C modeling
==============


Modelling characteristics: d-plan (QUAD9)
----------------------------------------------------

Boundary conditions:

.. csv-table::

    "side :math:`\mathrm{AB}` "," DDL_IMPO = (GROUP_NO = bordAB DY = 0.)"
    "side :math:`\mathrm{EF}` "," FACE_IMPO = (GROUP_MA = faceEF DNOR = 0.)"
    "press :math:`\mathrm{AE}` "," PRES_REP = (GROUP_MA = FaceAE PRES = 60.)"



.. csv-table::

    "Node names:", ":math:`A=\mathrm{N1}` "," :math:`B=\mathrm{N47}` "," :math:`C=\mathrm{N351}`"
    "", ":math:`D=\mathrm{N374}` "," :math:`E=\mathrm{N569}` "," :math:`F=\mathrm{N423}`"



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

Number of knots: 725

Number of meshes and types: 168 QUAD9


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


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.. csv-table::

    "**Location**", "**Size**", "**V** **Reference value**", "**Reference type**", "**Tolerance**"
    "point :math:`A` ", "", "", "", ""
    "-", "Field DEPL, comp. :math:`X` ", "5.7210-5", "'ANALYTIQUE'", "1%"
    "-", "Field DEPL, comp. :math:`Y` ", "0. ", "'ANALYTIQUE'", "1E-10 (absolute)"
    "M1" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "—60. ", "'ANALYTIQUE'", "1%"
    "M1" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "100. ", "'ANALYTIQUE'", "1%"
    "M1" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "5%"
    "M1" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "0. ", "'ANALYTIQUE'", "1E-2 (absolute)"
    ":math:`B` ", "", "", "", ""
    "-", "Field DEPL, comp. :math:`X` ", "3.6410-5", "'ANALYTIQUE'", "1%"
    "-", "Field DEPL, comp. :math:`Y` ", "0. ", "'ANALYTIQUE'", "1E-10 (absolute)"
    "M12" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "0. ", "'ANALYTIQUE'", "0.1 (absolute)"
    "M12" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "40. ", "'ANALYTIQUE'", "1%"
    "M12" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "1%"
    "M12" mesh, "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "0. ", "'ANALYTIQUE'", "1E-2 (absolute)"
    ":math:`C` ", "", "", "", ""
    "-", "Field DEPL, comp. :math:`X` ", "5.2845910—5", "'ANALYTIQUE'", "1%"
    "-", "Field DEPL, comp. :math:`Y` ", "2.1889510—5", "'ANALYTIQUE'", "1%"
    "M73 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "-36.56854", "'ANALYTIQUE'", "2%"
    "M85 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "-36.56854", "'ANALYTIQUE'", "2%"
    "M73 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "76.56854", "'ANALYTIQUE'", "1%"
    "M85 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "76.56854", "'ANALYTIQUE'", "1%"
    "M73 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "3%"
    "M85 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "3%"
    "M73 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "-56.56854", "'ANALYTIQUE'", "1%"
    "M85 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "-56.56854", "'ANALYTIQUE'", "1%"
    ":math:`D` ", "", "", "", ""
    "-", "Field DEPL, comp. :math:`X` ", "3.3629210—5", "'ANALYTIQUE'", "1%"
    "-", "Field DEPL, comp. :math:`Y` ", "1.3929710—5", "'ANALYTIQUE'", "1%"
    "M84 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "5.85786", "'ANALYTIQUE'", "2%"
    "M96 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "5.85786", "'ANALYTIQUE'", "2%"
    "M84 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "34.14214", "'ANALYTIQUE'", "1%"
    "M96 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "34.14214", "'ANALYTIQUE'", "1%"
    "M84 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "1%"
    "M96 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "1%"
    "M84 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "-14.14213", "'ANALYTIQUE'", "1%"
    "M96 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "-14.14213", "'ANALYTIQUE'", "1%"
    ":math:`E` ", "", "", "", ""
    "-", "Field DEPL, comp. :math:`X` ", "4.0446510—5", "'ANALYTIQUE'", "1%"
    "-", "Field DEPL, comp. :math:`Y` ", "4.0446510—5", "'ANALYTIQUE'", "1%"
    "M136 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "20. ", "'ANALYTIQUE'", "3%"
    "M136 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "20. ", "'ANALYTIQUE'", "3%"
    "M136 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "3%"
    "M136 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "-80. ", "'ANALYTIQUE'", "1%"
    ":math:`F` ", "", "", "", "'ANALYTIQUE'", ""
    "-", "Field DEPL, comp. :math:`X` ", "2.5738710—5", "'ANALYTIQUE'", "1%"
    "-", "Field DEPL, comp. :math:`Y` ", "2.5738710—5", "'ANALYTIQUE'", "1%"
    "M102 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXX}` ", "20. ", "'ANALYTIQUE'", "1%"
    "M102 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIYY}` ", "20. ", "'ANALYTIQUE'", "1%"
    "M102 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIZZ}` ", "12. ", "'ANALYTIQUE'", "1%"
    "M102 mesh", "Champ SIGM_ELNO, comp. :math:`\mathit{SIXY}` ", "-20. ", "'ANALYTIQUE'", "1%"



notes
---------

The evolution of the error induced by the following mesh :math:`\mathrm{AB}`, :math:`\mathrm{CD}` or :math:`\mathrm{EF}`, is clearly attenuated compared to modeling A.