Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum

Publikationstyp
Journal Article
Date Issued
2013-12-19
Sprache
English
Author(s)
Sander, Oliver  
Schiela, Anton  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/7049
Journal
Zeitschrift für angewandte Mathematik und Physik  
Volume
65
Issue
6
Start Page
1261
End Page
1288
Citation
Zeitschrift fur Angewandte Mathematik und Physik 6 (65): 1261-1288 (2013)
Publisher DOI
10.1007/s00033-013-0389-y
Scopus ID
2-s2.0-84920252421
Publisher
Springer International Publishing AG
© 2013, Springer Basel. 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.
DDC Class
510: Mathematik