13. K modeling#
13.1. Characteristics of modeling#
Meshing with ``3D_ INCO_UP « and » DEFORMATION =” GDEF_LOG “``elements incompressible types HEXA20 only.
Face with imposed radial displacement
Following axis \(z\):
total thickness \(e=0.01\)
2 layers of elements
The boundary conditions are:
Zero vertical displacement on “FACSUP” and “FACINF” faces \(\mathit{AEFD}\) (\(z=0\) and \(z=0.01\)): DZ = 0.
Normal movement stuck on the “FACEAB” faces (side \(\mathit{AB}\), DX = 0) and “FACEEF” (side \(\mathit{EF}\), DNOR = 0.)
Imposed displacement on the inside of the cylinder “FACEAE”: face \(\mathit{AE}\) DNOR = -6.10-5
13.2. Characteristics of the mesh#
Number of knots: 1501 knots
Number of meshes: 240 HEXA20
13.3. Tested sizes and results#
Displacements and constraints SIGM_NOEU are evaluated at points \(A\) and \(F\). The components of field SIEQ_NOEU are tested to the point \(A\) only.
Identification |
Reference type |
Reference |
Tolerance |
|
\(A\) |
\(\mathit{u}\) (X) |
ANALYTIQUE |
|
|
\(\mathit{v}\) (DY) |
ANALYTIQUE |
|
|
|
\(\mathit{\sigma_{xx}}\) |
ANALYTIQUE |
99.9566 |
0.01 |
|
\(\mathit{\sigma_{yy}}\) |
ANALYTIQUE |
-59.9955 |
0.03 |
|
\(\mathit{\sigma_{zz}}\) |
ANALYTIQUE |
19.9326 |
0.05 |
|
\(\mathit{\sigma_{xy}}\) |
ANALYTIQUE |
0.03 |
||
VMIS |
ANALYTIQUE |
138.5226 |
0.001 |
|
TRESCA |
ANALYTIQUE |
159.9521 |
0.001 |
|
PRIN_1 |
ANALYTIQUE |
-59.9955 |
0.0025 |
|
PRIN_2 |
ANALYTIQUE |
19.9326 |
0.005 |
|
PRIN_3 |
ANALYTIQUE |
99.9566 |
0.0005 |
|
VMIS_SG |
ANALYTIQUE |
138.5226 |
0.001 |
|
Identification |
Reference type |
Reference |
Tolerance |
|
\(F\) |
\(\mathit{u}\) (X) |
ANALYTIQUE |
-2.1217 10-5 |
0.005 |
\(\mathit{v}\) (DY) |
ANALYTIQUE |
2.1217 10-5 |
0.005 |
|
\(\mathit{\sigma_{xx}}\) |
ANALYTIQUE |
20.003 |
0.002 |
|
\(\mathit{\sigma_{yy}}\) |
ANALYTIQUE |
20.003 |
0.002 |
|
\(\mathit{\sigma_{zz}}\) |
ANALYTIQUE |
20.003 |
0.0025 |
|
\(\mathit{\sigma_{xy}}\) |
ANALYTIQUE |
20.003 |
0.0015 |
|
For Green-Lagrange deformations:
Identification |
Reference type |
Reference |
Tolerance |
|
\(A\) |
\({E}_{\mathit{xx}}\) |
ANALYTIQUE |
0.000599576100401 |
2E-4 |
\({E}_{\mathit{yy}}\) |
ANALYTIQUE |
-0.00059885996551 |
2.2E-3 |
|
13.4. notes#
Very good results are obtained since for all the quantities examined, the difference between the solution obtained with the code and the analytical solution is less than \(\text{0.5%}\) for trips and less to \(\text{5%}\) for constraints.