4. Implemented in Code_Aster#

4.1. Notion of dynamic macro-element#

A dynamic macro element is a reduced (generalized) model of a substructure. It includes:

  • the projection of the model (mass and stiffness matrices) of the substructure on the reduced basis,

  • information on the interfaces where the adjacent substructures will be connected and the link matrices associated with these interfaces.

Normally, as many dynamic macroelements as substructures are built. In the case where we are in the presence of substructures that differ only in their position in space, a single macro-element is sufficient. A rotation and/or translation of the macro-element is then applied during assembly.

4.2. The conduct of a study#

  • For each substructure: creation of the dynamic macro element

    • Calculation and assembly of mass, stiffness and substructure loading matrices: (CALC_MATR_ELEM, ASSE_MATRICE, CALC_VECT_ELEM, ASSE_VECTEUR)

    • Calculation of basic projection vectors: normal modes, static modes, interface modes (CALC_MODES, MODE_STATIQUE, DEFI_BASE_MODALE)

    • Definition of interfaces (DEFI_INTERF_DYNA)

    • Projection of substructure matrices onto base vectors (MACR_ELEM_DYNA)

The sequence of these operations can be carried out with a single call to the operator CREA_ELEM_SSD. This operator allows you to create a dynamic macro element by entering only the information on the model and the interfaces. It calculates the basic projection vectors (normal modes and bond modes), defines the interfaces, and projects the stiffness and mass matrices on the calculated basis. It chains the following operators: CALC_MATR_ELEM, ASSE_MATRICE, CALC_MODES,,, MODE_STATIQUE,, DEFI_INTERF_DYNA, DEFI_BASE_MODALE, MACR_ELEM_DYNA.

  • Assembly of the various substructures

    • Definition of the generalized model of the assembled structure: link between substructures and numbering the degrees of freedom of the system (DEFI_MODELE_GENE, NUME_DDL_GENE)

    • Assembly of generalized substructure matrices (ASSE_MATR_GENE, ASSE_VECT_GENE)

These operations for assembling dynamic macroelements can be carried out using the ASSE_ELEM_SSD operator. It defines the generalized model and assembles the generalized matrices of the various substructures. It chains the following operators: DEFI_MODELE_GENE, NUME_DDL_GENE, ASSE_MATR_GENE.

  • Response calculation on the generalized model (CALC_MODES, DYNA_VIBRA)

  • Restitution of the results in physical coordinates of the substructure or on a skeleton mesh (REST_SOUS_STRUCT)

  • A posteriori control of the results by verifying the continuity of the field of movement at the interfaces (POST_RELEVE_T, TEST_TABLE) and the invalidity of the work of the liaison forces (CALC_CORR_SSD)

4.3. Practical advice#

  • For standard cases: use the CREA_ELEM_SSD operator to create the dynamic macro element and the ASSE_ELEM_SSD operator to assemble the macro elements. This makes it significantly easier to write the command file.

  • For non-standard cases (particular projection base), it is sometimes necessary to return to elementary operators. The current limitations of CREA_ELEM_SSD and ASSE_ELEM_SSD are:

    • conservative structure (without damping)

    • projection base: normal modes + link modes (Craig-Bampton, Mac Neal, the first n interface modes)

    • All the components of the degrees of freedom of the interface nodes are considered for the calculation of the connection modes (the keyword MASQUE which allows you to select the active components of the interface nodes is not active for CREA_ELEM_SSD)

    • Normal modes are calculated using the CALC_MODES operator, the options on the dimension of the mode search subspace are those taken by default by this operator.

  • If you are in the presence of a specific interface or with a low number of DDL, the use of conventional methods (Craig-Bampton or Mac Neal) is recommended.

  • Interface modes are appropriate for distributed (non-point) interfaces. The quality of the results depends on the number of interface modes taken into account in the projection base. An ex-post check of the results is always recommended. This check can be done by verifying the continuity of the field of movement at the interfaces and/or the invalidity of the work of the liaison forces. It is necessary to increase the number of interface modes if we observe a detachment at the interface level or if the work of the liaison forces is not negligible.

  • Carefully choose the normal modes that serve as the basic projection vectors. The subspace generated by these basic vectors must contain at least the deformation of the substructure after assembly. One cannot, for example, observe the twisting of the substructure if one does not include a torsional deformation among the basic vectors.

  • For a Mac Neal interface, you must ensure that the substructure is maintained somewhere in order to avoid rigid body movement.