Journal of Theoretical
and Applied Mechanics

41, 3, pp. 593-621, Warsaw 2003

Affine tensors in shell theory

Géry De Saxcé, Claude Vallee
Resultant force and moment are structured as a single object called the torsor. Excluding all metric notions, we define the torsors as skew-symmetric bilinear mappings operating on the linear space of the affine vector-valued functions. Torsors are a particular family of affine tensors. On this ground, we define an intrinsic differential operator called the affine covariant divergence. Next, we claim that the torsor field characterizing the behavior of a continuous medium is affine covariant divergence free. Applying this general principle to the dynamics of three-dimensional media, Euler's equations are recovered. Finally, we investigated more thoroughly the dynamics of shells. Using adapted coordinates, this general principle provides a consistent way to obtain new equations with non-expected terms involving Coriolis's effects and the time evolution of the surface.
Keywords: tensorial analysis; continuum mechanics; dynamics of shells