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
UR - http://www.scopus.com/inward/record.url?scp=84858402789&partnerID=8YFLogxK
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 -