Affiliation:
1. Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Str. 9, 45127 Essen, Germany
Abstract
We show under some natural smoothness assumptions that pure in-plane drill rotations as deformation mappings of a
C
2
-smooth regular shell surface to another one parametrized over the same domain are impossible provided that the rotations are fixed at a portion of the boundary. Put otherwise, if the tangent vectors of the new surface are obtained locally by only rotating the given tangent vectors, and if these rotations have a rotation axis which coincides everywhere with the normal of the initial surface, then the two surfaces are equal provided they coincide at a portion of the boundary. In the language of differential geometry of surfaces, we show that any isometry which leaves normals invariant and which coincides with the given surface at a portion of the boundary is the identity mapping.
Funder
DFG, German Research Foundation
Subject
General Physics and Astronomy,General Engineering,General Mathematics
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