Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard 6 th European ATC Turin, April 22-24, 2013 Alternative Model Order Reduction in Elastic Multibody Systems Philip Holzwarth, Peter Eberhard
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Alternative Model Order Reduction in Elastic Multibody Systems
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Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard
6th European ATC
Turin, April 22-24, 2013
Alternative Model Order Reduction in
Elastic Multibody Systems
Philip Holzwarth, Peter Eberhard
Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard
Example: FE Structure
FEM-model of a structure
11873 nodes 4986 elements
about 35000 elastic degrees of freedom
goal is control
lower plate assumed to be rigid
modelled as point mass
connected with CERIG command to rods
hole in upper plate is interface to remaining part
of the structure
modelled with spider web of beams
diameter 1 mm
Young's modulus 1018 N/m2
density 100 kg/m3
Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard
Comparison with Modal
Reduction F
FE
F
F
)(
)(
)(
)()()(
H
H
H
HH
21
2
1
21
2
1 F
d)(
d)(
Q2
2
E
H
H
Q
Krylov (173) 2.06 10-7
Krylov+gram
(35/173)
5.16 10-6
POD (36/24) 2.64 10-5
modal (40) 7.27 10-3
alternative reduction methods
show better results
Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard
Outline
motivation
model order reduction in elastic MBS – Why is this an
important step to obtain a good model?
different methods to obtain reduced flexible bodies
examples
large systems (industrial application)
software package Morembs
summary
Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard
Basis of Elastic
Multibody Systems multibody system
elastic body
discretization
finite element,
finite difference,
...
continuum
elastic multibody system
rigid body
bearings and
coupling elements p bodies
f degrees of freedom
q reaction force
C
reduction of the
elastic degrees
of freedom
models are getting larger
and more detailed
many degrees of freedom
FE-models have to be reduced
with the floating frame of reference
formulation linear model order
reduction is possible
Institute of Engineering and Computational Mechanics University of Stuttgart, Germany Prof. Dr.-Ing. Prof. E.h. Peter Eberhard