Boundary value problems of two-dimensional anisotropic body with a parabolic boundary

Based upon Stroh formalism we derive a novel and convenient scheme for determining the elastic fields of a two-dimensional anisotropic body with a parabolic boundary subject to two kinds of boundary conditions, which are free surface and rigid surface, respectively. The corresponding Green's functions are found by using the conformal mapping method. When the parabolic curve degenerates into a half-infinite crack or rigid inclusion, the singular stress fields near the tip of defects ark obtained. In particular, those Green's functions for a concentrated moment M(0) applied at a point on the parabolic curve are also studied. It is easily found that arbitrary parabolic boundary value problems can be solved by using these Green's functions and associate integrals.