Solution de référence
=====================


Méthode de calcul utilisée pour la solution de référence
--------------------------------------------------------

Soit une grandeur :math:`G` possédant 3 composantes :math:`X,Y,Z`

Le maillage possède 3 entités géométriques (mailles ou noeuds): :math:`\mathit{X1},\mathit{X2},\mathit{X3}`

On fabrique tout d’abord 2 champs :math:`\mathit{ch1}` et :math:`\mathit{ch2}` par affectation de la grandeur :math:`G` sur les entités géométriques :math:`\mathit{X1}` , :math:`\mathit{X2}`  et :math:`\mathit{X3}` .


+----------------------+---------------------------------------------+---------------------------------------------+---------------------------------------------+
| Entité               | :math:`\mathit{X1}`                         | :math:`\mathit{X2}`                         | :math:`\mathit{X3}`                         |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| Composante           | :math:`X`           | :math:`Y` | :math:`Z` | :math:`X`           | :math:`Y` | :math:`Z` | :math:`X`           | :math:`Y` | :math:`Z` |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch1}` | 1.                  |           | 3.        | 1.                  |           | 3.        | 1.                  |           | 3.        |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch2}` |                     | 4.        | 2.        |                     | 4.        | 2.        |                     | 4.        | 2.        |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+

On définit ensuite les champs :math:`\mathit{ch3}` et :math:`\mathit{ch4}` par CREA_CHAMP opération ASSE.

On doit alors obtenir :


+----------------------+---------------------------------------------+---------------------------------------------+---------------------------------------------+
| Entité               | :math:`\mathit{X1}`                         | :math:`\mathit{X2}`                         | :math:`\mathit{X3}`                         |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| Composante           | :math:`X`           | :math:`Y` | :math:`Z` | :math:`X`           | :math:`Y` | :math:`Z` | :math:`X`           | :math:`Y` | :math:`Z` |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch1}` | 1.                  |           | 3.        | 1.                  |           | 3.        | 1.                  |           | 3.        |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch2}` |                     | 4.        | 2.        |                     | 4.        | 2.        |                     | 4.        | 2.        |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch3}` | 1.                  |           | 3.        | 1.                  | 8.        | 4.        | 1.                  | 12.       | 9.        |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch4}` | 6.                  |           |           | 8.                  |           |           | 18.                 |           |           |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+

Pour tester les différents cas de figure de l’opération 'ASSE' de la commande CREA_CHAMP, ce calcul est fait pour 5 types de champs:


.. csv-table::

    "A", "cham_no", "déplacements"
    "B", "cham_elem /ELNO", "contraintes"
    "C", "cham_elem /ELGA", "contraintes"
    "D", "cham_elem /ELNO", "variables internes"
    "E", "cham_elem /ELGA", "variables internes"



Résultats de référence
----------------------

Pour les 5 cas de figure précédents, on teste les valeurs graissées et soulignées du tableau ci‑dessous:


+----------------------+---------------------------------------------+---------------------------------------------+---------------------------------------------+
| Entité               | :math:`\mathit{X1}`                         | :math:`\mathit{X2}`                         | :math:`\mathit{X3}`                         |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| Composante           | :math:`X`           | :math:`Y` | :math:`Z` | :math:`X`           | :math:`Y` | :math:`Z` | :math:`X`           | :math:`Y` | :math:`Z` |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch3}` | 1.                  |           | 3.        | **1.**              | 8.        | 4.        | **1.**              | **12.**   | **9.**    |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+
| :math:`\mathit{ch4}` | 6.                  |           |           | 8.                  |           |           | **18.**             |           |           |
+----------------------+---------------------+-----------+-----------+---------------------+-----------+-----------+---------------------+-----------+-----------+


Incertitudes sur la solution
----------------------------

Aucune incertitude.