4. B modeling#
4.1. Characteristics of modeling#
Meshing with incompressible 3D elements of type TETRA10 only
\(\mathrm{AB}\) is on the \(\mathrm{OX}\) axis (unlike the \(A\) modeling).
For stripping purposes, we define node \(\mathrm{NOEUMI}=A+(0.0.e/4)\) where the deformations and stresses are the same as in \(A\).
Conditions limits :
DDL_IMPO = GROUP_NO =' FACSUP ', DZ = 0
GROUP_NO =” FACINF “, DZ = 0 sides \(\mathit{AEFD}\) (\(z\mathrm{=}0\) and \(z\mathrm{=}0.01\)) GROUP_NO =” FACEAB “, DY = 0 side \(\mathit{AB}\)
FACE_IMPO = GROUP_MA =” FACEEF “, DNOR = 0 sides \(\mathit{EF}\)
PRES_REP = GROUP_MA =” FACEAE “, PRES = 60 sided \(\mathit{AE}\)
4.2. Characteristics of the mesh#
Number of knots: 13907
Number of meshes: 8519 TETRA10
4.3. Tested sizes and results#
Result at point \(A\):
first column 3D_ INCO_UPG without imposing \(\mathrm{GONF}=0\)
second column 3D_ INCO_UPG by imposing \(\mathrm{GONF}=0\)
third column 3D_ INCO_UP with quadratic elements
fourth column3D_ INCO_UP with linear elements
fifth column3D_ INCO_UPO with linear elements
Identification |
Reference type |
Reference value |
Tolerance |
||||
1 |
2 |
3 |
4 |
5 |
|||
\(u\) |
“ANALYTIQUE” |
|
0.50% |
0.50% |
0.50% |
0.50% |
0.50% |
\(v\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\sigma }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
—60. |
1.00% |
1.00% |
1.00% |
4.00% |
3.00% |
\({\sigma }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.50% |
1.00% |
|
\({\sigma }_{\mathrm{zz}}\) |
“ANALYTIQUE” |
2.50% |
2.50% |
2.50% |
10.00% |
3.00% |
|
\({\sigma }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
2.5 |
2.5 |
2.5 |
2.5 |
2.5 |
|
\({\varepsilon }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
-6. 10-4 |
0.50% |
0.50% |
0.50% |
1.50% |
2.0% |
\({\varepsilon }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
|
0.50% |
0.50% |
0.50% |
1.00% |
1.00% |
\({\varepsilon }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
|
|
|
|
|
|
\({\varepsilon }_{\mathrm{eq}}\) - INVA_2 |
“ANALYTIQUE” |
6.92 10-4 |
0.50% |
0.50% |
0.50% |
1.00% |
1.50% |
\({\varepsilon }_{\mathrm{eq}}\) - PRIN_1 |
“ANALYTIQUE” |
—6. 10-4 |
0.50% |
0.50% |
0.50% |
1.50% |
2.0% |
\({\varepsilon }_{\mathrm{eq}}\) - PRIN_2 |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\varepsilon }_{\mathrm{eq}}\) - PRIN_3 |
“ANALYTIQUE” |
|
0.50% |
0.50% |
0.50% |
1.00% |
1.0% |
\({\sigma }_{\mathrm{eq}}\) - VMIS |
“ANALYTIQUE” |
138.56 |
1.00% |
1.00% |
1.00% |
1.00% |
1.5% |
\({\sigma }_{\mathrm{eq}}\) - TRESCA |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.00% |
1.5% |
|
\({\sigma }_{\mathrm{eq}}\) - PRIN_1 |
“ANALYTIQUE” |
-60. |
3.00% |
3.00% |
3.00% |
4.00% |
3.00% |
\({\sigma }_{\mathrm{eq}}\) - PRIN_2 |
“ANALYTIQUE” |
3.00% |
3.00% |
3.00% |
10.00% |
3.00% |
|
\({\sigma }_{\mathrm{eq}}\) - PRIN_3 |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.50% |
1.00% |
|
\({\sigma }_{\mathrm{eq}}\) - VMIS |
“ANALYTIQUE” |
138.56 |
1.00% |
1.00% |
1.00% |
1.00% |
1.5% |
Result at point \(F\):
first column 3D_ INCO_UPG without imposing \(\mathrm{GONF}=0\)
second column 3D_ INCO_UPG by imposing \(\mathrm{GONF}=0\)
third column 3D_ INCO_UP with quadratic elements
fourth column3D_ INCO_UP with linear elements
fifth column3D_ INCO_UPO with linear elements
Identification |
Reference type |
Reference value |
Tolerance |
||||
1 |
2 |
3 |
4 |
5 |
|||
\(u\) |
“ANALYTIQUE” |
2.12 10-5 |
0.50% |
0.50% |
0.50% |
0.50% |
0.50% |
\(v\) |
“ANALYTIQUE” |
2.12 10-5 |
0.50% |
0.50% |
0.50% |
0.50% |
0.50% |
\({\sigma }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.50% |
1.50% |
|
\({\sigma }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.00% |
1.00% |
|
\({\sigma }_{\mathrm{zz}}\) |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.50% |
1.00% |
|
\({\sigma }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
-20. |
1.00% |
1.00% |
1.00% |
1.00% |
1.00% |
\({\varepsilon }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\varepsilon }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\varepsilon }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
-1.5 10-4 |
0.50% |
0.50% |
0.50% |
1.00% |
1.00% |
Checking the transition to the nodes for the middle nodes (only for the result obtained without imposing GONF = 0) - value at node \(\mathrm{NOEUMI}\):
Identification |
Reference type |
Reference value |
Tolerance ( \(\text{\%}\) ) |
\({\sigma }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
-60. |
|
\({\sigma }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
|
|
\({\sigma }_{\mathrm{zz}}\) |
“ANALYTIQUE” |
|
|
\({\varepsilon }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
-6. 10-4 |
|
\({\varepsilon }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
|
|
4.4. notes#
The results obtained here are a bit worse than in the case of modeling \(A\), but the discretization is coarser since there are about 2 times fewer nodes in this test case. The results are still satisfactory since the differences are less than \(\text{0.2 \%}\) for the movements, less than \(\text{0.5 \%}\) for the deformations and less than \(\text{1 \%}\) for the constraints. We note again that there is no significant improvement in the result when \(\mathrm{tr}\varepsilon =0\) is explicitly imposed.