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Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane
Author(s) -
Mogilevskaya S. G.,
Rothenburg L.,
Dusseault M. B.
Publication year - 2000
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/1096-9853(200010)24:12<947::aid-nag106>3.0.co;2-4
Subject(s) - piecewise , boundary (topology) , mathematics , plane (geometry) , mathematical analysis , geometry , homogeneous , boundary element method , boundary value problem , polynomial , finite element method , structural engineering , engineering , combinatorics
The complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is verified through comparison with known semi‐analytical and numerical solutions that involve interaction between a circular opening and specific systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole. Copyright © 2000 John Wiley & Sons, Ltd.