Indentation problems of two-dimensional anisotropic thermoelasticity with perturbed boundaries

Complex variable representations in the Stroh formalism are used to analyze the problem of rigid stamp indentation on an irregularly shaped surface of an anisotropic thermoelastic body. The shape of boundary surface considered in this work includes a cosine wave-shaped surface and a triangular hole that are assumed to be slightly different from a straight line and an ellipse, respectively, for which the exact solutions exist. Based on a perturbation technique, an approximate solution for the punch problem of rigid stamp indentation on a wave-shaped surface or a triangular hole that is viewed as being perturbed from a straight line or an elliptical hole is provided. First-order perturbation solutions for both temperature and stress functions are given explicitly. Numerical results of contact stress under the punch face are discussed in detail and shown in graphic form.