Compensating role self-balanced stress fields in constructing nonsingular solutions using a non-Euclidean model of a continuous medium for an incompressible sphere

A self-balanced stress field for an incompressible sphere is constructed based on a non-Euclidean model of a continuous medium. The total stress field is presented as the sum of the elastic and self-balanced fields. The requirement that there are no singular contributions to the stress field leads to the fact that the coefficients at the singularities of the elastic and self-balanced stress fields can be related by a linear transformation, ensuring the removal of singularities. The compensating role of self-balanced stress fields allows one to construct a nonsingular equilibrium stress field for a spherically symmetric state of a continuous medium.