Convergence rate; Extended finite element method; Fracture analysis; Node-based smoothed finite element method; Numerical method; Stress intensity factor (SIF); Convergence rates; Node-based smoothed finite element methods; Stress intensity; Convergence of numerical methods; Crack tips; Cracks; Elasticity; Fracture; Integration; Stiffness matrix; Stress intensity factors; Finite element method
Abstract :
[en] This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Vu-Bac, N.; Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, D-99423 Weimar, Germany
Nguyen-Xuan, H.; Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
Chen, L.; Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore, Singapore
BORDAS, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Kerfriden, P.; School of Engineering, Institute of Theoretical, Cardiff University, United Kingdom
Simpson, R. N.; School of Engineering, Institute of Theoretical, Cardiff University, United Kingdom
Liu, G. R.; University of Cincinnati, Cincinnati, OH 45221-0070, United States
Rabczuk, T.; Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, D-99423 Weimar, Germany
External co-authors :
yes
Language :
English
Title :
A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis
Publication date :
2011
Journal title :
Computer Modeling in Engineering and Sciences
ISSN :
1526-1492
Volume :
73
Issue :
4
Pages :
331-355
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
Funders :
Vietnam National Foundation for Science and Technology Development (NAFOSTED)