9. H modeling#
9.1. Characteristics of modeling#
We use a AXIS model. A single calculation with contact penalty is carried out. In this model, the imposed crush goes up to \(10\mathit{mm}\).
9.2. Characteristics of the mesh#
Knots: 243.
Stitches: 100 TRIA3, 162 QUAD4.
9.3. Tested sizes and results#
First calculation (smoothing, algorithm “PENALISATION”)
Identification |
Reference type |
Reference value |
Tolerance |
mesh \(\mathit{M31}\) knot \(\mathit{N291}(G)\) instant \(1.0\) |
“ANALYTIQUE” |
-1978.7 \(N\) |
7.0% |
mesh \(\mathit{M286}\) knot \(\mathit{N55}(G\text{'})\) instant \(1.0\) |
“ANALYTIQUE” |
-1978.7 \(N\) |
1.0% |
mesh \(\mathit{M293}\) knot \(\mathit{N55}(G\text{'})\) instant \(1.0\) |
“ANALYTIQUE” |
-1978.7 \(N\) |
15.0% |
mesh \(\mathit{M31}\) knot \(\mathit{N291}(G)\) instant \(2.0\) |
“ANALYTIQUE” |
-2798.3 \(N\) |
5.0% |
mesh \(M286\) knot \(N55(G\text{'})\) instant \(2.0\) |
“ANALYTIQUE” |
-2798.3 \(N\) |
3.0% |
mesh \(M293\) knot \(N55(G\text{'})\) instant \(2.0\) |
“ANALYTIQUE” |
-2798.3 \(N\) |
15.0% |
mesh \(M31\) knot \(N291(G)\) instant \(3.0\) |
“ANALYTIQUE” |
-3427.2 \(N\) |
2.0% |
mesh \(M286\) knot \(N55(G\text{'})\) instant \(3.0\) |
“ANALYTIQUE” |
-3427.2 \(N\) |
3.0% |
mesh \(M293\) knot \(N55(G\text{'})\) instant \(3.0\) |
“ANALYTIQUE” |
-3427.2 \(N\) |
14.0% |
mesh \(M31\) knot \(N291(G)\) instant \(4.0\) |
“ANALYTIQUE” |
-3957.4 \(N\) |
3.0% |
mesh \(M286\) knot \(N55(G\text{'})\) instant \(4.0\) |
“ANALYTIQUE” |
-3957.4 \(N\) |
4.0% |
mesh \(M293\) knot \(N55(G\text{'})\) instant \(4.0\) |
“ANALYTIQUE” |
-3957.4 \(N\) |
15.0% |
mesh \(M31\) knot \(N291(G)\) instant \(5.0\) |
“ANALYTIQUE” |
-4424.5 \(N\) |
6.0% |
stitch \(M286\) knot \(N55(G\text{'})\) instant \(5.0\) |
“ANALYTIQUE” |
-4424.5 \(N\) |
4.0% |
stitch \(M293\) knot \(N55(G\text{'})\) instant \(5.0\) |
“ANALYTIQUE” |
-4424.5 \(N\) |
15.0% |
9.4. notes#
The mesh consists of 2 hemispheres meshed differently (the upper sphere is in QUAD4, the lower sphere in TRIA3). The contact pressure measured on the upper surface is in good agreement with the analytical solution (the difference of the order of 5% is explained by extrapolation).
On the lower surface, on the contrary, there are significant differences because there are 2 cells that conspire at point \(G\text{'}\) (mesh of TRIA3), however, if we average the results obtained on these 2 cells, we find a pressure in good agreement with the analytical solution.
The penalty coefficient used here (big front \({R}_{\mathit{sphere}}\ast E\)) makes it possible to obtain results comparable to those of exact dualization algorithms (G modeling).