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

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.

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Correspondence to Yongxing Shen.

Additional information

Foundation item: the National Natural Science Foundation of China (No. 11402146), and the Young 1 000 Talent Program of China

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Jiang, F., Shen, Y. Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems. J. Shanghai Jiaotong Univ. (Sci.) 23, 158–165 (2018). https://doi.org/10.1007/s12204-018-1921-1

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  • DOI: https://doi.org/10.1007/s12204-018-1921-1

Key words

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

CLC number

  • O 241.82