Abstract:
A representation for singularities in the zero and first harmonics 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 singular contribution of the zero and first harmonics of the non-classical stress field is
calculated. The requirement of regular behavior of the internal stress field allowed to compensate for the singularity
in the elasticity theory solution by choosing a singularity of the non-classical stress field.
Key words:Airy stress function, non-Euclidean model of a continuous medium, deformation incompatibility.
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