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


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

**COQUE_3D**


.. image:: images/1000000000000447000003137BAA9D5F4C915881.png
    :width: 6.8437in
    :height: 4.9189in


.. _RefImage_1000000000000447000003137BAA9D5F4C915881.png:


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

Number of knots: 1480

Number of meshes and type: 360 QUAD9


Quantities tested and results of modeling A
----------------------------------------

To compare the results of the linear elastic calculation (MECA_STATIQUE) with the reference solution, the displacements of 4 nodes of the pipe section corresponding to point :math:`D` (:math:`\mathrm{CERCLE2}`) are compared.


.. csv-table::

    "**Load increment**", ":math:`\mathrm{DY}` **from point** :math:`D`"
    ":math:`\mathrm{Mz}=\mathrm{3.08670D}+\mathrm{06Nm}` "," :math:`\mathrm{DY}` (:math:`m`)"


Linear calculation:


.. csv-table::

    "Location", "Value to test", "Test type", "Tolerance"
    ":math:`\mathit{N1157}` — :math:`\mathit{DX}` ", "6.51271E-04"," NON_REGRESSION ", "6.49E-06%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DX}` ", "1.2830E-04"," NON_REGRESSION ", "1.88E-04%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DX}` ", "4.01834E-04"," NON_REGRESSION ", "1.6E-05%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DX}` ", "4.01834E-04"," NON_REGRESSION ", "1.6E-05%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DY}` ", "1.08154E-03"," NON_REGRESSION ", "9.44E-05%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DY}` ", "1.09424E-03"," NON_REGRESSION ", "3.15E-04%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DY}` ", "1.08427E-03"," NON_REGRESSION ", "2.92E-04%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DY}` ", "1.08427E-03"," NON_REGRESSION ", "2.92E-04%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DZ}` ", "0.00000E+00"," NON_REGRESSION ", "1.00E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DZ}` ", "0.00000E+00"," NON_REGRESSION ", "1.00E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DZ}` ", "6.34660E-06"," NON_REGRESSION ", "8.70E-06%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DZ}` ", "-6.34660E-06"," NON_REGRESSION ", "8.69E-06%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRX}` ", "0.00000E+00"," NON_REGRESSION ", "1.00E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRX}` ", "0.00000E+00"," NON_REGRESSION ", "1.00E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRX}` ", "-8.06992E-06"," NON_REGRESSION ", "7.78E-06%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRX}` ", "8.06992E-06"," NON_REGRESSION ", "7.78E-06%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRY}` ", "0.00000E+00"," NON_REGRESSION ", "1.00E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRY}` ", "0.00000E+00"," NON_REGRESSION ", "1.00E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRY}` ", "-4.85229E-05"," NON_REGRESSION ", "5.35E-05%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRY}` ", "4.85229E-05"," NON_REGRESSION ", "5.35E-05%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRZ}` ", "5.84655E-04"," NON_REGRESSION ", "6.51E-05%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRZ}` ", "6.81747E-04"," NON_REGRESSION ", "5.81E-05%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRZ}` ", "-9.39844E-05"," NON_REGRESSION ", "6.63E-06%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRZ}` ", "-9.39844E-05"," NON_REGRESSION ", "6.63E-06%"


Elastoplastic calculation (non regression)


.. csv-table::

    "Location", "Value to test", "Test type", "Tolerance"
    ":math:`\mathit{N1157}` — :math:`\mathit{DX}` ", "6.51271E-04"," NON_REGRESSION ", "0.160%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DX}` ", "1.28830E-04"," NON_REGRESSION ", "0.028%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DX}` ", "4.01834E-04"," NON_REGRESSION ", "0.149%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DX}` ", "4.01834E-04"," NON_REGRESSION ", "0.149%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DY}` ", "1.08154E-03"," NON_REGRESSION ", "0.209%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DY}` ", "1.09424E-03"," NON_REGRESSION ", "0.206%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DY}` ", "1.08427E-03"," NON_REGRESSION ", "0.208%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DY}` ", "1.08427E-03"," NON_REGRESSION ", "0.208%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DZ}` ", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DZ}` ", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DZ}` ", "6.34660E-06"," NON_REGRESSION ", "0.022%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DZ}` ", "-6.34660E-06"," NON_REGRESSION ", "0.022%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRX}` ", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRX}` ", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRX}` ", "-8.06992E-06"," NON_REGRESSION ", "0.382%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRX}` ", "8.06992E-06"," NON_REGRESSION ", "0.382%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRY}` ", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRY}` ", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRY}` ", "-4.85229E-05"," NON_REGRESSION ", "0.533%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRY}` ", "4.85229E-05"," NON_REGRESSION ", "0.533%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRZ}` ", "5.84655E-04"," NON_REGRESSION ", "0.173%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRZ}` ", "6.81747E-04"," NON_REGRESSION ", "0.224%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRZ}` ", "-9.39844E-05"," NON_REGRESSION ", "0.533%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRZ}` ", "-9.39844E-05"," NON_REGRESSION ", "0.533%"


We also test the total number of Newton iterations using non-regression:


.. csv-table::

    "Parameter", "Value to test", "Test type", "Tolerance"
    "EVOL_NOLI — ITER_GLOB ", "1"," NON_REGRESSION ", "0"


Large displacement calculation (not regression):


.. csv-table::

    "Location", "NUME_ORDRE ", "Value to test", "Test type", "Tolerance"
    ":math:`\mathit{N1157}` — :math:`\mathit{DX}` ", "10", "6.51271E-04"," NON_REGRESSION "," 0.161%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DX}` ", "10", "1.28830E-04"," NON_REGRESSION ", "0.274%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DX}` ", "10", "4.01834E-04"," NON_REGRESSION ", "0.169%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DX}` ", "10", "4.01834E-04"," NON_REGRESSION ", "0.169%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DY}` ", "10", "1.08154E-03"," NON_REGRESSION "," 0.164%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DY}` ", "10", "1.09424E-03"," NON_REGRESSION ", "0.115%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DY}` ", "10", "1.08427E-03"," NON_REGRESSION ", "0.139%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DY}` ", "10", "1.08427E-03"," NON_REGRESSION ", "0.139%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DZ}` ", "10", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DZ}` ", "10", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DZ}` ", "10", "6.34660E-06"," NON_REGRESSION ", "4.398%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DZ}` ", "10", "-6.34660E-06"," NON_REGRESSION ", "4.398%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRX}` ", "10", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRX}` ", "10", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRX}` ", "10", "-8.06992E-06"," NON_REGRESSION ", "0.423%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRX}` ", "10", "8.06992E-06"," NON_REGRESSION ", "0.423%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRY}` ", "10", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRY}` ", "10", "0.00000E+00"," NON_REGRESSION ", "1.00000E-08%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRY}` ", "10", "-4.85229E-05"," NON_REGRESSION ", "0.565%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRY}` ", "10", "4.85229E-05"," NON_REGRESSION ", "0.565%"
    ":math:`\mathit{N1157}` — :math:`\mathit{DRZ}` ", "10", "5.84655E-04"," NON_REGRESSION "," 0.265%"
    ":math:`\mathit{N1104}` — :math:`\mathit{DRZ}` ", "10", "6.81747E-04"," NON_REGRESSION ", "0.021%"
    ":math:`\mathit{N1109}` — :math:`\mathit{DRZ}` ", "10", "-9.39844E-05"," NON_REGRESSION ", "1.46%"
    ":math:`\mathit{N1099}` — :math:`\mathit{DRZ}` ", "10", "-9.39844E-05"," NON_REGRESSION ", "1.46%"


We also test the total number of Newton iterations using non-regression:


.. csv-table::

    "Parameter", "Value to test", "Test type", "Tolerance"
    "EVOL_NOLI — ITER_GLOB ", "2"," NON_REGRESSION ", "0"