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

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

The structure is meshed into pipe elements with 4 nodes (mesh SEG4, modeling TUYAU).


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

11 SEG4 stitches (5 elements in the elbow, 3 in each straight pipe)


Calculation of the "Global" Rotation term
------------------------

This term of "global" rotation was developed as part of a tripartite action EDF - CEA - FRAMATOME [:ref:`bib2 <bib2>`], with a view to future integration into the sizing code RCC -M.

It is expressed from the rotations of two representative points of the elbow (entry and exit), by:

:math:`{R}_{G}=\sqrt{\Delta {R}_{x}^{2}+\Delta {R}_{y}^{2}+\Delta {R}_{z}^{2}}`

where

:math:`\begin{array}{}\Delta {R}_{x}={\mathrm{DRX}}_{\mathrm{sortiecoude}}-{\mathrm{DRX}}_{\mathrm{entréecoude}}\\ \Delta {R}_{y}={\mathrm{DRY}}_{\mathrm{sortiecoude}}-{\mathrm{DRY}}_{\mathrm{entréecoude}}\\ \Delta {R}_{z}={\mathrm{DRZ}}_{\mathrm{sortiecoude}}-{\mathrm{DRZ}}_{\mathrm{entréecoude}}\end{array}`

This term is calculated by the Python MACR_ROTA_GLOBALE macro command, which is embedded in the body of the command file. The result of this macro command is an Aster function of the global rotation as a function of the moment. A non-regression test validates this function.


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


.. _DdeLink__2110_1115317466:


Tests against 3D calculation for global rotation:

.. csv-table::

    "**Instant**", "**Reference**", "**Tolerance**"
    "8", "9.39907E—03", "1.5%"



.. csv-table::

    "**Instant**", "**Identification**", "**Reference Type**", "**Reference Value**", "**%** Tolerance"
    "1", "Point :math:`D`, :math:`\mathit{DY}` :math:`(m)` ", "'AUTRE_ASTER'", "1.09257D—02", "3."
    "8", "Point :math:`D`, :math:`\mathit{DY}` :math:`(m)` ", "'AUTRE_ASTER'", "2.20209D—02", "3.2"
    "1", "Point :math:`D`, :math:`\mathit{MZ}` :math:`(\mathit{Nm})` ", "'ANALYTIQUE'", "3.086702E6", "0.1"
    "8", "Dot :math:`D`, :math:`\mathit{MZ}` :math:`(\mathit{Nm})` ", "'ANALYTIQUE'", "5.889813E6", "0.1"
    "1", "Dot :math:`A`, :math:`\mathit{DY}` :math:`(m)` ", "'AUTRE_ASTER'", "3.08670D+06", "0.1"
    "8", "Dot :math:`A`, :math:`\mathit{DY}` :math:`(m)` ", "'AUTRE_ASTER'", "5.88981D+06", "0.1"


Non-regression tests for the options in CALC_CHAMP or POST_CHAMP:

.. csv-table::

    "**Option**", "**Component**", "**Mesh**", "**Mesh**", "**Subpoint**", "**Order Number**", "**Reference Type**", "**Precision**"
    "SIEQ_ELGA "," VMIS ", "M1", "2", "2", "61", "1"," NON_REGRESSION ", ", "-"
    "SIEQ_ELGA "," VMIS ", "M1", "3", "3", "3", "55", "3"," NON_REGRESSION ", ", "-"
    "SIEQ_ELGA "," VMIS_SG ", "M1", "2", "2", "98", "8"," NON_REGRESSION ", ", "-"
    "SIEQ_ELGA "," VMIS_SG ", "M1", "3", "3", "3", "42", "8"," NON_REGRESSION ", "" -"
    "EPEQ_ELGA "," INVA_2 ", "M1", "1", "1", "1", "77", "4"," NON_REGRESSION ", ", "-"
    "EPEQ_ELGA "," INVA_2 ", "M1", "1", "1", "8", "5"," NON_REGRESSION ", "" -"
    "EPEQ_ELGA "," INVA_2SG ", "M1", "1", "1", "61", "8"," NON_REGRESSION ", ", "-"
    "EPEQ_ELGA "," INVA_2SG ", "M1", "3", "3", "9", "8"," NON_REGRESSION ", "" -"


 Special quantity tests for the earthquake at point :math:`D` **:**


.. csv-table::

    "**Load Increment**", "", "Type of **Reference**"
    ":math:`\mathit{Mz}=3.08670D+06\mathit{Nm}` "," :math:`\mathit{EN}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=3.48715D+06\mathit{Nm}` "," :math:`\mathit{ET}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=4.288041D+06\mathit{Nm}` "," :math:`\mathit{EFY}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=5.489370D+06\mathit{Nm}` "," :math:`\mathit{EFZ}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=5.889810D+06\mathit{Nm}` "," :math:`\mathit{ESTAR}` "," NON_REGRESSION"


 Special quantity tests for the earthquake at point :math:`C` **:**


.. csv-table::

    "**Load Increment**", "", "Type of **Reference**"
    ":math:`\mathit{Mz}=3.08670D+06\mathit{Nm}` "," :math:`\mathit{EN}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=3.48715D+06\mathit{Nm}` "," :math:`\mathit{ET}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=4.288041D+06\mathit{Nm}` "," :math:`{\mathit{EFY}}_{2}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=5.489370D+06\mathit{Nm}` "," :math:`{\mathit{EFZ}}_{2}` "," NON_REGRESSION"
    ":math:`\mathit{Mz}=5.889810D+06\mathit{Nm}` "," :math:`{\mathit{ESTAR}}_{2}` "," NON_REGRESSION"



.. _DdeLink__1985_1610502030:

Validating POST_CHAMP/MIN_MAX_SPsur the SIEQ_ELGA option. The reference type is AUTRE_ASTER, not in relation to the 3D calculation, but to the calculation of option SIEQ_ELGA by CALC_CHAMP.


.. csv-table::

    "**Component**", "**Component**", "**Mesh**", "**Point**", "**Order Number**", "**Reference Value**", "**Tolerance**"
    "VMIS/MAXI "," VALE ", "M3", "3", "1", "1", "1.0700867E8", "2E-6"
    "VMIS/MINI "," VALE ", "M3", "3", "3", "1", "1", "8.3875662E6", "2E-6"
    "VMIS/MAXI_ABS "," VALE ", "M3", "M3", "3", "2", "1", "8.3938035E7", "2E-6"
    "VMIS/MINI_ABS "," VALE ", "M3", "M3", "2", "1", "70047.61", "2E-6"
    "VMIS/MAXI "," NUCOU ", "M3", "3", "1", "1", "1.0", "2E-6"
    "VMIS/MAXI "," NUSECT ", "M3", "3", "1", "1", "1.0", "2E-6"
    "VMIS/MAXI "," POSIC ", "M3", "M3", "1", "1", "-1.0", "2E-6"
    "VMIS/MAXI "," POSIS ", "M3", "M3", "1", "1", "-1.0", "2E-6"
    "VMIS/MAXI "," VALE ", "M1", "1", "1", "1", "8.8409900E7", "2E-6"
    "VMIS/MINI "," VALE ", "M1", "1", "1", "1", "5.883180E6", "2E-6"
    "VMIS/MAXI "," NUCOU ", "M2", "2", "2", "1", "1.0", "2E-6"
    "VMIS/MINI "," NUCOU ", "M3", "3", "3", "1", "1.0", "2E-6"
    "VMIS/MAXI "," NUSECT ", "M4", "4", "1", "1", "12.0", "2E-6"
    "VMIS/MINI "," NUSECT ", "M5", "5", "2", "1", "16.0", "2E-6"
    "VMIS/MAXI "," POSIC ", "M6", "6", "3", "1", "-1.0", "2E-6"
    "VMIS/MINI "," POSIC ", "M7", "7", "1", "1", "0", "2E-6"
    "VMIS/MAXI "," POSIS ", "M8", "8", "2", "1", "1.0", "2E-6"
    "VMIS/MINI "," POSIS ", "M9", "9", "3", "1", "1.0", "2E-6"
    "VMIS/MAXI "," VALE ", "M1", "1", "2", "4", "1.27695000E8", "2E-6"
    "VMIS/MINI "," VALE ", "M5", "5", "3", "5", "2.2075500E7", "1E-5"


Validation of CREA_CHAMP/ELGA_SPMX_R. Reference NON_REGRESSION.


.. csv-table::

    "VMIS/MAXI "," VALE ", "M1", "1", "1", "-", "-", "-"
    "VMIS/MINI "," INST ", "M5", "5", "3", "-", "-", "-"


Validation of POST_CHAMP/VARI_ELNO/MAXI, V5 component.


.. csv-table::

    "**Component**", "**Mesh**", "**Node**", "**Reference Type**", "**Reference Value**", "**Tolerance**"
    "VALE ", "M5", "N13"," NON_REGRESSION "," ", "-", "-"



.. csv-table::

    "NUCOU ", "M5", "N13"," AUTRE_ASTER "," ", "1", "2E-6"
    "NUSECT ", "M5", "N13"," AUTRE_ASTER "," ", "12.0", "2E-6"
    "POSIC ", "M5", "N13"," AUTRE_ASTER "," ", "-1.0", "2E-6"
    "POSIS ", "M5", "N13"," AUTRE_ASTER "," ", "1.0", "2E-6"


Using the Mfront behavior does not change the accuracy of the solutions tested compared to 3D.