Civil Engineering Reference
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central processing unit implementing the PSD method and to expand it to the sub-
structuration case.
An alternative solution, far more consistent with the decentralized character of
the implementation at ELSA, has been chosen. It involves implementing the sub-
structuration due to two processes using two different computers. The first process is
carried out by the central processing unit responsible for the dofs tested in the
laboratory, whereas the second process - the one in charge of the modeled part -
operates with a working station implementing the finite element software. Both
processes exchange minimum information via the network. The advantage of such
an approach is obvious. The modifications in laboratory software are minor and the
process dedicated to the numerical part does not specifically need to deal with the
tested part. The communication between both processes has to be safe and has to
potentially allow connections between two different operating systems, while being
standard on the Internet. This is why Berkeley's communication system (
Berkeley
sockets
) has been chosen. Practical details about this implementation can be found in
[BUC 94].
We have already said that system described by equation [5.1] could be integrated
in time by a step by step-type numerical scheme. The speed and displacement
vectors at step (
n
+ 1) are expressed as a function of the acceleration vector and
vectors obtained at the previous time step (see equations [5.2]). If these expressions
[5.2] are introduced into the
D
-off-center shape of the equilibrium described in [5.3],
we obtain the following linear system for acceleration
a
:
1
ˆ
n
1
ˆ
n
1
Ma
f
[5.5]
ˆ
f
a pseudo-force vector. If we take into
account approximation [5.4] of the reaction forces of the OS scheme, the expression
of both quantities is given by:
M
is a pseudo-mass matrix and
1
where
ˆ
2
I
MM
'
J
(1
DE D
)
C
t
(1
)
K
ˆ
n
1
n
1
n
n
1
[5.6]
f
(1
D
)
f
D
f
(1
D
)
r
n
n
1
n
2
I
n
D
r
(1
D
)
v
''
D
v
DJ
(
tC
E
t K
)
a
Now if we distinguish the data coming from the numerical sub-structure (S),
from the data coming from the tested part (T), the [5.5] system can be rewritten as
follows:
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