Mixed boundary-value problems of two-dimensional anisotropic elasticity with perturbed boundaries

The mixed boundary-value problems of two-dimensional anisotropic elasticity are considered in this paper. The boundary treated may be the one perturbed by a straight line or an ellipse. A general solution up to the first-order perturbation has been found by using Stroh's formalism, analytical continuation method, conformal mapping function, and perturbation technique. As to higher-order perturbation solutions, general procedure is depicted in this paper. In order to illustrate the use of general solution, two typical examples are solved completely. One is a cosine wave-shaped surface indented by a rigid flat-ended punch, the other is a triangular hole boundary indented by a rigid stamp.