Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. A second order semidiscrete Cosserat rod model suitable for dynamic simulations in real time
 Simos, T.E. ; European Society of Computational Methods in Sciences and Engineering ESCMSE: Numerical analysis and applied mathematics. International Conference on Numerical Analysis and Applied Mathematics 2009. Vol.2 : Rethymno, Crete, Greece, 18  22 September 2009 New York, N.Y.: AIP Press, 2009 (AIP Conference Proceedings 1168) ISBN: 9780735407084 ISBN: 9780735407091 ISSN: 0094243X pp.10571060 
 International Conference on Numerical Analysis and Applied Mathematics (ICNAAM) <2009, Rethymno/Crete> 

 English 
 Conference Paper 
 Fraunhofer ITWM () 
Abstract
We present an alternative approach for a semidiscrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semidiscrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The righthand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.