Inhalt des Dokuments
Preprint 32-2012
Variational Analysis of the Coupling Between a Geometrically Exact Cosserat Rod and an Elastic Continuum
Author(s) :
Oliver Sander
,
Anton Schiela
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 32-2012
MSC 2000
- 74K10 Rods
-
74B20 Nonlinear elasticity
Abstract :
We formulate the static mechanical coupling of a geometrically exact Cosserat rod
to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have
to connect a one-dimensional model with director variables to a three-dimensional
model without directors.
Two alternative coupling conditions are proposed,
which correspond to two different configuration trace spaces.
For both we show existence of solutions of the coupled problems, using the direct
method of the calculus of variations. From the first-order optimality conditions
we also derive the corresponding conditions for the dual variables. These are
then interpreted in mechanical terms.
Keywords :
coupling conditions, energy minimization, Cosserat rod, hyperelastic material