### Abstract

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.

Original language | English |
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Title of host publication | Proceedings of the 6th International Conference on Engineering Computational Technology |

Publication status | Published - 2008 Dec 1 |

Externally published | Yes |

Event | 6th International Conference on Engineering Computational Technology, ECT 2008 - Athens, Greece Duration: 2008 Sep 2 → 2008 Sep 5 |

### Other

Other | 6th International Conference on Engineering Computational Technology, ECT 2008 |
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Country | Greece |

City | Athens |

Period | 08/9/2 → 08/9/5 |

### Fingerprint

### Keywords

- Cracks without remeshing
- Extended finite element method
- Fracture mechanics
- Partition of unity methods
- Smoothed finite element method
- Strain smoothing

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings of the 6th International Conference on Engineering Computational Technology*

**The smoothed extended finite element method.** / Natarajan, S.; Bordas, S.; Minh, Q. D.; Nguyen, H. X.; Rabczuk, Timon; Cahill, L.; McCarthy, C.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 6th International Conference on Engineering Computational Technology.*6th International Conference on Engineering Computational Technology, ECT 2008, Athens, Greece, 08/9/2.

}

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, Timon

AU - Cahill, L.

AU - McCarthy, C.

PY - 2008/12/1

Y1 - 2008/12/1

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

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

M3 - Conference contribution

SN - 9781905088249

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

ER -