### Abstract

The isogeometric analysis is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyze quasi-static elastic problems including crack problems in two-dimensional domains. This method takes the advantages from the common boundary representation of the isogeometric analysis and the boundary element method. The background of the developed method is to use non-uniform rational B-splines (NURBS) for the Galerkin approximation of both geometry and field variables (i.e.the displacement and traction on the boundary). The basic ingredient of the method is a pair of weakly-singular weak-form integral equations for the displacement and traction on the boundary. These integral equations contain at most weakly-singular kernels of ln. r, where r is the distance from a source point to a field point. Various numerical examples are examined to validate the accuracy and efficiency of the proposed method. A model of crack propagation is also discussed to illustrate the use of the method for crack growth simulation. Through the numerical examples, it is observed that the isogeometric SGBEM produces highly accurate results yet it is simple to implement.

Original language | English |
---|---|

Pages (from-to) | 252-275 |

Number of pages | 24 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 306 |

DOIs | |

Publication status | Published - 2016 Jul 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Crack
- Isogeometric analysis
- NURBS
- SGBEM
- Weakly singular

### ASJC Scopus subject areas

- Computer Science Applications
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)

### Cite this

*Computer Methods in Applied Mechanics and Engineering*,

*306*, 252-275. https://doi.org/10.1016/j.cma.2016.04.002

**An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems.** / Nguyen, B. H.; Tran, H. D.; Anitescu, C.; Zhuang, X.; Rabczuk, Timon.

Research output: Contribution to journal › Article

*Computer Methods in Applied Mechanics and Engineering*, vol. 306, pp. 252-275. https://doi.org/10.1016/j.cma.2016.04.002

}

TY - JOUR

T1 - An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems

AU - Nguyen, B. H.

AU - Tran, H. D.

AU - Anitescu, C.

AU - Zhuang, X.

AU - Rabczuk, Timon

PY - 2016/7/1

Y1 - 2016/7/1

N2 - The isogeometric analysis is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyze quasi-static elastic problems including crack problems in two-dimensional domains. This method takes the advantages from the common boundary representation of the isogeometric analysis and the boundary element method. The background of the developed method is to use non-uniform rational B-splines (NURBS) for the Galerkin approximation of both geometry and field variables (i.e.the displacement and traction on the boundary). The basic ingredient of the method is a pair of weakly-singular weak-form integral equations for the displacement and traction on the boundary. These integral equations contain at most weakly-singular kernels of ln. r, where r is the distance from a source point to a field point. Various numerical examples are examined to validate the accuracy and efficiency of the proposed method. A model of crack propagation is also discussed to illustrate the use of the method for crack growth simulation. Through the numerical examples, it is observed that the isogeometric SGBEM produces highly accurate results yet it is simple to implement.

AB - The isogeometric analysis is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyze quasi-static elastic problems including crack problems in two-dimensional domains. This method takes the advantages from the common boundary representation of the isogeometric analysis and the boundary element method. The background of the developed method is to use non-uniform rational B-splines (NURBS) for the Galerkin approximation of both geometry and field variables (i.e.the displacement and traction on the boundary). The basic ingredient of the method is a pair of weakly-singular weak-form integral equations for the displacement and traction on the boundary. These integral equations contain at most weakly-singular kernels of ln. r, where r is the distance from a source point to a field point. Various numerical examples are examined to validate the accuracy and efficiency of the proposed method. A model of crack propagation is also discussed to illustrate the use of the method for crack growth simulation. Through the numerical examples, it is observed that the isogeometric SGBEM produces highly accurate results yet it is simple to implement.

KW - Crack

KW - Isogeometric analysis

KW - NURBS

KW - SGBEM

KW - Weakly singular

UR - http://www.scopus.com/inward/record.url?scp=84964324857&partnerID=8YFLogxK

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U2 - 10.1016/j.cma.2016.04.002

DO - 10.1016/j.cma.2016.04.002

M3 - Article

AN - SCOPUS:84964324857

VL - 306

SP - 252

EP - 275

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -