Removal of the stress field singularity for the Williams problem (1952) basing on a non-Euclidean continuum model

A singular solution for the elastic stress field in the Williams problem on the equilibrium of plates with corner cutouts is considered. A scheme has been constructed for the minimal expansion of the classical elastic continuum model without taking into account the Saint-Venant compatibility conditions for deformations, which leads to a non-Euclidean continuum model. Within this model framework, the total stress field is shown to contain no singularity for all cutout angles.