Explicit Analytic Solution for the Plane Elastostatic Problem with a Rigid Inclusion of Arbitrary Shape Subject to Arbitrary Far-Field Loadings

We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with rigid inclusion. Our analysis is based on boundary integral formulation of elastostatic problem and geometric function theory. Specifically, we use coordinate system provided by exterior conformal mapping inclusion to define density basis functions inclusion, Faber polynomials associated inside The latter, which constitutes main novelty our approach, allows us obtain explicit series plane arbitrary shape terms given far-field loading.