Reference problem
=====================


Geometry
---------


.. image:: images/10000000000003B5000003530F5256798620A785.jpg
    :width: 3.3807in
    :height: 3.552in


.. _RefImage_10000000000003B5000003530F5256798620A785.jpg:

**Figure** 1.1-1 **: Representation of geometry**


.. csv-table::

    "Point :math:`A`:", ":math:`(\mathrm{0,0}\mathrm{,0})`"
    "Point :math:`B`:", ":math:`(\mathrm{1,0}\mathrm{,0})`"
    "Point :math:`C`:", ":math:`(\frac{\sqrt{(2)}}{2},\frac{\sqrt{(2)}}{2}\mathrm{,0})`"
    "Point :math:`D`:", ":math:`(\mathrm{0,0}\mathrm{,1})`"


**Table** 1.1-1 **: Point coordinates**


Material properties
----------------------

The material is steel:

:math:`E\mathrm{=}2.04{10}^{11}`, :math:`\nu \mathrm{=}0.3`, :math:`\alpha =1.092{10}^{-5}`.


Boundary conditions and loads
-------------------------------------


Loading on a vertical edge (support for one of the axes of the coordinate system)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The validation of the ARETE_IMPO keyword must require the equivalence of the following conditions:


* 1.3.1.1 conditions:

Face :math:`\mathrm{DBC}` imposed: :math:`\mathrm{DNOR}=10`

Deadlock at points :math:`D,B,C`: :math:`\mathrm{DX}=\mathrm{0,}\mathrm{DY}=\mathrm{0,}\mathrm{DZ}=0`

Displacement imposed on the nodes of the :math:`\mathrm{DA}` edge: :math:`\mathrm{DZ}=0`


* 1.3.1.2 conditions:

Face :math:`\mathrm{DBC}` imposed: :math:`\mathrm{DNOR}=10`

Deadlock at points :math:`D,B,C`: :math:`\mathrm{DX}=\mathrm{0,}\mathrm{DY}=\mathrm{0,}\mathrm{DZ}=0`

Imposed :math:`\mathrm{DA}` edge: :math:`\mathrm{DTAN}=0` except at point :math:`D`.

We will validate the equivalence between these conditions by testing the movements at node :math:`A`.


Loading on oblique edges
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The validation of the ARETE_IMPO keyword must require the equivalence of the following conditions:


* 1.3.2.1 conditions:

Blocking at the nodes on the face :math:`\mathrm{ABC}`: :math:`\mathrm{DX}=\mathrm{0,}\mathrm{DY}=\mathrm{0,}\mathrm{DZ}=0`

Displacement imposed at the nodes of edge :math:`\mathrm{DA}`: :math:`\mathrm{DZ}=-1` (except at points :math:`D` and :math:`A`)

Oblique connection to the nodes of edge :math:`\mathrm{DB}` (except at points :math:`D` and :math:`B`): :math:`\mathrm{DX}=1`, :math:`\mathrm{ANGL}\text{\_}\mathrm{NAUT}=(\mathrm{0,45}\mathrm{,0})`

Oblique connection to the nodes of edge :math:`\mathrm{DC}` (except at points :math:`D` and :math:`C`): :math:`\mathrm{DX}=1`, :math:`\mathrm{ANGL}\text{\_}\mathrm{NAUT}=(\mathrm{45,45}\mathrm{,0})`


* 1.3.2.2 conditions:

Blocking at the nodes on the face :math:`\mathrm{ABC}`: :math:`\mathrm{DX}=\mathrm{0,}\mathrm{DY}=\mathrm{0,}\mathrm{DZ}=0`

Imposed :math:`\mathrm{DA}` edge: :math:`\mathrm{DTAN}=1` except at points :math:`D` and :math:`A`.

Imposed :math:`\mathrm{DB}` edge: :math:`\mathrm{DTAN}=1` except at points :math:`D` and :math:`B`.

Imposed :math:`\mathrm{DC}` edge: :math:`\mathrm{DTAN}=1` except at points :math:`D` and :math:`C`.

We will validate the equivalence between these conditions by testing the movements at node :math:`D`.