DISLOCATION AND POINT-FORCE-BASED APPROACH TO THE SPECIAL GREENS-FUNCTION BEM FOR ELLIPTIC HOLE AND CRACK PROBLEMS IN 2 DIMENSIONS

In this paper we give the theoretical foundation for a dislocation and point-force-based approach to the special Green's function boundary e lement method and formulate, as an example, the special Green's functi on boundary element method for elliptic hole and crack problems. The c rack is treated as a particular case of the elliptic hole. We adopt a physical interpretation of Somigliana's identity and formulate the bou ndary element method in terms of distributions of point forces and dis location dipoles in the infinite domain with an elliptic hole. There i s no need to model the hole by the boundary elements since the tractio n free boundary condition there for the point force and the dislocatio n dipole is automatically satisfied. The Green's functions are derived following the Muskhelishvili complex variable formalism and the bound ary element method is formulated using complex variables. All the boun dary integrals, including the formula for the stress intensity factor for the crack, are evaluated analytically to give a simple yet accurat e special Green's function boundary element method. The numerical resu lts obtained for the stress concentration and intensity factors are ex tremely accurate. (C) 1997 by John Wiley & Sons, Ltd.