E modeling
==============


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

The symmetry of revolution of the problem allows axisymmetric modeling: The block is represented by the section of its half and the sphere is represented by its surface potentially in contact, they are meshed with axisymmetric 2D elements.

A node-mesh contact is defined between the two structures.

An imposed displacement load is applied to the upper part of the sphere, which is rigidified by a high Young's modulus.


.. image:: images/1000000000000179000001D8DC22DCCDBD5A4E55.png
    :width: 3.9264in
    :height: 4.9161in


.. _RefImage_1000000000000179000001D8DC22DCCDBD5A4E55.png:

**Boundary condition:**


* symmetry of revolution: the nodes located on the :math:`Y` axis (group of nodes :math:`«\mathrm{LB}»` and :math:`«\mathrm{LS}»`) are blocked in the direction :math:`X` (DX = 0),


* embedding the base: the nodes in group :math:`«\mathrm{PLANX}»` are blocked in the directions :math:`X` and :math:`Y` (DX = DY = 0),


* rigid body movements are suppressed by imposing a link following :math:`y` between node :math:`E` belonging to the sphere and node :math:`D` belonging to the massif.

**Loads:**

An imposed displacement is applied to the upper part of the sphere (group of nodes :math:`«\mathrm{NDPL}»`) in the direction :math:`Y`: Loading from 0 to :math:`–100.\mathrm{mm}`


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

Number of knots: 688

Number of meshes and type: 625 QUAD4 and 241 SEG2.


Tested values
---------------


.. csv-table::

    "**Identification**", "**Movement** :math:`(\mathrm{mm})` ", "**Reference**", "**Aster**", "**% tolerance**"
    "Reaction :math:`(N)` ", "20", "—2.03804E+06", "-2.0892265E+06", "5"
    "Reaction :math:`(N)` ", "40", "—4.07608E+06", "-4.0928499E+06", "5"
    "Reaction :math:`(N)` ", "60", "—6.11412E+06", "-5.8467590E+06", "5"
    "Reaction :math:`(N)` ", "80", "—8.15217E+06", "-7.6820567E+06", "10"
    "Reaction :math:`(N)` ", "100", "—1.01902E+07", "-9.1299258E+06", "15"



notes
---------

The results are slightly better than those of modeling A.

We notice a calculation time 5 times greater than the latter, using method CONTRAINTE.