5. C modeling#

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

5.1. TP implementation#

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

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

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

  • Partition \(\mathit{SPHHAU}\) 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)

_images/1000020100000218000001C8B42208123154EC17.png

Figure 5.1: Top disk partition

5.1.2. 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 \(\mathit{CONT}1\) and \(\mathit{CONT}2\). 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).

_images/100002010000022D000002F14194C59F3FD35F0B.png

Figure 5.2: Quadrangle mesh obtained for C modeling

5.2. Tested sizes and results#

Identification

Reference type

Reference value

Tolerance

\({\sigma }_{\mathit{yy}}\) point \(\mathit{C1}\)

“ANALYTIQUE”

\(\mathrm{-}\mathrm{2798,3}\mathit{Mpa}\)

5.0%