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

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

We use a BARRE model.


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

The mesh contains 1 element of type SEG2.


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

Support reactions and internal forces at the two nodes of the mesh.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**Full gravity matrix according to** :math:`X` **:**

.. csv-table::

    "**Size**", "**Location**", "**Component**", "**Component**", "**Reference Value (N)**", "**Tolerance (%)**"
    "REAC_NODA ", "Node N001"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "-100", "1.0E-4"
    "REAC_NODA ", "Node N002"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"
    "FORC_NODA ", "Node N001"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "FORC_NODA ", "Node N002"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"


**Full gravity matrix according to** :math:`Y` **:**

.. csv-table::

    "**Size**", "**Location**", "**Component**", "**Component**", "**Reference Value (N)**", "**Tolerance (%)**"
    "REAC_NODA ", "Node N001"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "REAC_NODA ", "Node N002"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "FORC_NODA ", "Node N001"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"
    "FORC_NODA ", "Node N002"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"


**Full gravity matrix according to** :math:`Z` **:**

.. csv-table::

    "**Size**", "**Location**", "**Component**", "**Component**", "**Reference Value (N)**", "**Tolerance (%)**"
    "REAC_NODA ", "Node N001"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "REAC_NODA ", "Node N002"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "FORC_NODA ", "Node N001"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"
    "FORC_NODA ", "Node N002"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"


**Diagonal gravity matrix by** :math:`X` **:**

.. csv-table::

    "**Size**", "**Location**", "**Component**", "**Component**", "**Reference Value (N)**", "**Tolerance (%)**"
    "REAC_NODA ", "Node N001"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "-100", "1.0E-4"
    "REAC_NODA ", "Node N002"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"
    "FORC_NODA ", "Node N001"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "FORC_NODA ", "Node N002"," :math:`\mathrm{DX}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"


**Diagonal gravity matrix by** :math:`Y` **:**

.. csv-table::

    "**Size**", "**Location**", "**Component**", "**Component**", "**Reference Value (N)**", "**Tolerance (%)**"
    "REAC_NODA ", "Node N001"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "REAC_NODA ", "Node N002"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "FORC_NODA ", "Node N001"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"
    "FORC_NODA ", "Node N002"," :math:`\mathit{DY}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"


**Diagonal gravity matrix by** :math:`Z` **:**

.. csv-table::

    "**Size**", "**Location**", "**Component**", "**Component**", "**Reference Value (N)**", "**Tolerance (%)**"
    "REAC_NODA ", "Node N001"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "REAC_NODA ", "Node N002"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "-50", "1.0E-4"
    "FORC_NODA ", "Node N001"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"
    "FORC_NODA ", "Node N002"," :math:`\mathit{DZ}` "," ", "'ANALYTIQUE'", "0", "1.0E-4"



Projection of the mass matrix on a modal basis
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**Full matrix**

.. csv-table::

    "**TABLE**", "**Reference type**", "**Reference value (kg)**", "**Tolerance (%)**"
    "TABX ", "'ANALYTIQUE'", "100.0", "1.0E-4"
    "TABY ", "'ANALYTIQUE'", "100.0", "1.0E-4"
    "TABZ ", "'ANALYTIQUE'", "100.0", "1.0E-4"


**Diagonal matrix**

.. csv-table::

    "**TABLE**", "**Reference type**", "**Reference value (kg)**", "**Tolerance (%)**"
    "TABX ", "'ANALYTIQUE'", "100.0", "1.0E-4"
    "TABY ", "'ANALYTIQUE'", "100.0", "1.0E-4"
    "TABZ ", "'ANALYTIQUE'", "100.0", "1.0E-4"



Kinetic energy
~~~~~~~~~~~~~~~~~~

**Full matrix**

.. csv-table::

    "**TABLE**", "**NOM_PARA**", "**Reference type**", "**Reference value (J)**", "**Tolerance (%)**"
    "TABX "," TOTALE ", "'ANALYTIQUE'", "''", "50.0", "1.0E-4"
    "TABY "," TOTALE ", "'ANALYTIQUE'", "''", "50.0", "1.0E-4"
    "TABZ "," TOTALE ", "'ANALYTIQUE'", "''", "50.0", "1.0E-4"