Modeling A
==============


Characteristics of modeling
-----------------------------------

The system is divided into 2 sub-structures:


.. image:: images/10000000000004E200000097B6FED25CD7D50F2F.png
    :width: 6.3374in
    :height: 0.739in


.. _RefImage_10000000000004E200000097B6FED25CD7D50F2F.png:

In this situation, the two substructures are connected at the level of the 2nd mass. The dynamic interface of the 1st substructure consists of a mass m at the level of the node :math:`\mathit{NO3}` of the mesh and coincides with the dynamic interface of the 2nd substructure which has no mass and is simply blocked at the level of the node :math:`\mathit{NO1}`.


.. image:: images/1000000000000274000000D172FF9519019C87EA.png
    :width: 3.461in
    :height: 1.0972in


.. _RefImage_1000000000000274000000D172FF9519019C87EA.png:

The eigenmodes of the complete system are calculated using the modal calculation method by substructuring with 'Craig-Bampton' interfaces (blocked interfaces). The bases of each substructure are composed of a dynamic mode and a constrained mode.

The transient response of the system is calculated on the modal basis calculated by substructuring.

The time steps used are equal to: :math:`{10}^{-2}s` in 'EULER', :math:`{10}^{-2}s` in '', in 'NEWMARK', :math:`{10}^{-2}s` in 'DEVOGE', :math:`{10}^{-1}s` in 'ADAPT_ORDRE2' (for the latter, this is the initial time step of the algorithm and the maximum time step is set to formula :math:`\mathrm{0,15}s` then formula :math:`\mathrm{0,2}s` to optimize calculation time).


Characteristics of the substructure mesh
-------------------------------------------------

Number of knots: 3

Number of meshes and types: 2 SEG2


Tested sizes and results
------------------------------

**Calculation by modal recombination without substructuring: Method** ADAPT_ORDRE2 and RUNGE_KUTTA_54


.. csv-table::

    "**Identification**", "**Reference**"
    "Method: ADAPT_ORDRE2 ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathit{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathit{m.s}}^{-2}`)", "3.3375 10—1"
    "Method: RUNGE_KUTTA_54 ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathrm{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathrm{m.s}}^{-2}`)", "3.3375 10—1"
    "**Calculation by substructuration**", ""
    "Method: EULER ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathrm{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathrm{m.s}}^{-2}`)", "3.3375 10—1"
    "Method: DEVOGE ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathrm{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathrm{m.s}}^{-2}`)", "3.3375 10—1"
    "Method: NEWMARK ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathit{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathit{m.s}}^{-2}`)", "3.3375 10—1"
    "Method: RUNGE_KUTTA_32 ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathit{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathit{m.s}}^{-2}`)", "3.3375 10—1"
    "Method: ADAPT_ORDRE2 ", ""
    "Node :math:`{x}_{2}`, displacement (:math:`m`)", "4.1700 10—1"
    "Knot :math:`{x}_{2}`, speed (:math:`{\mathrm{m.s}}^{-1}`)", "—4.3011 10—1"
    "Node :math:`{x}_{2}`, acceleration (:math:`{\mathrm{m.s}}^{-2}`)", "3.3375 10—1"