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We provide an analytical solution for the elastic fields in a two-dimensionalunbounded isotropic body with a rigid inclusion. Our analysis is based on theboundary integral formulation of the elastostatic problem and geometricfunction theory. Specifically, we use the coordinate system provided by theexterior conformal mapping of the inclusion to define a density basis functionson the boundary of the inclusion, and we use the Faber polynomials associatedwith the inclusion for a basis inside the inclusion. The latter, whichconstitutes the main novelty of our approach, allows us to obtain an explicitseries solution for the plane elastostatic problem for an inclusion ofarbitrary shape in terms of the given arbitrary far-field loading.

Explicit analytic solution for the plane elastostatic problem with a rigid inclusion of arbitrary shape subject to arbitrary far-field loadings