8. F modeling

8.1. Characteristics of modeling

Mesh with incompressible 3D_ INCO_UPG (DEFORMATION =” GDEF_LOG “) elements of type 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

8.2. Characteristics of the mesh

Number of knots: 1501 knots

Number of meshes: 240 HEXA20

8.3. 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 point \(A\) only.

Identification		Reference type	Reference	Tolerance
\(A\)	\(\mathit{u}\) (X)	ANALYTIQUE		10-3
	\(\mathit{v}\) (DY)	ANALYTIQUE	10-5	10-3
	\(\mathit{\sigma_{xx}}\)	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

8.4. 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.