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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Numerical aspects in the dynamic simulation of geometrically exact rods
 Verwer, J.G.: Selected papers from NUMDIFF12 : 12th Seminar on Numerical Solution of Differential and DifferentialAlgebraic Equations, 4  18 September 2009, Halle, Germany Amsterdam: Elsevier, 2012 (Applied numerical mathematics 62.2012, Nr.10) ISSN: 01689274 S.14111427 
 Seminar on Numerical Solution of Differential and DifferentialAlgebraic Equations (NUMDIFF) <12, 2009, Halle> 

 Englisch 
 Konferenzbeitrag 
 Fraunhofer ITWM () 
Abstract
Classical geometrically exact Kirchhoff and Cosserat models are used to study the nonlinear deformation of rods. Extension, bending and torsion of the rod may be represented by the Kirchhoff model. The Cosserat model additionally takes into account shearing effects. Second order finite differences on a staggered grid define discrete viscoelastic versions of these classical models. Since the rotations are parametrisecl by unit quaternions, the space discretisation results in differentialalgebraic equations that are solved numerically by standard techniques like index reduction and projection methods. Using absolute coordinates, the mass and constraint matrices are sparse and this sparsity may be exploited to speedup time integration. Further improvements are possible in the Cosserat model, because the constraints are just the normalisation conditions for unit quaternions such that the null space of the constraint matrix can be given analytically. The results of the theoretical investigations are illustrated by numerical tests.