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Title: An on-line time dependent parametric model order reduction scheme with focus on dynamic stress recovery
Authors: Tamarozzi, Tommaso ×
Heirman, Gert H.K.
Desmet, Wim #
Issue Date: Jan-2014
Publisher: North-Holland Pub. Co.
Series Title: Computer Methods in Applied Mechanics and Engineering vol:268 pages:336-358
Abstract: In view of the tendency towards ever lighter and more powerful machines and even shorter design
cycles, it becomes essential to have virtual prototyping tools that allow for fast and reliable
numerical simulations. Current state-of-the-art structural dynamics and flexible multibody simulation
techniques usually involve the solution of matrix systems with thousands to millions of
variables. Model order reduction schemes are used to keep computational effort affordable at the
expense of a minimal loss of accuracy. These techniques typically face difficulties with systems
in which flexible bodies can be loaded in many degrees of freedom and rarely allow for accurate
local stress and strain evaluation. The present work proposes to address both issues for the particular
but frequent case of moving loads or boundary conditions. This behavior is found in most
of the contact problems and systems that include sliding components for which many loading or
boundary locations are possible but only a few of them are active at a certain moment in time.
The proposed scheme exploits a reduction vector space that continuously varies in time by means
of a parametric definition of the external load position. Contrary to the majority of the parametric
model order reduction schemes that allow mainly for quasi-static parametric variations, the
proposed approach can be used efficiently for time simulation of dynamically varying parametric
models. This is achieved by considering the implicit time dependency of the reduction vector
space using Galerkin projections or alternatively by direct substitution of the reduced kinetic
energy, potential energy and generalized forces in the Lagrange equations. It is shown, by developing
a consistent mathematical framework, that the price to pay for the very compact reduction
space obtained is the evaluation of some extra terms in the equations of motion. Numerical examples
are used to assess the accuracy of the proposed method. Results show the potential of
this strategy with particular focus on displacement and stress fields and furthermore highlight
its real-time potential. Moreover the developed framework together with the numerical results
allow for a deeper physical understanding of the complex phenomena related to this category of
time varying multiple-input/multiple output systems.
ISSN: 0045-7825
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Production Engineering, Machine Design and Automation (PMA) Section
× corresponding author
# (joint) last author

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