Restrictions on the singularity method applied to elasticity

The choice of which fundamental singular solutions to use as basis functions in the so-called singularity method applied to elasticity appears to be restricted by boundary condition types and region geometry. In practice, only the point load solution is consistently reliable but even it fails in certain instances when the elastic body is not a convex region and almost always when the region is not simply connected. Fortunately, all multiply connected regions can be partitioned into simply-connected (although not always convex) ones. A method for doing this is presented along with examples of fundamental solutions which do not work in the singularity method.