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

B. H. Nguyen, H. D. Tran, C. Anitescu, X. Zhuang, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)


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 languageEnglish
Pages (from-to)252-275
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2016 Jul 1
Externally publishedYes


  • Crack
  • Isogeometric analysis
  • Weakly singular

ASJC Scopus subject areas

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


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