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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

Keywords: smoothed finite element method, extended finite element method, strain smoothing, partition of unity methods.

Summary

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.

References

1: 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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 89 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY 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 doi:10.4203/ccp.89.20 purchase the full-text of this paper 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. Summary 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. References 1 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 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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