Theoretical foundations were provided for a dislocation and point-force based approach to special Green's function boundary element methods. The example given was the special Green's function boundary element method for elliptical hole and crack problems. The crack was treated as being a particular case of the elliptical hole. A physical interpretation of Somigliana's identity was given, and the boundary element method was formulated in terms of distributions of point forces and dislocation dipoles in an infinite domain containing an elliptic hole. There was no need to model the hole by using boundary elements, since the traction-free boundary condition for the point force and dislocation dipole was automatically satisfied. The Green's functions were derived using the Muskhelishvili complex variable formalism, and the boundary element method was formulated using complex variables. All of the boundary integrals, including the formula for the stress intensity factor of the crack, were evaluated analytically in order to give a simple yet accurate special Green's function boundary element method. The numerical results which were obtained for the stress concentration and intensity factors were extremely accurate.

Dislocation and Point-Force Based Approach to the Special Green's Function Boundary Element Method for Elliptic Hole and Crack Problems in Two Dimensions. M.Denda, I.Kosaka: International Journal for Numerical Methods in Engineering, 1997, 40, 2857-89