TY - RPRT
A1 - Lang, H.
A1 - Arnold, M.
T1 - Numerical aspects in the dynamic simulation of geometrically exact rods
N2 - 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 parametrised by unit quaternions, the space discretisation results in differential-algebraic 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 speed-up 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.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 179
KW - Kirchhoff and Cosserat rods
KW - geometrically exact rods
KW - deformable bodies
KW - multibody dynamics
KW - artial differential algebraic equations
Y1 - 2009
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2202
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-16443
ER -