4. B modeling#
4.1. Characteristics of modeling#
Meshing with ``3D_ INCO_UPG « and » DEFORMATION =” SIMO_MIEHE “``elements incompressible type TETRA10 only
\(\mathit{AB}\) is on the \(\mathit{OX}\) axis (in contrast to modeling A).
The mesh was obtained with GMSH for a density of \(\mathrm{0,01}\).
The boundary conditions are:
Zero vertical displacement on “FACSUP” and “FACINF” faces \(\mathit{AEFD}\) (\(z=0\) and \(z=0.01\)): DZ = 0.
Movement blocked in dy on the “FACEAB” side (side \(\mathit{AB}\), DY = 0)
Normal movement stuck on side “FACEEF” (side \(\mathit{EF}\), DNOR = 0.)
Radial displacement imposed on the inside face of the “FACEAE” cylinder: face \(\mathit{AE}\) DNOR = -6.10-5
4.2. Characteristics of the mesh#
Number of knots: 2064
Number of meshes: 1121 TETRA10
4.3. Tested sizes and results#
Displacements and constraints SIGM_NOEU are evaluated at points \(A\) and \(F\). The components of field SIEQ_NOEU are tested at point \(A\) only.
Identification |
Reference type |
Reference |
Tolerance |
|
\(A\) |
\(\mathit{u}\) (X) |
ANALYTIQUE |
|
|
\(\mathit{v}\) (DY) |
ANALYTIQUE |
|
||
\(\mathit{\sigma_{xx}}\) |
ANALYTIQUE |
-59.9955 |
0.025 |
|
\(\mathit{\sigma_{yy}}\) |
ANALYTIQUE |
99.9566 |
0.02 |
|
\(\mathit{\sigma_{zz}}\) |
ANALYTIQUE |
19.9326 |
0.03 |
|
\(\mathit{\sigma_{xy}}\) |
ANALYTIQUE |
0.03 |
||
VMIS |
ANALYTIQUE |
138.5226 |
0.01 |
|
TRESCA |
ANALYTIQUE |
159.9521 |
0.01 |
|
PRIN_1 |
ANALYTIQUE |
-59.9955 |
0.025 |
|
PRIN_2 |
ANALYTIQUE |
19.9326 |
0.03 |
|
PRIN_3 |
ANALYTIQUE |
99.9566 |
0.015 |
|
VMIS_SG |
ANALYTIQUE |
138.5226 |
0.01 |
|
Identification |
Reference type |
Reference |
Tolerance |
|
\(F\) |
\(\mathit{u}\) (X) |
ANALYTIQUE |
2.1217 10-5 |
|
\(\mathit{v}\) (DY) |
ANALYTIQUE |
2.1217 10-5 |
|
|
\(\mathit{\sigma_{xx}}\) |
ANALYTIQUE |
20.003 |
0.005 |
|
\(\mathit{\sigma_{yy}}\) |
ANALYTIQUE |
20.003 |
0.005 |
|
\(\mathit{\sigma_{zz}}\) |
ANALYTIQUE |
20.003 |
0.005 |
|
\(\mathit{\sigma_{xy}}\) |
ANALYTIQUE |
-20.003 |
0.01 |
|
4.4. notes#
The results obtained are completely correct since the constraints are obtained with a precision of less than \(\text{3%}\) See \(\text{1 %}\) at point F. The gap is a bit bigger here. only for HEXA20, but can be explained by the fact that loading is imposed here in a slightly less precise manner since the displacement u at point A, is only set to a precision of \(\text{0.158%}\) against \(\text{0.077%}\) (evening the factor 2, which can be found on constraints).