9. G modeling

9.1. Characteristics of modeling

Meshing with ``3D_ INCO_UPG « and » DEFORMATION =” GDEF_LOG “``elements incompressible types TETRA10 only.

Face with imposed radial displacement Face locked in dy

\(\mathit{AB}\) is on the \(\mathit{OX}\) axis (unlike 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.

• Normal movement stuck on the “FACEAB” faces (side \(\mathit{AB}\), DY = 0) and “FACEEF” (side \(\mathit{EF}\), DNOR = 0.)

• Imposed displacement on the inside of the cylinder “FACEAE”: face \(\mathit{AE}\) DNOR = -6.10-5

9.2. Characteristics of the mesh

Number of knots: 2064

Number of meshes: 1121 TETRA10

9.3. 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	10-5	10-3
	\(\mathit{v}\) (DY)	ANALYTIQUE		10-3
	\(\mathit{\sigma_{xx}}\)	ANALYTIQUE	-59.9955	0.02
	\(\mathit{\sigma_{yy}}\)	ANALYTIQUE	99.9566	0.02
	\(\mathit{\sigma_{zz}}\)	ANALYTIQUE	19.9326	0.03
	\(\mathit{\sigma_{xy}}\)	ANALYTIQUE		0.03
	VMIS	ANALYTIQUE	138.5226	0.002
	TRESCA	ANALYTIQUE	159.9521	0.002
	PRIN_1	ANALYTIQUE	-59.9955	0.02
	PRIN_2	ANALYTIQUE	19.9326	0.03
	PRIN_3	ANALYTIQUE	99.9566	0.015
	VMIS_SG	ANALYTIQUE	138.5226	0.002

Identification		Reference type	Reference	Tolerance
\(F\)	\(\mathit{u}\) (X)	ANALYTIQUE	2.1217 10-5	10-4
	\(\mathit{v}\) (DY)	ANALYTIQUE	2.1217 10-5	10-4
	\(\mathit{\sigma_{xx}}\)	ANALYTIQUE	20.003	0.003
	\(\mathit{\sigma_{yy}}\)	ANALYTIQUE	20.003	0.005
	\(\mathit{\sigma_{zz}}\)	ANALYTIQUE	20.003	0.002
	\(\mathit{\sigma_{xy}}\)	ANALYTIQUE	-20.003	0.01

9.4. notes

The results obtained are completely correct since the constraints are obtained with an accuracy of less than \(\text{3%}\) See \(\text{1%}\) at point F. The gap is a bit bigger here important only for HEXA20, but can be explained by the fact that the loading is imposed here in a slightly less precise manner since the displacement u at point A is only defined to a precision of \(\text{0.158%}\) against \(\text{0.077%}\) (evening factor 2, that can be found on the constraints).