New numerical quadrature of integrand with singularity of 1/r and its application

被引：3
作者：
Xu, Dongdong [1 ]
Zheng, Hong [1 ]
Xia, Kaiwen [2 ]
机构：
[1] Chinese Acad Sci, Inst Rock & Soil Mech, State Key Lab Geomech & Geotech Engn, Wuhan, Peoples R China
[2] Univ Toronto, Dept Civil Engn, Toronto, ON, Canada
来源：
ADVANCES IN COMPUTATIONAL MODELING AND SIMULATION, PTS 1 AND 2 | 2014年 / 444-445卷
基金：
中国国家自然科学基金;
关键词：
NMM; stress intensity factor; Duffy transformation; 1/r singularity; FINITE-ELEMENT-METHOD; STATIC CRACK-GROWTH; MANIFOLD METHOD; IMPLEMENTATION; PARTITION;
D O I：
10.4028/www.scientific.net/AMM.0.641
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
A new quadrature method is proposed for numerical integration of integrands with the singularity of 1/r occurring at the computation of stiffness matrix when a singular physical cover is introduced to the numerical manifold method (NMIVI) for linear fracture problems. The detailed proof is presented, which shows the Jacobian has a factor of r that can be used to eliminate the singularity. Compared with the Duffy transformation, it proves more simple and easier to implement while owning the same precision. A numerical example in elastic fracture by the NMM is presented to illustrate the performance of the proposed method. The result has a good agreement with the reference solution.
引用
收藏
页码：641 / +
页数：3
相关论文
共 23 条
  • [1] [Anonymous], 1992, ROCK MECH P 33 S S
  • [2] Babuska I, 1997, INT J NUMER METH ENG, V40, P727, DOI 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO
  • [3] 2-N
  • [4] ELEMENT-FREE GALERKIN METHODS
    BELYTSCHKO, T
    LU, YY
    GU, L
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1994, 37 (02) : 229 - 256
  • [5] Chinese Aeronautical Establishment, 1993, HDB STRESS INT FACT
  • [6] Daux C, 2000, INT J NUMER METH ENG, V48, P1741, DOI 10.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO
  • [7] 2-L
  • [8] QUADRATURE OVER A PYRAMID OR CUBE OF INTEGRANDS WITH A SINGULARITY AT A VERTEX
    DUFFY, MG
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (06) : 1260 - 1262
  • [9] Fairweather G., 1979, Advances in Computer Methods for Partial Differential Equations - III, P331
  • [10] Modeling quasi-static crack growth with the extended finite element method Part II:: Numerical applications
    Huang, R
    Sukumar, N
    Prévost, JH
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2003, 40 (26) : 7539 - 7552
123