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Journal of Shanghai Jiaotong University (Science)

, Volume 23, Issue 1, pp 158–165 | Cite as

Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems

  • Feng Jiang (姜 锋)
  • Yongxing Shen (沈泳星)
Article

Abstract

The displacement discontinuity method (DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue, enlightened by the mapped finite element method (FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM (MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.

Key words

displacement discontinuity method (DDM) singularity auxiliary map convergence rate Hadamard finite part 

CLC number

O 241.82 

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Copyright information

© Shanghai Jiaotong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Feng Jiang (姜 锋)
    • 1
    • 2
  • Yongxing Shen (沈泳星)
    • 1
    • 2
  1. 1.State Key Laboratory of Metal Matrix CompositesShanghai Jiao Tong UniversityShanghaiChina
  2. 2.University of Michigan - Shanghai Jiao Tong University Joint InstituteShanghai Jiao Tong UniversityShanghaiChina

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