Publisher DOI: 10.1007/s00033-013-0389-y
Title: Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum
Language: English
Authors: Sander, Oliver 
Schiela, Anton 
Issue Date: 19-Dec-2013
Publisher: Springer International Publishing AG
Source: Zeitschrift fur Angewandte Mathematik und Physik 6 (65): 1261-1288 (2013)
Abstract (english): 
© 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.
URI: http://hdl.handle.net/11420/7049
ISSN: 1420-9039
Journal: Zeitschrift für angewandte Mathematik und Physik 
Institute: Mathematik E-10 
Document Type: Article
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