Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems
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. , 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 wordsdisplacement discontinuity method (DDM) singularity auxiliary map convergence rate Hadamard finite part
CLC numberO 241.82
Unable to display preview. Download preview PDF.
- TAO Q, EHLIG-ECONOMIDES C A, GHASSEMI A, et al. Investigation of stress-dependent fracture permeability in naturally fractured reservoirs using a fully coupled poroelastic displacement discontinuity model [C]//SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana: Society of Petroleum Engineers, 2009: 1–4.Google Scholar
- HADAMARD J. Lectures on Cauchy’s problem in linear partial differential equations [M]. New Haven: Yale University Press, 1925.Google Scholar
- GONNET P. Adaptive quadrature re-revisited [D]. Zurich: Department of Computer Science, Swiss Federal Institute of Technology, 2009.Google Scholar