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.
JIANG Feng (姜锋), SHEN Yongxing* (沈泳星)
. Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems[J]. Journal of Shanghai Jiaotong University(Science), 2018
, 23(1)
: 158
-165
.
DOI: 10.1007/s12204-018-1921-1
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