6. D modeling

6.1. Characteristics of modeling

Meshing with elements « AXIS_INCO_UPG » and « DEFORMATION =” SIMO_MIEHE “`` incompressible types TRIA6 and QUAD8.

The boundary conditions are:

• Zero vertical displacement on “FACSUP” faces (side \(\mathit{EF}\)) and “FACINF” (side \(\mathit{AB}\)): DY = 0.

• Radial displacement imposed on the inside “FACEAE” (side \(\mathit{AE}\)): DX = 6. 10-5

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

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		10-5
	\(\mathit{\sigma_{xx}}\)	ANALYTIQUE	-59.9955	10-3
	\(\mathit{\sigma_{yy}}\)	ANALYTIQUE	19.9326	10-3
	\(\mathit{\sigma_{zz}}\)	ANALYTIQUE	99.9566	10-3
	\(\mathit{\sigma_{xy}}\)	ANALYTIQUE		10-5
	VMIS	ANALYTIQUE	138.5226	10-3
	TRESCA	ANALYTIQUE	159.9521	10-3
	PRIN_1	ANALYTIQUE	-59.9955	10-3
	PRIN_2	ANALYTIQUE	19.9326	10-3
	PRIN_3	ANALYTIQUE	99.9566	10-3
	VMIS_SG	ANALYTIQUE	138.5226	10-3

Identification		Reference type	Reference	Tolerance
\(F\)	\(\mathit{u}\) (X)	ANALYTIQUE	10-5	10-3
	\(\mathit{v}\) (DY)	ANALYTIQUE		10-5
	\(\mathit{\sigma_{xx}}\)	ANALYTIQUE		0.03
	\(\mathit{\sigma_{yy}}\)	ANALYTIQUE	20.0	10-3
	\(\mathit{\sigma_{zz}}\)	ANALYTIQUE	40.006	10-3
	\(\mathit{\sigma_{xy}}\)	ANALYTIQUE		10-3

For Green-Lagrange deformations:

Identification		Reference type	Reference	Tolerance
\(A\)	\({E}_{\mathit{xx}}\)	ANALYTIQUE	-0.000598704996172	2E-3

6.4. notes

The precision obtained is very good since all the constraints are obtained. with an accuracy of less than \(\text{0.5%}\).