The deformators of high ranks and the kröner incompatibility tensors with two-dimensional structure of subscripts
- Authors: Georgievskii D.V.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 486, No 4 (2019)
- Pages: 430-432
- Section: Mechanics
- URL: https://journals.eco-vector.com/0869-5652/article/view/14445
- DOI: https://doi.org/10.31857/S0869-56524864430-432
- ID: 14445
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Abstract
In n-dimensional space (multidimensional continuum) the compatibility equations are derived for the components of the generalized deformators of rank m which are connected with the generalized displacements of rank m - 1 by analogues of the Cauchy kinematic relations (m≥1, n≥2). They may be written in form of equal to zero for all the components of the incompatibility tensor of rank m(n - 2) or for dual to it the generalized Riemann-Christoffel tensor of rank 2m. The number of independent components of these tensors coinciding with the number of compatibility equations in terms of the generalized deformations, is obtained.
About the authors
D. V. Georgievskii
Lomonosov Moscow State University
Author for correspondence.
Email: georgiev@mech.math.msu.su
Russian Federation, 1, Leninskie gory, Moscow, 119991
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