B modeling
==============


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

The system is modelled by:


* 3 discrete elements K_T_D_L,


* 2 discrete M_T_D_N elements.


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

The mesh consists of 3 SEG2 meshes.


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


Natural frequencies
~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**MODE**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`1` "," :math:`1.000E+00` "," :math:`0.1`"
    ":math:`2` "," :math:`2.236E+00` "," :math:`0.1`"



Static training modes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Fashion :math:`1`: absolute movements :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`0.6E+00` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`0.4E+00` "," :math:`0.1`"


Fashion :math:`2`: absolute movements :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`0.6E+00` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`0.4E+00` "," :math:`0.1`"



Static modes for static correction
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Fashion :math:`1`: absolute movements :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`1.317E-02` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`1.216E-02` "," :math:`0.1`"


Fashion :math:`2`: absolute movements :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`1.216E-02` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`1.317E-02` "," :math:`0.1`"



Global response on a full modal basis
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Global response on a complete modal basis (single-support calculation)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The :math:`1` and :math:`2` modes are taken into account.


* **calculation** :math:`n°1`

COMB_MODE =' SRSS '

             For each active :math:`\mathrm{ddl}` :math:`2` and :math:`\mathrm{3 }`:


* :math:`\mathrm{1 }` mode response: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}`


* :math:`\mathrm{2 }` mode response: :math:`{R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}`


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}` (cumulative mode)

absolute displacements: :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`1.01321E-02` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`1.01321E-02` "," :math:`0.1`"



Global response on a complete modal basis (single-support calculation via a multi-support calculation correlated with the same :math:`{\mathit{SRO}}_{\mathit{NO}1}` spectrum at both supports)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The :math:`1` and :math:`2` modes are taken into account.


* **calculation** :math:`n°2`

COMB_MODE =' SRSS '

             For each active :math:`\mathrm{ddl}` :math:`2` and :math:`\mathrm{3 }`:


* :math:`\mathrm{1 }` mode response: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}`


* :math:`\mathrm{2 }` mode response: :math:`{R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}`


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}` (cumulative mode)

absolute displacements: :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`1.01321E-02` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`1.01321E-02` "," :math:`0.1`"



Global response on a complete modal basis (correlated multi-support calculation)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


* **calculation** :math:`n°3`

COMB_MODE =' SRSS '

             For each active degree of freedom :math:`2` and :math:`\mathrm{3 }`:


* answer of mode :math:`\mathrm{1 }`: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}` (accumulation of supports)


* answer of mode :math:`2`: :math:`{R}_{2}={\mathit{Rm}}_{21}+{\mathit{Rm}}_{22}` (accumulation of supports)


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}` (cumulative mode)

absolute displacements: :math:`\mathit{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathit{NO}2` "," :math:`7.22208e-3` "," :math:`0.1`"
    ":math:`\mathit{NO}3` "," :math:`7.22208e-3` "," :math:`0.1`"



* **calculation** :math:`n°4`

COMB_MODE =' SRSS '

             For each active degree of freedom :math:`2` and :math:`\mathrm{3 }`:


* answer of mode :math:`\mathrm{1 }`: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}` (accumulation of supports)


* answer of mode :math:`\mathrm{2 }`: :math:`{R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}` (accumulation of supports)


* global answer: :math: `R=\ left| {R} | {R} _ {1}\ right|+\ left| {R} _ {2}\ right|` (accumulation of modes)

absolute displacements: :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`7.98287e-3` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`7.98287e-3` "," :math:`0.1`"



* **calculation** :math:`n°5`

COMB_MODE =' DPC '

             For each active degree of freedom :math:`2` and :math:`\mathrm{3 }`:


* answer of mode :math:`\mathrm{1 }`: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}` (accumulation of supports)


* answer of mode :math:`\mathrm{2 }`: :math:`{R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}` (accumulation of supports)


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}` (cumulative mode)

absolute displacements: :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`7.22208e-3` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`7.22208e-3` "," :math:`0.1`"



* **calculation** :math:`n°6`

COMB_MODE =' CQC '

             For each active degree of freedom :math:`2` and :math:`\mathrm{3 }`:


* answer of mode :math:`\mathrm{1 }`: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}` (accumulation of supports)


* answer of mode :math:`\mathrm{2 }`: :math:`{R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}` (accumulation of supports)


* global response: :math:`R=\sqrt{{\rho }_{12}{R}_{1}{R}_{2}}` (cumulative mode)

absolute displacements: :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`7.21139e-3` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`7.21139e-3` "," :math:`0.1`"



* **calculation** :math:`n°7`

COMB_MODE =' DSC '

             For each active degree of freedom :math:`2` and :math:`\mathrm{3 }`:


* answer of mode :math:`\mathrm{1 }`: :math:`{R}_{1}={\mathrm{Rm}}_{11}+{\mathrm{Rm}}_{12}` (accumulation of supports)


* answer of mode :math:`\mathrm{2 }`: :math:`{R}_{2}={\mathrm{Rm}}_{21}+{\mathrm{Rm}}_{22}` (accumulation of supports)


* global response: :math:`R=\sqrt{{\rho }_{12}{R}_{1}{R}_{2}}` (cumulative mode)

absolute displacements: :math:`\mathrm{DEPL}`


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`\mathrm{NO2}` "," :math:`7.20071e-3` "," :math:`0.1`"
    ":math:`\mathrm{NO3}` "," :math:`7.20071e-3` "," :math:`0.1`"