C modeling
====

In this modeling, a grid in quadrangles is produced, with refinement near the contact zone.




TP implementation
----




Realization of geometry
~~~~

In this modeling, we must partition the geometry so that it can be meshed into quadrangles.

In module GEOM, an illustration of the possible partition is given in the figure:


*   Take face :math:`\mathit{SPHHAU}` and explain all its points (New Entity → Explode: Vertex menu), then we get the 4 points :math:`A2`, :math:`B2`, :math:`C2` and :math:`D2`


*   Create the points :math:`M`, :math:`N` and :math:`P` in order to generate the red partition lines (New Entity → Basic → Point menu): :math:`(\mathrm{0,}\mathrm{25,}0)`, :math:`(\mathrm{25,}\mathrm{25,}0)` and :math:`(\mathrm{25,}\mathrm{50,}0)`


*   Generate partition lines (New Entity → Basic → Line menu)


*   Partition :math:`\mathit{SPHHAU}` with the lines above (Menu Operations → Partition).


*   By symmetry, you can generate a new lower face (Menu Operations → Transformation → Mirror Image) by choosing the X axis to achieve the symmetry


*   It remains to assemble the two new spheres to form a single object GEOM (Menu New Entity → Build → Compound*) *.


*   Define all groups as in modeling A, which will be needed to assign boundary conditions and loads (New Entity → Group → Create Group menu)


.. image:: images/1000020100000218000001C8B42208123154EC17.png
    :width: 2.3626in
    :height: 2.398in


.. _RefImage_1000020100000218000001C8B42208123154EC17.png:

Figure 5.1: Top disk partition




Realization of the mesh
~~~~

For the mesh, we choose to refine around the contact zone using a geometric progression on the circumference and on the radius. It may be necessary to reorient some segments in the Mesh module:


*   The mesh is defined by the menu Mesh→ Create Mesh with the geometry to be meshed. The mesh will be carried out in triangles, and the automatic meshing hypotheses "Assign a set of hypotheses →2D: Automatic Quadrangulation" will be used by choosing the number of segments 15. We calculate the mesh (Menumesh → Compute).


*   We define sub-mesh (Menumesh → Create Sub-mesh) with groups :math:`\mathit{CONT}1` and :math:`\mathit{CONT}2`. It is carried out using the Wire Discretization algorithm, the Start and End Length hypothesis (for example, 0.2mm and 2.0mm) and the advanced hypothesis Propagation of Node Distribution on Opposite Edges. A linear mesh containing approximately 3500 quadrangles and 4000 nodes is then obtained.


*   Change the mesh from linear to quadratic: "Modification -> Convert to/from quadratic".


*   We will then import the groups from the geometry (Menu Mesh → Create Groups from Geometry).


.. image:: images/100002010000022D000002F14194C59F3FD35F0B.png
    :width: 1.722in
    :height: 2.2417in


.. _RefImage_100002010000022D000002F14194C59F3FD35F0B.png:

Figure 5.2: Quadrangle mesh obtained for C modeling




Tested sizes and results
----


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    ":math:`{\sigma }_{\mathit{yy}}` point :math:`\mathit{C1}` ", "'ANALYTIQUE'", ":math:`\mathrm{-}\mathrm{2798,3}\mathit{Mpa}` "," 5.0%"