An object-oriented approach to the Generalized Finite Element Method

Authors:  Phillipe D. Alves, Felı´cio B. Barros, Roque L.S. Pitangueira

Abstract: 
The Generalized Finite Element Method (GFEM) is a meshbased approach that can be consider ed 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 environmen t is an objectoriented 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 possibl e to combine different kinds of element s 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.

Keywords:
Finite Element Method (FEM)
Generalized Finite Element Method (GFEM)
Partition of unity enrichment
Object-oriented programming (OOP)
Extended Finite Element Method (XFEM)
Computational Mechanics

Published in: Advances Engineering Software (Volume 59, March 2013)

Publisher: Elsevier

ISSN Information: 0965-9978

An object-oriented approach to the Generalized Finite Element Method

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