Reference problem
====


Geometry
----

The structure studied is a slice of a cylinder, modelled axisymmetrically, (cf HPLA100)


.. image:: images/10006098000069D500005FE9EE2D3CCC8AF7DBBA.svg
    :width: 509
    :height: 461


.. _RefImage_10006098000069D500005FE9EE2D3CCC8AF7DBBA.svg:


Material properties
----

The material is homogeneous, isotropic, and linear thermoelastic. The mechanical coefficients are

:math:`E\mathrm{=}{2.10}^{5}M\mathrm{/}{\mathit{mm}}^{2}`; :math:`\nu \mathrm{=}0.3`

The expansion coefficient is a function of temperature:

:math:`\alpha \mathrm{=}{10}^{\mathrm{-}5}°{C}^{\mathrm{-}1}` for :math:`T\mathrm{=}100°C`, :math:`\alpha \mathrm{=}{10}^{\mathrm{-}4}°{C}^{\mathrm{-}1}` for :math:`T\mathrm{=}0°C`

The reference temperature is :math:`0°C`. The thermal coefficients are equal to:

:math:`\lambda \mathrm{=}1W\mathrm{/}mK`, :math:`\rho {C}_{p}\mathrm{=}1000\mathit{MJ}\mathrm{/}{m}^{3}K`


Boundary conditions and thermal calculation loads
----

On its inner edge, the cylinder is subjected to an exchange with a fluid that changes abruptly from :math:`100°C` to :math:`0°C`:


*   zero flow at the edges :math:`\mathit{AB}`, :math:`\mathit{BC}`, :math:`\mathit{CD}`


*   on edge :math:`\mathit{AD}`, convective exchange condition, with:

:math:`H\mathrm{=}100W\mathrm{/}{\mathit{mm}}^{2}\mathrm{/}°C`

:math:`\mathit{Text}\mathrm{=}100°C` to :math:`t\mathrm{=}\mathrm{0s}`, then :math:`0°C` to :math:`t\mathrm{=}\mathrm{0.01s}`, and then kept constant.


Boundary conditions and loads for mechanical calculation
----

**Symmetry conditions**

Unrestrained case: zero displacement following :math:`\mathit{Oy}` along side :math:`\mathit{AB}`.

Blocked case: zero displacement following :math:`\mathit{Oy}` along sides AB and :math:`\mathit{CD}`.

Loading: thermal expansion.