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


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


.. image:: images/1000031600001E2E00001F366FFE4AFEE07A4479.svg
    :width: 389
    :height: 402


.. _RefImage_1000031600001E2E00001F366FFE4AFEE07A4479.svg:


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

Number of knots: 23.

Number of meshes and types: 4 QUAD8.


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


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**", "**tolerance**"
    ":math:`A` :math:`{\sigma }_{\mathrm{rr}}` ", "—1.00003", "—1.06833", "6.83", "7.0"
    ":math:`{\sigma }_{\theta \theta }` ", "—4.43821", "—4.46731", "0.66", "2.0"
    ":math:`{\sigma }_{\mathrm{zz}}` ", "0.19518", "0.16596", "14.9", "15.0"
    ":math:`{e}_{\mathrm{rel}}` ", "", "2.37% ", "", "5.0"
    ":math:`E` mat. 1 :math:`{\sigma }_{\mathrm{rr}}` ", "—1.95508", "—1.97893", "1.22", "2.0"
    ":math:`{\sigma }_{\theta \theta }` ", "—3.48316", "—3.49330", "0.29", "2.0"
    ":math:`{\sigma }_{\mathrm{zz}}` ", "0.19518", "0.18498", "0.18498", "5.22", "6.0"
    ":math:`{e}_{\mathrm{rel}}` ", "", "1.05% ", "", "5.0"
    ":math:`E` mat. 2 :math:`{\sigma }_{\mathrm{rr}}` ", "—1.95508", "—1.98398", "1.48", "2.0"
    ":math:`{\sigma }_{\theta \theta }` ", "—2.16049", "—2.13394", "1.23", "2.0"
    ":math:`{\sigma }_{\mathrm{zz}}` ", "—0.32135", "—0.32204", "0.22", "2.0"
    ":math:`{e}_{\mathrm{rel}}` ", "", "0.152% ", "", "5.0"
    ":math:`B` :math:`{\sigma }_{\mathrm{rr}}` ", "—1.99999", "—2.00095", "0.048", "2.0"
    ":math:`{\sigma }_{\theta \theta }` ", "—2.11555", "—2.11595", "0.012", "2.0"
    ":math:`{\sigma }_{\mathrm{zz}}` ", "—0.32135", "—0.32174", "0.12", "2.0"
    ":math:`{e}_{\mathrm{rel}}` ", "", "0.057% ", "", "5.0"



notes
---------

Since the mesh is coarse (4 elements following :math:`\text{Or}`), some constraints near the axisymmetry axis are poorly approximated. On the other hand, the jump of :math:`{\sigma }_{\theta \theta }` and :math:`{\sigma }_{\mathrm{zz}}` at the interface of the 2 materials is well detected.


notes
---------

Overall estimated relative error= 1.40%.