6. D modeling#
6.1. Characteristics of modeling#
Incompressible AXI elements (TRIA6 + QUAD8)
For the purposes of stripping, the nodes are defined:
\(\mathrm{NOEUMIA}=A+(0.0.01/4)\) where the deformations and stresses are the same as in \(A\)
\(\mathrm{NOEUMIB}=B+(0.0.01/4)\) where the deformations and stresses are the same as in \(B\)
Boundary conditions:
DDL_IMPO = GROUP_NO =' FACSUP ', DY = 0 :math:`y=0.1`
GROUP_NO =” FACINF “, DY = 0 \(y=0\)
PRES_REP = GROUP_MA =” FACEAE “, PRES = 60 sided \(\mathrm{AE}\)
6.2. Characteristics of the mesh#
Number of knots: 175.
Number of meshes and types: 20 QUAD8, 40 TRIA6.
6.3. Tested sizes and results#
Results at point \(A\):
first column AXIS_INCO_UPG without imposing \(\mathrm{GONF}=0\)
second column AXIS_INCO_UPG by imposing \(\mathrm{GONF}=0\)
third column AXIS_INCO_UP with quadratic mesh
fourth column AXIS_INCO_UP with linear mesh
fifth column AXIS_INCO_UPO with linear elements
Identification |
Reference type |
Reference value |
Tolerance |
||||
1 |
2 |
3 |
4 |
5 |
|||
\(u\) |
“ANALYTIQUE” |
|
0.10% |
0.10% |
0.10% |
0.10% |
0.10% |
\(v\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\sigma }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
—60. |
0.50% |
0.50% |
0.50% |
0.70% |
1.50% |
\({\sigma }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
03/20/12 |
0.50% |
0.50% |
0.50% |
1.00% |
9.00% |
\({\sigma }_{\mathrm{zz}}\) |
“ANALYTIQUE” |
0.50% |
0.50% |
0.50% |
0.50% |
6.00% |
|
\({\sigma }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
10-5 |
0.01 |
10-5 |
0.08 |
0.2 |
|
\({\varepsilon }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
-6. 10-4 |
0.50% |
0.50% |
0.50% |
0.60% |
0.60% |
\({\varepsilon }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\varepsilon }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\varepsilon }_{\mathrm{eq}}\) - INVA_2 |
“ANALYTIQUE” |
6.92 10-4 |
0.50% |
0.50% |
0.50% |
0.50% |
3.0% |
\({\varepsilon }_{\mathrm{eq}}\) - PRIN_1 |
“ANALYTIQUE” |
—6. 10-4 |
0.50% |
0.50% |
0.50% |
1.00% |
6.0% |
\({\varepsilon }_{\mathrm{eq}}\) - 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% |
0.50% |
0.60% |
\({\sigma }_{\mathrm{eq}}\) - VMIS |
“ANALYTIQUE” |
138.56 |
1.00% |
1.00% |
1.00% |
1.00% |
3.00% |
\({\sigma }_{\mathrm{eq}}\) - TRESCA |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.00% |
3.00% |
|
\({\sigma }_{\mathrm{eq}}\) - PRIN_1 |
“ANALYTIQUE” |
-60. |
1.00% |
1.00% |
1.00% |
1.00% |
2.00% |
\({\sigma }_{\mathrm{eq}}\) - PRIN_2 |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.00% |
23.% |
|
\({\sigma }_{\mathrm{eq}}\) - PRIN_3 |
“ANALYTIQUE” |
1.00% |
1.00% |
1.00% |
1.00% |
5.5% |
|
\({\sigma }_{\mathrm{eq}}\) - VMIS |
“ANALYTIQUE” |
138.56 |
1.00% |
1.00% |
1.00% |
1.00% |
3.00% |
Results at point \(F\):
first column AXIS_INCO_UPG without imposing \(\mathrm{GONF}=0\)
second column AXIS_INCO_UPG by imposing \(\mathrm{GONF}=0\)
third column AXIS_INCO_UP with quadratic mesh
fourth column AXIS_INCO_UP with linear mesh
fifth column AXIS_INCO_UPO with linear elements
Identification |
Reference type |
Reference value |
Tolerance |
||||
1 |
2 |
3 |
4 |
5 |
|||
\(u\) |
“ANALYTIQUE” |
|
0.10% |
0.10% |
0.10% |
0.10% |
2.0% |
\(v\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\sigma }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
0.03 |
0.03 |
0.03 |
0.10 |
0.70 |
|
\({\sigma }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
0.50% |
0.50% |
0.50% |
0.50% |
1.1% |
|
\({\sigma }_{\mathrm{zz}}\) |
“ANALYTIQUE” |
0.50% |
0.50% |
0.50% |
0.50% |
0.60% |
|
\({\sigma }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
|
|
|
0.01 |
0.2 |
|
\({\varepsilon }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
-1.5 10-4 |
0.50% |
0.50% |
0.50% |
0.50% |
1.0% |
\({\varepsilon }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
\({\varepsilon }_{\mathrm{xy}}\) |
“ANALYTIQUE” |
10-5 |
10-5 |
10-5 |
10-5 |
10-5 |
|
Checking the transition to the nodes for the middle nodes (only for the result obtained without imposing \(\mathrm{GONF}=0\))
\(\mathrm{NOEUMIA}\)
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” |
|
|
\(\mathrm{NOEUMIB}\)
Identification |
Reference type |
Reference value |
Tolerance ( \(\text{\%}\) ) |
\({\sigma }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
|
|
\({\sigma }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
|
|
\({\sigma }_{\mathrm{zz}}\) |
“ANALYTIQUE” |
|
|
\({\varepsilon }_{\mathrm{xx}}\) |
“ANALYTIQUE” |
-1.5 10—4 |
|
\({\varepsilon }_{\mathrm{yy}}\) |
“ANALYTIQUE” |
1.5 10—4 |
|
6.4. notes#
The precision obtained is very good.