4. B modeling#
4.1. Characteristics of modeling#
Axisymmetric shell elements
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 |
\(J\) |
|
\(H\) |
|
\(F\) |
|
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 |
|