Common errors on mapping of nonelliptic curves in anisotropic elasticity

For an isotropic elastic material under a two-dimensional plane-stress or plane-strain deformation that involves a closed boundary of a given geometry T, it is a common practice to use a conformal mapping to map T to a circle of unit radius. For an anisotropic elastic material. the mapping produces the correct solution to the physical problem when T is art ellipse. There are published land unpublished) papers that report solutions to anisotropic elasticity problems with a nonelliptic curve T. They all fail to solve the physical problem correctly. The purpose of this paper is to show the common errors made by many researchers, and to alert newcomers on the subject so that they do not fall into the same trap.