Maintianing solution invariants in the numerical solution of ODEs
SIAM Journal on Scientific and Statistical Computing
On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach
Computer Methods in Applied Mechanics and Engineering
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
SIAM Journal on Scientific Computing
CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
ACM SIGGRAPH 2008 papers
| Hi-index | 0.00 |
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.