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


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

The symmetry of revolution of the problem allows axisymmetric modeling: The sphere and the block are represented respectively by a half disk and the section of half of the block, 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: 916

Number of meshes and type: 625 QUAD4 and 289 SEG2


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


.. csv-table::

    "**Identification**", "**Movement** :math:`(\mathrm{mm})` ", "**Reference**", "**Aster**", "**% tolerance**"
    "Reaction :math:`(N)` ", "20", "—2.03804E+06", "—2.06806E+06", "5"
    "Reaction :math:`(N)` ", "40", "—4.07608E+06", "—4.04698E+06", "5"
    "Reaction :math:`(N)` ", "60", "—6.11412E+06", "—5.82730E+06", "5"
    "Reaction :math:`(N)` ", "80", "—8.15217E+06", "—7.66632E+06", "10"
    "Reaction :math:`(N)` ", "100", "—1.01902E+07", "—9.11899E+06", "15"



notes
---------

The most important error is for the last result. Nevertheless, it is still acceptable.

We illustrated the deformation of the massif at the final time step:


.. image:: images/10000000000000A50000008B0476BC635C00FE07.png
    :width: 1.7189in
    :height: 1.448in


.. _refImage_10000000000000a50000008b0476 BC635C00FE07 .png: