A note on the application of the flamant solution of classical elasticity to circular domains

It is a well known fact that the Flamant solution of classical elasticity cannot be used at an interior point of an elastic body since the resulting displacement field would be multivalued. In this note we demonstrate that the solution to the problem of a concentrated force at a point on an interior circular boundary has a multivalued displacement component but that the exclusion of the point of application of the load from the domain renders the displacement field single-valued everywhere.