B 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 all the cells representing the sphere, rigidified by kinematic conditions.


.. image:: images/10000000000001AF000001D6A65BAEBA48EE634C.png
    :width: 4.489in
    :height: 4.8953in


.. _RefImage_10000000000001AF000001D6A65BAEBA48EE634C.png:

**Boundary condition:**


.. csv-table::

    "* Symmetry conditions:", "the nodes of the frame located on axis :math:`Y` (group of nodes :math:`«\mathrm{LB}»`) are blocked in the direction :math:`X` (DX = 0)."
    "", "All the nodes belonging to the sphere (group of nodes :math:`«\mathrm{MAT1}»`) are blocked in the X direction (DX = 0)."
    "* Embedding the base:", "the nodes of :math:`«\mathrm{PLANX}»` are blocked in the directions :math:`X` and :math:`Y` (DX = DY = 0)."



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

**Loads:**

An imposed displacement is applied to the part representing the sphere (node group :math:`«\mathrm{MAT1}»`) in the direction :math:`Y`: Loading from 0 to :math:`–100.\mathrm{mm}`


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

Number of knots: 458

Number of meshes and type: 419 QUAD4 and 171 SEG2.


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


.. csv-table::

    "**Identification**", "**Movement** :math:`(\mathrm{mm})` ", "**Reference**", "**Aster**", "**% difference**"
    "Reaction :math:`(N)` "," :math:`d=-20\mathrm{mm}` ", "—2.06771E+06", "-2.0677082E+06", "10"
    "Reaction :math:`(N)` "," :math:`d=-40\mathrm{mm}` ", "—4.04742E+06", "-4.0474212E+06", "10"
    "Reaction :math:`(N)` "," :math:`d=-60\mathrm{mm}` ", "—5.82779E+06", "-5.8277879E+06", "10"
    "Reaction :math:`(N)` "," :math:`d=-80\mathrm{mm}` ", "—7.66673E+06", "-7.6667317E+06", "10"
    "Reaction :math:`(N)` "," :math:`d=–100\mathrm{mm}` ", "—9.11942E+06", "-9.1194226E+06", "15"



notes
---------

The results are almost identical to those of modeling A.

A reduced calculation time is noted by modeling only the contact surface of the rigidified sphere under kinematic conditions.