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Main Title: Variational Analysis of the Coupling Between a Geometrically Exact Cosserat Rod and an Elastic Continuum
Author(s): Sander, Oliver
Schiela, Anton
Type: Research Paper
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.
Subject(s): coupling conditions
energy minimization
Cosserat rod
hyperelastic material
Issue Date: 28-Sep-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 74K10 Rods
74B20 Nonlinear elasticity
49K20 Problems involving partial differential equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 32
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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