Anti-plane States in an Anisotropic Elastic Body Containing an Elliptical Hole

Abstract

One considers an unbounded, anisotropic elastic body containing an elliptical hole free from external loads but loaded by shear stresses far from the hole. The anti-plane equilibrium of the anisotropic elastic body is determined by using the complex representation of the anti-plane elastic states and the conformal mapping technique. The solution is obtained in compact, elementary form. One verifies by direct calculus that the obtained solution satisfies all boundary conditions. When the smaller semiaxis of the elliptical hole tends to zero; i.e. the hole becomes the classical Griffith-Irwin crack; the potential obtained for the elliptic hole case tends then to that obtained for the classical crack problem by solving the corresponding Riemann-Hilbert problem.