Well-conditioning global–local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics

Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomi...

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Bibliographic Details
Published in:Computational mechanics Vol. 58; no. 5; pp. 819 - 831
Main Authors: Malekan, Mohammad, Barros, Felicio Bruzzi
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2016
Springer
Springer Nature B.V
Subjects:
Analysis
Blending
Classical and Continuum Physics
Computational Science and Engineering
Convergence
Elastic analysis
Engineering
Enrichment
Finite element analysis
Finite element method
Fracture mechanics
Ill-conditioned problems (mathematics)
Linear elastic fracture mechanics
Mathematical analysis
Methods
Original Paper
Polynomials
Strain energy
Theoretical and Applied Mechanics
Condition number
Global–local
Partition of unity
Stable generalized/eXtended FEM
Blending element
ISSN:0178-7675, 1432-0924
Online Access:Get full text
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Summary:Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global–local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global–local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global–local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global–local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global–local enrichments lead to ill-conditioned system matrices and bad convergence rate.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-016-1318-7