Variational Analysis of the Coupling Between a Geometrically Exact Cosserat Rod and an Elastic Continuum

Please always quote using this URN: urn:nbn:de:0296-matheon-11695
  • 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.

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Author:Oliver Sander, Anton Schiela
Referee:Ralf Kornhuber
Date of first Publication:2012/09/28
Institute:Research Center Matheon
Freie Universit├Ąt Berlin
Technische Universit├Ąt Berlin
Zuse Institute Berlin (ZIB)
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B20 Nonlinear elasticity
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Kxx Thin bodies, structures / 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
Preprint Number:984

$Rev: 13581 $