TY - GEN

T1 - The smoothed extended finite element method

AU - Natarajan, S.

AU - Bordas, S.

AU - Minh, Q. D.

AU - Nguyen, H. X.

AU - Rabczuk, T.

AU - Cahill, L.

AU - McCarthy, C.

PY - 2008

Y1 - 2008

N2 - This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM.

AB - This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM.

KW - Cracks without remeshing

KW - Extended finite element method

KW - Fracture mechanics

KW - Partition of unity methods

KW - Smoothed finite element method

KW - Strain smoothing

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M3 - Conference contribution

AN - SCOPUS:84858402789

SN - 9781905088249

T3 - Proceedings of the 6th International Conference on Engineering Computational Technology

BT - Proceedings of the 6th International Conference on Engineering Computational Technology

T2 - 6th International Conference on Engineering Computational Technology, ECT 2008

Y2 - 2 September 2008 through 5 September 2008

ER -