- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (6)
- Authors
- Guzev, Mikhail A.; Riabokon, Evgenii P.
- Contact information
- Guzev, Mikhail A.: Perm National Research Polytechnic University Perm, Russian Federation; Institute for Applied Mathematics Far Eastern Branch of the Russian Academy of Sciences Vladivostok, Russian Federation; OCRID: 0000-0001-9344-154X; Riabokon, Evgenii P.: Perm National Research Polytechnic University Perm, Russian Federation; OCRID: 0000-0003-0555-3977
- Keywords
- nonsingular stress field; planar deformation; microstructure; spectral biharmonic equation
- Abstract
A material with a microstructure is considered. A material is described on the basis of a non-Euclidean model of a continuous medium. In equilibrium, the total stress field is represented as the sum of elastic and self-balanced stresses, the parameterization of which is given through the scalar curvature of the Ricci tensor. It is proposed to use the spectral biharmonic equation to calculate the scalar curvature. Using the example of a plane strain state of a material, it is shown that the amplitude coefficients of elastic and self-balanced fields can be chosen so that singularities of the same type compensate each other in the full stress field
- Pages
- 815–821
- DOI
- 10.17516/1997-1397-2021-14-6-815-821
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/144765
Journal of Siberian Federal University. Mathematics & Physics / Construction of Nonsingular Stress Fields for Non-Euclidean Model in Planar Deformations
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