C modeling
==============


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

The symmetry of the problem makes it possible to represent only a quarter of the model in 3D: the sphere and the block are represented respectively by the contact surface of the sphere and a quarter of a cylinder, meshed with 3D solid elements CUB8.

A node-mesh contact is defined between the sphere and the block.

An imposed displacement load is applied to the entire surface of the sphere, which is rigidified by kinematic conditions.


.. image:: images/10000000000001720000018532F7F696FB8E16D1.png
    :width: 3.8535in
    :height: 4.0516in


.. _RefImage_10000000000001720000018532F7F696FB8E16D1.png:

**Boundary condition:**


.. csv-table::

    "* Symmetry conditions:", "the nodes located in plane :math:`(O,y,z)` (group of nodes :math:`«\mathrm{SBYZ}»`) are blocked in the direction :math:`X` (DX = 0),"
    "", "the nodes located in plane :math:`(O,x,y)` (group of nodes :math:`«\mathrm{SBXY}»`) are blocked in the direction :math:`Z` (DZ = 0),"
    "", "the nodes of the sphere (group of nodes "SPHSUP") are blocked in the directions :math:`X` and :math:`Z` (DX = DZ = 0)"
    "* Base embedding:", "the nodes in group :math:`«\mathrm{BASE}»` (plane :math:`Y=0.`) are blocked in the directions :math:`X`, :math:`Y`, and :math:`Z` (DX = DY = DZ = 0)."



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

**Loads:**

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


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

Number of knots: 6852

Number of meshes and type: 5326 HEXA8, 387 PENTA6 and 183 QUAD4.


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


.. csv-table::

    "**Identification**", "**Movations**", "**Reference**", "**Aster**", "**% tolerance**"
    "Reaction :math:`(N)` "," :math:`d=–20\mathrm{mm}` ", "—3.201351E+06", "-3.2100211E+06", "1"
    "Reaction :math:`(N)` "," :math:`d=–40\mathrm{mm}` ", "—6.402702E+06", "-6.1671049E+06", "5"
    "Reaction :math:`(N)` "," :math:`d=–60\mathrm{mm}` ", "—9.604053E+06", "-9.1689400E+06", "5"
    "Reaction :math:`(N)` "," :math:`d=–80\mathrm{mm}` ", "—1.280540E+07", "-1.1738899E+07", "10"
    "Reaction :math:`(N)` "," :math:`d=–100\mathrm{mm}` ", "—1.600675E+07", "-1.4244367E+07", "12"



notes
---------

The results are less accurate than those from 2D models. 3D meshing loses the exact character of the axisymmetric case. In addition, in order to save calculation time and memory space, 3D meshing is less refined than 2D meshing.