A computational framework for a two-scale generalized/extended finite element method

Mohammad Malekan (School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil)
Felício Barros (School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil)
Roque Luiz da Silva Pitangueira (School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil)
Phillipe Daniel Alves (Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA)
Samuel Silva Penna (School of Engineering, Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil)

Engineering Computations

ISSN: 0264-4401

Publication date: 2 May 2017

Abstract

Purpose

This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.

Design/methodology/approach

The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized.

Findings

The generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated.

Originality/value

This work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.

Keywords

Citation

Malekan, M., Barros, F., Pitangueira, R., Alves, P. and Penna, S. (2017), "A computational framework for a two-scale generalized/extended finite element method", Engineering Computations, Vol. 34 No. 3, pp. 988-1019. https://doi.org/10.1108/EC-02-2016-0050

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Publisher

:

Emerald Publishing Limited Bingley, United Kingdom

Copyright © 2017, Emerald Publishing Limited

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