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Determination of coefficients of crack tip asymptotic fields by an element‐free Galerkin scaled boundary method
Author(s) -
HE Y. Q.,
YANG H. T.,
DEEKS A. J.
Publication year - 2012
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/j.1460-2695.2012.01662.x
Subject(s) - finite element method , boundary (topology) , galerkin method , boundary knot method , boundary element method , series (stratigraphy) , mathematical analysis , singular boundary method , boundary value problem , convergence (economics) , asymptotic expansion , mathematics , structural engineering , engineering , geology , paleontology , economic growth , economics
This study applies a new scaled boundary element‐free Galerkin (EFG) method to determine the coefficients of the Williams’ series expansion for the elastic crack tip asymptotic stress field. Scaled boundary methods can calculate the coefficients of Williams’ series without any special crack tip treatment. Unlike the conventional scaled boundary finite element method, in this paper an EFG approach is used in the circumferential direction of the scaled boundary model. The EFG method offers high accuracy, rapid convergence and smooth stress solutions without post‐processing, and no mesh generation is required. The proposed method is verified through numerical examples comparing the new approach with analytical, reference and conventional scaled boundary FEM solutions, and results are obtained which indicate that the new approach converges even more rapidly than the conventional scaled boundary finite element method.