An object-oriented approach to the Generalized Finite Element Method

The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.

► The GFEM, an instance of the Partition of Unity Method, is reviewed.
► A FEM object-oriented environment is expanded to enclose the GFEM.
► Emphasis is placed on the class design, so that a minimum impact is necessary.
► Different elements, mathematical models and enrichment strategies are combined.
► Numerical examples are presented to demonstrate the robustness of the system.
► The system allows a plain incorporation of nonlinear capabilities.