4. B modeling#

4.1. Characteristics of modeling#

Axisymmetric shell elements

_images/1000045000000EC8000018CE03D68347C69B2FAD.svg

Discretized geometry is shown above. The Love‑Kirchhoff shell theory is chosen (for this purpose a transverse shear coefficient of 106 is taken). The metric correction in thickness is neglected. The thickness is \(1\mathrm{mm}\).

knot

GROUP_NO

\(J\)

\(\mathrm{GRNO13}\)

\(H\)

\(\mathrm{GRNO14}\)

\(F\)

\(\mathrm{GRNO6}\)

4.2. Characteristics of the mesh#

Number of knots: 21

Number of meshes and type: 10 SEG3

4.3. Boundary conditions in movement and rotation#

4.3.1. Gravity#

Move \(\mathrm{DY}\) is stuck at point \(F\) alone (\(\mathrm{GRNO6}\)).

4.3.2. Rotation#

Move \(\mathrm{DY}\) is stuck at point \(F\) (\(\mathrm{GRNO6}\)) at point \(J\) (\(\mathrm{GRNO13}\)).

The rotation around the \(Z\) axis is zero at these two points.

4.3.3. Thermal expansion case no. 1#

The movement \(\mathrm{DY}\) as well as the rotation around the axis \(Z\) are blocked throughout the structure (GROUP_NO = “GRNO15”).

4.3.4. Thermal expansion case no. 2#

Move \(\mathrm{DY}\) is stuck at point \(F\) (GROUP_NO = “GRNO06”) and at point \(J\) (GROUP_NO = “GRNO13”). The rotation around the \(Z\) axis is zero on the same node groups.

4.4. B modeling results#

Identification

Knot (Knit)

Value tested

Reference

Gravity

\(J\)

\(\mathrm{DX}(\mathrm{mm})\)

—2.40000 10—8

\(H\)

\(\mathrm{DY}(\mathrm{mm})\)

5.00000 10—9

\(H\)

\(\mathrm{DRZ}\)

2.40000 10—9

\(J(\mathrm{M10})\)

\(\mathrm{NXX}(N)\)

8.00000 10—4

\(J(\mathrm{M10})\) Inner skin

\(\mathrm{SIXX}(\mathrm{MPa})\)

8.00000 10—4

Rotation - centrifugal force

\(F\)

\(\mathrm{DX}(\mathrm{mm})\)

2.91200 10—7

\(F(\mathrm{M1})\)

\(\mathrm{NXX}(N)\)

9.60000 10—4

\(F(\mathrm{M1})\) Inner skin

\(\mathrm{SIXX}(\mathrm{MPa})\)

9.60000 10—4

Dilation case 1

\(F(\mathrm{M1})\)

\(\mathrm{MXX}(\mathrm{N.mm})\)

—2.38095 10—1

\(F(\mathrm{M1})\) Inner skin

\(\mathrm{SIXX}(\mathrm{Mpa})\)

1.428571

Dilation case 2

\(F\)

\(\mathrm{DX}(\mathrm{mm})\)

26.0000 10—6

\(F(\mathrm{M1})\)

\(\mathrm{NXX}(N)\)

—2.00000 10—1

\(F(\mathrm{M1})\) Inner skin

\(\mathrm{SIXX}(\mathrm{MPa})\)

—2.00000 10—1