Reduction of Finite Element Models for Explicit Car Crash
Simulations
Kamila Flidrova, PSA Peugeot Citroën
Each year, there is about 1,2 million of persons in the world
who are dead on roads, there of more than 40 000 in Europe.
This is the reason why the road safety became one of principal
priorities of car constructors. Today, consumerist context
and especially the Euro NCAP tests impose that the cars have
to present the best behavior possible in crash. Before a car
commercialization, this one is submitted to a lot of tests,
in order to ensure, in case of accident, the maximal security
of car passengers as well as of other users of road as, for
example, pedestrians and two-wheelers. Virtual and physical
crash tests determine the direction of the conception and
development of a car. During conception phase, numerical simulations
have to improve, in order to be more predictive. For computational
time reasons, the car crash models are relatively coarse.
The aim of this paper is to propose better stiffness modelling
of cast components for the numerical car crash explicit simulations.
To have the representative stiffness of cast
components (engine for example) in numerical models is very
important, especially for fracture modeling of adjacent components
(suspensions of engine for example). If the stiffness of these
components isn’t correctly represented in the numerical
model, the loading forces which are transmitted on the adjacent
components, especially made to break at certain level of load
during the crash, aren’t correct. Because of computational
time reasons, it’s not possible to use volumic finite
elements to mesh the big car components (engine for example)
in the simulations of complete car crash.
It seems that the reduction methods of finite element models
is a good solution to dispose simultaneously of a representative
stiffness and a reasonable computational time.
Reduction methods were already implemented and used successfully
in implicit finite element codes. Their use
in explicit finite element codes is conditioned
by the form of mass matrix which
must be diagonal. Because the mass matrix obtained
by reduction of finite element model is full,
it is necessary to carry
out its diagonalization. The first proposition
concerning this subject was made by Faucher
and Combescure and
the results of their work were implemented
in explicit finite element code Radioss. The
used reduction method was that of
Craig-Bampton. It’s well known that the mass matrix
obtained by this type of reduction is full.
Faucher and Combescure proposed to project
the reduced matrices onto a new base of
projection which is completely orthogonalized
with respect to the mass matrix. The new reduced
mass matrix is after
this operation diagonal. The disadvantage of
this method is that the assembly of the substructure
with the rest of model
is no more direct, because the degrees of freedom
of substructure are no more physics and Lagrange
multipliers have to be used
for the procedure of assemblage.
To overcome this problem, a new strategy of diagonal mass
matrix determination of the reduced system
is proposed. Firstly, the static (Guyan) condensation
is performed for the stiffness
matrix. The mass matrix of the reduced system
is evaluated separately. The idea is to find
a reduced diagonal mass matrix
which reproduces the same global inertial behavior
as the original structure performing the rigid
body motion. The second
reduction method presented in this paper is
based on use of free-interface dynamic modes.
The advantage of this
reduction method is that obtained reduced mass
matrix is directly diagonal. In addition, this
matrix is unitary and thereby
well conditioned. On the other hand, the disadvantage
is the appearance of rigid body modes which
demands special treatments.
Simple test model was defined for the first implementation
of the two reduction methods described previously.
Results will be compared to those of reference finite element
model.
Once the modeling methodology will be validated,
an application to an industrial model will
be proposed.
<< Back to Agenda |
© Copyright 2008 Altair Engineering, Inc. All Rights Reserved.