Extensions and Refinements

Analytical solutions are derived for a concentrated force and a concentrated displacement discontinuity in both isotropic and orthotropic linearly elastic half-planes. These solutions can be used to generalize the boundary element methods developed previously for an infinite region to the case of a semi-infinite region with a traction-free boundary. It is also shown how the solution for a concentrated force in an isotropic half-plane can be extended to the case of bonded half-planes with continuity of displacements and tractions across the common boundary. Other topics in this chapter include: anti-plane strain; piecewise homogeneous regions; an alternate development of the displacement discontinuity method using Volterra’s formulas; a direct boundary integral method based on Somigliana’s traction formula; the dual boundary element method; special displacement discontinuity elements for crack tips; and crack growth simulation. Finally, a simplified Galerkin formulation of the displacement discontinuity method is provided to show how the system of algebraic equations can be written in terms of the displacement discontinuities at the element endpoints rather than at collocation points, even though the stresses are strongly singular at the endpoints.