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Dislocation and point‐force‐based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions
Author(s) -
Denda M.,
Kosaka I.
Publication year - 1997
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/(sici)1097-0207(19970815)40:15<2857::aid-nme195>3.0.co;2-3
Subject(s) - boundary element method , stress intensity factor , mathematical analysis , mathematics , boundary value problem , boundary knot method , traction (geology) , boundary (topology) , dislocation , finite element method , physics , geology , condensed matter physics , geomorphology , thermodynamics
In this paper we give the theoretical foundation for a dislocation and point‐force‐based approach to the special Green's function boundary element method and formulate, as an example, the special Green's function boundary element method for elliptic hole and crack problems. The crack is treated as a particular case of the elliptic hole. We adopt a physical interpretation of Somigliana's identity and formulate the boundary element method in terms of distributions of point forces and dislocation dipoles in the infinite domain with an elliptic hole. There is no need to model the hole by the boundary elements since the traction free boundary condition there for the point force and the dislocation dipole is automatically satisfied. The Green's functions are derived following the Muskhelishvili complex variable formalism and the boundary element method is formulated using complex variables. All the boundary integrals, including the formula for the stress intensity factor for the crack, are evaluated analytically to give a simple yet accurate special Green's function boundary element method. The numerical results obtained for the stress concentration and intensity factors are extremely accurate. © 1997 John Wiley & Sons, Ltd.