Reference : On the Smoothed eXtended Finite Element Method for Continuum
Scientific congresses, symposiums and conference proceedings : Unpublished conference
Engineering, computing & technology : Aerospace & aeronautics engineering
Computational Sciences
On the Smoothed eXtended Finite Element Method for Continuum
Natarajan, Sundararajan []
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Rabczuk, Timon []
Guo, Zaoyang []
17th. UK Conference on Computational Mechanics (ACME-UK)
6-8 April 2009
[en] Strain smoothing ; XFEM ; Smoothed extended finite element method ; numerical integration
[en] In this paper, we combine the strain smoothing technique proposed by Liu et al [1] coined as the smoothed finite element method (SFEM) to partition of unity methods, namely the extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM) [3]. SmXFEM shares properties both with the SFEM and the XFEM. The proposed method eliminates the need to compute and integrate the derivatives of shape functions (which are singular at the tip for linear elastic fracture mechanics). The need for isoparametric mapping is eliminated because the integration is done along the boundary of the finite element or smoothing cells, which allows elements of arbitrary shape. We present numerical results for various differential equations that have singularity or steep gradient at the boundary. The method is verified on several examples and comparisons are made to the conventional XFEM.
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