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


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

:math:`\mathrm{2D}` axisymmetric modeling:


.. image:: images/100007CC000069BB000067DFBB97E607D5BD7D2E.svg
    :width: 220
    :height: 216


.. _RefImage_100007CC000069BB000067DFBB97E607D5BD7D2E.svg:

**Figure 3.1-a: Geometry and modeling mesh**


.. csv-table::

    "Boundary conditions:", ":math:`\mathrm{Uy}=0` on :math:`\mathrm{NO1}` and :math:`\mathrm{NO2}`"
    "", ":math:`\mathit{Uy}={u}^{\mathit{meca}}=30\mathit{mm}` on :math:`\mathrm{NO3}` AND :math:`\mathrm{NO4}`"



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

Number of knots: 4

Number of meshes and types: 1 QUAD4, 1 SEG2.


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


.. csv-table::

    "**Identification**", "**Size**", "**Reference**", "**Tolerance**"
    ":math:`t=\mathrm{1.1s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{SIYY}` ", "120.547945205", "1.0E-4%"
    ":math:`t=\mathrm{1.4s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{SIYY}` ", "191.76201373", "1.0E-4%"
    ":math:`t=\mathrm{2.0s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{SIYY}` ", "249.42791762", "1.0E-4%"
    ":math:`t=\mathrm{1.1s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{DY}` ", "4.0", "1.0E-4%"
    ":math:`t=\mathrm{1.4s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{DY}` ", "13.0", "1.0E-4%"
    ":math:`t=\mathrm{2.0s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{DY}` ", "31.0", "1.0E-4%"
    ":math:`t=\mathrm{1.1s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{V1}` ", "0.00239726027397", "1.0E-4%"
    ":math:`t=\mathrm{1.4s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{V1}` ", "0.0110411899313", "1.0E-4%"
    ":math:`t=\mathrm{2.0s}` :math:`\mathrm{NO3}` "," :math:`\mathrm{V1}` ", "0.0287528604119", "1.0E-4%"
    ":math:`t=\mathrm{1.1s}` :math:`\mathit{NO3}` "," :math:`\mathit{V7}` ", "20.5479452055", "1.0E-4%"
    ":math:`t=\mathrm{1.4s}` :math:`\mathit{NO3}` "," :math:`\mathit{V7}` ", "91.76201373", "1.0E-4%"
    ":math:`t=\mathrm{2.0s}` :math:`\mathit{NO3}` "," :math:`\mathit{V7}` ", "149.42791762", "1.0E-4%"
    ":math:`t=\mathrm{1.1s}` :math:`\mathrm{NO3}` "," :math:`{\epsilon }^{\mathit{th}}` ", "0.001", "1.0E-4%"
    ":math:`t=\mathrm{1.1s}` :math:`\mathit{NO3}` "," :math:`{\epsilon }_{\mathit{yy}}^{\mathit{meca}}` ", "0.003", "1.0E-4%"
    ":math:`t=\mathrm{1.4s}` :math:`\mathrm{NO3}` "," :math:`{\epsilon }_{\mathit{yy}}^{\mathit{meca}}` ", "0.012", "1.0E-4%"
    ":math:`t=\mathrm{2,0}s` :math:`\mathrm{NO3}` "," :math:`{\epsilon }_{\mathit{yy}}^{\mathit{meca}}` ", "0.03", "1.0E-4%"
    ":math:`t=\mathrm{1.1s}` :math:`\mathrm{NO3}` "," :math:`{\epsilon }_{\mathit{yy}}^{\mathit{plas}}` ", "0.00239726027397", "1.0E-4%"
    ":math:`t=\mathrm{1.4s}` :math:`\mathrm{NO3}` "," :math:`{\epsilon }_{\mathit{yy}}^{\mathit{plas}}` ", "0.0110411899313", "1.0E-4%"
    ":math:`t=\mathrm{2,0}s` :math:`\mathrm{NO3}` "," :math:`{\epsilon }_{\mathit{yy}}^{\mathit{plas}}` ", "0.0287528604119", "1.0E-4%"




     :math:`{\epsilon }^{\mathit{th}}`: thermal deformations - :math:`{\epsilon }^{\mathit{meca}}`: mechanical deformations - :math:`{\epsilon }^{\mathit{plas}}`: plastic deformations