The deformators of high ranks and the kröner incompatibility tensors with two-dimensional structure of subscripts

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.