Numerical Integration Technique in Computation of Extended Finite Element Method

Abstract:

The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and reserves all merits of CFEM. In other side, it needs not mesh repartition to geometric and physical interface. Numerical integration techniques of the XFEM computation are studied, including displacement mode of the XFEM, control equation and infirm solution form of discontinuous medium mechanics problem, region scatteration, element integral strategy.

• Periodical: Advanced Materials Research (Volumes 446-449)
• Pages: 3557-3560
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.446-449.3557
• Online since: January 2012
• Authors: Feng Wang, Di Zhang, Jing Yu, Hui Xu
• Keywords: Crack, Discontinuous Problem, Extended Finite Element Method (XFEM), Gauss Integral, Numerical Simulation

References

[1] Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 46: 131-150.

DOI: 10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j

[2] Daux C, Moes N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method [J]. International Journal for Numerical Methods in Engineering, 2000, 48: 1741-1760.

DOI: 10.1002/1097-0207(20000830)48:12<1741::aid-nme956>3.0.co;2-l

[3] Sukumar N, Moes N, Moran B, Belytschko T. Extended finite element method for three-dimensional crack modeling [J]. International Journal for Numerical Methods in Engineering, 2000, 48:1549-1570.

DOI: 10.1002/1097-0207(20000820)48:11<1549::aid-nme955>3.0.co;2-a

[4] Stolarska M, Chopp D L, Moes N, Belytschko T. Modeling crack growth by level sets in the extended finite element method [J]. International Journal for Numerical Methods in Engineering, 2001, 51:943-960.

DOI: 10.1002/nme.201

[5] Moes N, Gravouil A, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model [J]. International Journal for Numerical Methods in Engineering, 2002, 53:2549-2568.

DOI: 10.1002/nme.429

[6] Gravouil A, Moes N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets-Part II: Level set update [J]. International Journal for Numerical Methods in Engineering, 2002, 53:2569-2586.

DOI: 10.1002/nme.430

[7] YU Tian-tang. Numerical aspects of the extended finite element method [J]. Rock and Soil Mechanics, 2007, 28: 305-310. (In Chinese)

[8] XIA Xiao-zhou. The Meso Numerical Simulation and the Macro-meso Mechanics Research for Concrete Material [D]. Nanjing: Hohai University PhD Dissertation, 2007. (In Chinese)