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An efficient dual boundary element technique for a two‐dimensional fracture problem with multiple cracks
Author(s) -
Chen W. H.,
Chen T. C.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620381009
Subject(s) - boundary element method , traction (geology) , mathematics , discretization , integral equation , mathematical analysis , displacement (psychology) , boundary (topology) , geometry , finite element method , quadratic equation , body force , boundary value problem , volume integral , structural engineering , mechanics , physics , engineering , mechanical engineering , psychology , psychotherapist
An efficient dual boundary element technique for the analysis of a two‐dimensional finite body with multiple cracks is established. In addition to the displacement integral equation derived for the outer boundary, since the relative displacement of the crack surfaces is adopted in the formulation, only the traction integral equation is established on one of the crack surfaces. For each crack, a virtual boundary is devised and connected to one of the crack surfaces to construct a closed integral path. The rigid body translation for the domain enclosed by the closed integral path is then employed for evaluating the hypersingular integral. To solve the dual displacement/traction integral equations simultaneously, the constant and quadratic isoparametric elements are taken to discretize the closed integral paths/crack surfaces and the outer boundary, respectively. The present method has distinct computational advantages in solving a fracture problem which has arbitrary numbers, distributions, orientations and shapes of cracks by a few boundary elements. Several examples are analysed and the computed results are in excellent agreement with other analytical or numerical solutions.