Reference problem
====


Geometry
----


.. image:: images/Object_1.svg
    :width: 732
    :height: 320


.. _RefImage_Object_1.svg:

**Figure 1.1-a: Diagram of thermal loads and geometry (A and B models)**


.. image:: images/1000000000000330000001C2845C98EF216427D8.png
    :width: 693
    :height: 344


.. _RefImage_1000000000000330000001C2845C98EF216427D8.png:

**Figure 1.1-b: Isovalues of the thermal field on the initial thermal mesh (A and B models)**

It is a cracked metal "cylinder head" (steel 1 6MND5, :math:`E\mathrm{=}{210.10}^{3}\mathit{Mpa}`,, :math:`\nu \mathrm{=}0.2`, :math:`\rho {C}_{p}\mathrm{=}{\mathrm{526,10}}^{4}J\mathrm{/}{m}^{3}°C` *,* :math:`\lambda \mathrm{=}\mathrm{33,5}W\mathrm{/}m°C`).

In both models (A and B), an isotropic transient linear thermal calculation (THER_LINEAIRE or THER_NON_LINE) is performed in lumped modeling (PLAN_DIAG) on a thermal mesh TRIA3/SEG2.

In the second modeling, this calculation is linked with an elastic calculation (MECA_STATIQUE or STAT_NON_LINE) in plane stress modeling (C_PLAN) on a mechanical mesh in TRIA6/SEG3.


.. image:: images/Object_3.svg
    :width: 732
    :height: 320


.. _RefImage_Object_3.svg:

Figure 1.1-c: Schematic of thermo-mechanical loads and geometry (modeling B)


.. image:: images/100000000000028A000001DFD952BDA0216532A0.png
    :width: 693
    :height: 344


.. _RefImage_100000000000028A000001DFD952BDA0216532A0.png:

**Figure 1.1-d: Decay in deformation potential energy during the free adaptation process of meshes (B modeling)**


.. image:: images/10000000000002BD000001C81FEA3933136A65BF.png
    :width: 4.0161in
    :height: 2.6126in


.. _RefImage_10000000000002BD000001C81FEA3933136A65BF.png:

**Figure 1.1-e: Deformed mechanical mesh (B modeling)**

The various key areas of the calculation are designated: GM38 for the entire volume part in TRIA, GM33 for the outgoing heat flow, GM36 /37 for the exchange conditions, GM39 /40 for the embedment, GM34 for the distributed pressure and GM35 for the distributed pressure and at which the average temperature will be measured.


Material properties
----

Throughout the structure (GROUP_MAGM38), the following material characteristics are applied:

:math:`\begin{array}{c}E\mathrm{=}21000\mathit{MPa}\\ \nu \mathrm{=}0.2\\ \rho C\mathrm{-}p\mathrm{=}526{10}^{4}J\mathrm{/}{m}^{3}°C\\ \lambda \mathrm{=}\mathrm{33,5}W\mathrm{/}m°C\end{array}`


Boundary conditions and loads
----

The breakdown of loads by zone can be summarised in the form of the following table:


.. csv-table::

    "**Geometric areas (** **GROUP_NO/GROUP_MA/** ****) **", "**Loads**"
    "GM33 "," FLUX_REP
    FLUN = :math:`\mathrm{-}400W\mathrm{/}{m}^{2}`"
    "GM36 "," ECHANGE
    COEF_H = :math:`1000W\mathrm{/}{m}^{2}°C`
    TEMP_EXT = :math:`350°C`"
    "GM37 "," ECHANGE
    COEF_H = :math:`5000W\mathrm{/}{m}^{2}°C`
    TEMP_EXT = :math:`150°C`"
    "GM39 /40 "," DDL_IMPO
    DX=DY=0."
    "GM34 "," PRES_REP
    PRES = :math:`\mathrm{-}0.1N`"