Compensating Role Self-Balanced Stress Fields in Constructing Nonsingular Solutions Using a Non-Euclidean Model of a Continuous Medium for an Incompressible Sphere
M. A. Guzev1,2, W. Liu3, Ch. Qi3, E. P. Riabokon2
1Institute of Applied Mathematics, Far-Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia
2Perm National Research Polytechnic University, Perm, 614990, Russia
3Beijing University of Civil Engineering and Architecture, Beijing, 100044, China
Keywords: inconsistency condition, non-Euclidean continuous model, singularities, self-balanced stress field
Abstract
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.
DOI: 10.1134/S0021894421050047
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