Polygonal holes in anisotropic media

Based upon the solutions obtained by using Stroh's formalism, a general and simplified formula for polygonal holes in anisotropic media is provided in this paper. The polygon used here is a generalized terminology which covers ellipses, polygons and their geometric limits. For some special holes such as ellipses, circles, cracks, triangles, ovals and squares, a further simplified solution is derived. The validity of these formulae is then discussed based on the satisfaction of conformal mapping requirement. The results show that the solutions are exact for (1) anisotropic media containing elliptic holes or cracks, and (2) isotropic media containing general polygonal holes. For general anisotropic media with polygonal holes, the solutions are well approximated if the critical points of the mapping functions are far away from the holes.