# Improving the performances of dynamic substructuring

*by M. Corus, EDF R&D / AMA*

*Code_Aster* helps to build scale models on the basis of traditional under-structuring technique, by the means of a combination of commands. The traditional step consists in:

1. computing - for each substructure of the complete model - a base of modes with particular boundary conditions for the interfaces which have to be connected to the other substructures;

2. defining coupling interfaces to be coherent with the previously computed modes;

3. computing the static raisings for these interfaces, or the deformations with imposed displacement associated with each D.O.F. interface;

4. building of a projection basis made up of these two vectors subsets;

5. building a macro element including this various information for each substructure;

6. building a generalized model, by defining the connections between each macro element;

7. assembling the generalized model;

**The total performances of the substructuring were improved while working on each key point of this methodology.**

A computing method for coupling modes was initially introduced into the operator MODE_STATIQUE. The traditional approaches (point 2) require the computation of as many vectors as of degrees of freedom (D.O.F.) carried by the interfaces. It is a question of building a relevant subspace, of much lower size, allowing the correct transition of information (displacements and forces) from one substructure to the other. The technique introduced into the code is based on the use of an astute pre-conditioner allowing the effective calculation of the modes of the interface operators.

**The profits carried out impact directly the computing times which are shorter, but also the memory occupation, by reducing the number of vectors to be stored.**

In the second time, we enriched the possibilities offered by operator DEFI_MODELE_GENE by authorizing the coupling and connection of strongly incompatible interfaces. The incompatibilities of grids, being the non-coincidence of nodes (2D/2D or 3D/3D case) or the difference in modelization (2D/3D), are managed by rebuilding all the D.O.F. - for the interface defined as slave - starting from the kinematics of the interface defined as master. Moreover, the introduction of the concept of interface modes forces to manage the incompatibility of the displacement fields to the interface. This difficulty is overcome by considering weak coupling conditions, where connection conditions are projected in the subspace generated by the interface modes of the master substructure.

Lastly to reduce the construction of the assembled scale model, we set up a new generalized classification allowing to eliminate the stresses of connections, rather than using Lagrange multipliers. This last evolution not only limits the size of the scale models but also improves the conditioning of the matrices, and thus accelerates the resolution of the generalized problem.

In parallel the operator REST_SOUS_STRUCT was re-examined with an aim of performance enhancement.

These evolutions were tested on a blading model composed of a disc (31,000 D.O.F.) and of 46 wings (9800 D.O.F./wing), that is to say a complete model of approximately 480,000 D.O.F. The implementation of common substructuring methods on this model lead to computing times of about 32,000 seconds (that is to say almost 9 hours) for the first 300 modes of the structure. The reference computation carried out on the complete model lasts approximately 18,000 seconds (that is to say 5 hours) for the first 300 modes. The evolutions brought to the various operators lead to times of about 500 seconds for the first 300 modes, with the same quality results. We thus carried out a time-saver of about 60 compared to the first case, and of 33 compared to the second.

It should also be noted that before these developments, in version 10.2 the restitution of the modes computed on physical basis stopped after 48 hours, by lack of CPU time. With the improvements made to REST_SOUS_STRUCT, the restitution takes 300 seconds with an office equipment.