Experimental Methods in Earthquake Engineering - Dynamic Behavior of Concrete and Seismic Engineering - page 183

The context completely changes when we consider the continuous PSD method.
The experimental process is synchronous and the physical time between two
integration time steps is extremely short: 1 or 2 ms. As it is difficult to carry out a
non-linear calculation step in so short a period of time, a delayed approach like the
one used previously (see section 5.2.3) is no longer possible, as the experimental
process cannot wait for the numerical process any longer. Therefore, the coupling
method should be synchronous and the data exchange should take place without any
interruption.

The integration algorithm for the whole structure (both numerical and
experimental) should have the following properties: be second order , be stable
within the limits of stability of the explicit scheme implemented for the experimental
part, introduce minimum dissipation and operate with non-stop data exchange.

To do so, we implement a partitioned approach that features the following
characteristics ([MAG 98], [MAG 00]):
- an implicit scheme for the numerical part, coupled with the explicit scheme of
the central finite differences used for the experimental part;
- two different time steps for each part of the structure (

' for the experimental

part and ' for the numerical part);
- sub-cycling of the explicit part with a number of sub-steps which can be very
large (

''| Tt / 1, 000);

- assessment in advance of the state of the numerical structure, and interpolation
of the forces to be imposed on the experimental structure by the numerical part to
limit the digital dissipation of the scheme.

The master computer carries out the integration of the equations of motion of the
numerical structure as its priority task. On each 1 or 2 ms cycle of the control
system, the remaining time is used for the basic acquisition and data transfer tasks.
These basic tasks can be given priorities and the main one can be dedicated to the
calculation of the motion of the numerical structure. This strategy has been used to
obtain preliminary results for a simple structure [MAG 98]. An alternative consists
of having the calculations of the numerical structure carried out by another
computer: this strategy has successfully been used in a recent test campaign on
bridges.

5.4. Final comments

As we have seen, modeling plays a crucial part for the PSD method: choice of
the system of the equations to integrate and model (whether linear or not) of the