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

doi:10.1007/s12204-018-1921-1

Abstract

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

摘要： 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.

关键词: displacement discontinuity method (DDM)| singularity| auxiliary map| convergence rate| Hadamard finite part

CLC Number:

O 241.82

JIANG Feng (姜锋), SHEN Yongxing* (沈泳星). Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems[J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(1): 158-165.

References

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