Line Singularity inside an Elliptic Inhomogeneity

The problem of an elliptic insert with a point of elastic singularity and a perfectly adhering interface is solved using the complex variable method. In particular, it is found that the remote field is insensitive to the inhomogeneity shape and interface status. Unified formulae for the special cases of free elliptic disk and rigid matrix are written and discussed. A closed form solution for an arbitrary line singularity inside a circular inhomogeneity is also derived as a special case.