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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 20

The Smoothed Extended Finite Element Method

S. Natarajan1, S. Bordas2, Q.D. Minh3, H.X. Nguyen3, T. Rabczuk4, L. Cahill5 and C. McCarthy6

1GE-Aviation, India Technology Center, Bangalore, India
2Department of Civil Engineering, University of Glasgow, United Kingdom
3Division of Computational Mechanics, Department of Mathematics and Informatics, University of Natural Sciences - VNU-HCM, Vietnam
4Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand
5Department of Mechanical Engineering, University of Limerick, Ireland
6Composites Research Centre, Materials and Surface Science Institute, Department of Mechanical Engineering, University of Limerick, Ireland

Full Bibliographic Reference for this paper
S. Natarajan, S. Bordas, Q.D. Minh, H.X. Nguyen, T. Rabczuk, L. Cahill, C. McCarthy, "The Smoothed Extended Finite Element Method", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 20, 2008. doi:10.4203/ccp.89.20
Keywords: smoothed finite element method, extended finite element method, strain smoothing, partition of unity methods.

The extended finite element method (XFEM) has emerged as a valid alternative to remeshing for crack propagation problems and is now employed with success for three dimensional crack propagation analysis of complex structures. The basic idea of the XFEM is to add special functions to describe the crack kinematics within the finite elements, so as to avoid the need for a conforming mesh. To introduce the discontinuity, discontinuous functions are added; to help capture the singularity, near-tip fields from the Westergaard asymptotic expansion are used.

Recently, strain smoothing has appeared in the finite element literature and resulted in the discovery of the smoothed FEM (SFEM) [1]. The idea is to write the strain field as a spatial average of the compatible strains and use this smoothed strain to obtain the element stiffness matrix. This enables the use of polygonal and very distorted meshes and was shown to yield locking-free results for incompressible two and three-dimensional elasticity, elasto-plasticity, plate and shells.

In this paper, we combine strain smoothing to the XFEM to obtain the smoothed XFEM (SmXFEM), which shares properties from both the SFEM and XFEM. The integration of the XFEM weak form is performed on the boundary of the split elements, which should simplify implementation, help deal with distorted meshes and arbitrary polygonal meshes. We study the convergence properties of the SmXFEM through two-dimensional linear elastic fracture mechanics examples, which indicate the potential of the proposed approach.

G.R. Liu, K.Y. Dai, T.T. Nguyen, "A smoothed finite element method for mechanics problems", Computat. Mech., 39, 859-877, 2007. doi:10.1007/s00466-006-0075-4

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