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17 November 2018
Article (Scientific journals)
Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization
Agathos, Konstantinos; Bordas, Stéphane; Chatzi, Eleni
2018In Computer Methods in Applied Mechanics and Engineering
Peer reviewed


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Keywords :
XFEM; GFEM; Conditioning; Fracture mechanics
Abstract :
[en] Partition of unity enrichment is known to significantly enhance the accuracy of the finite element method by allowing the incorporation of known characteristics of the solution in the approximation space. However, in several cases it can further cause conditioning problems for which a number of remedies have been proposed in the framework of the extended/generalized finite element method (XFEM/GFEM). Those solutions often involve significant modifications to the initial method and result in increased implementation complexity. In the present work, a simple procedure for the local near-orthogonalization of enrichment functions is introduced, which significantly improves the conditioning of the resulting system matrices, while requiring only minor modifications to the initial method. Although application to different types of enrichment functions is possible, the resulting scheme is specialized for the singular enrichment functions used in linear elastic fracture mechanics and tested through benchmark problems.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Agathos, Konstantinos
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Chatzi, Eleni
External co-authors :
Language :
Title :
Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization
Publication date :
September 2018
Journal title :
Computer Methods in Applied Mechanics and Engineering
Publisher :
Elsevier, Lausanne, Netherlands
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
FnR Project :
FNR10318764 > Stephane Bordas > Fretting fatigue > Multi-analysis of fretting fatigue using physical and virtualexperiments > 01/07/2016 > 30/06/2019 > 2015
Funders :
Swiss National Science Foundation # 200021_153379 “A Multiscale Hysteretic XFEM Scheme for the Analysis of Composite Structures”


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