Singularity Removal in the Elasticity Theory Solution Based on a Non-Euclidean Model of a Continuous Medium

A representation for singularities of the classical elastic stress field was obtained using the Airy stress function for a plane-strained state of a continuous medium. For a non-Euclidean model of a continuous medium, the structure of the internal stress field of a plane-strained state was shown to consist of a classical elastic stress field and a non-classical stress field determined through the incompatibility function of deformations. The requirement for the absence of singularities in the internal stress field allowed to compensate for the singularity in the elasticity theory solution for the zero harmonic by choosing a singularity of the non-classical stress field.