called GFEM global-local. The application of this method,
however, is limited to models, for which both global and local meshes use the same formulation of finite element.
Here, the two scale of the analysis are discretized not only by different meshes, but also with different types of finite
elements. Combining mixed-dimensional elements and a multi-scale analysis can be highly effective to capture
the local structure features without overburden the global analysis of the problem. An iterative procedure, that
balances the forces of the two multi-dimensional models, is combined with the global-local analysis of GFEM. A
numerical example is presented, considering the coupling of a large-scale model with Timoshenko beam elements
and a small-scale model with quadrilateral plane elements.