5. C modeling#
5.1. Characteristics of modeling#
Modeling of a quarter cylinder.
3D shell elements: QUAD9
Discretized geometry is shown above.
\(\mathrm{point}\) |
|
\(K\) |
|
\(L\) |
|
\(M\) |
|
\(N\) |
|
\(P\) |
|
\(Q\) |
|
The shear correction factor \({A}_{\mathrm{CIS}}\) is \(5/6\) (Reissner shell theory).
5.2. Characteristics of the mesh#
Number of external nodes: 121
Number of meshes and types: 32 QUAD9 + 8 SEG3
5.3. Boundary conditions in movement and rotation#
5.3.1. Gravity#
Move \(\mathrm{DZ}\) is stuck on the group of nodes \(\mathrm{LM}\).
The movement \(\mathrm{DY}\) as well as the rotations around the axes \(X\) and \(Z\) are blocked on the group of nodes \(\mathrm{KL}\).
The movement \(\mathrm{DX}\) as well as the rotations around the axes \(Y\) and \(Z\) are blocked on the group of nodes \(\mathrm{MN}\).
5.3.2. Rotation#
The \(\mathrm{DZ}\) movement as well as the rotations around the \(X\) and \(Y\) axes are blocked on the node groups \(\mathrm{KNSANSKN}\) and \(\mathrm{LMSANSLM}\).
The movement \(\mathrm{DY}\) as well as the rotations around the axes \(X\) and \(Z\) are blocked on the group of nodes \(\mathrm{KL}\).
The movement \(\mathrm{DX}\) as well as the rotations around the axes \(Y\) and \(Z\) are blocked on the group of nodes \(\mathrm{MN}\).
The \(\mathrm{DZ}\) movement and the rotation around the \(Y\) axis are blocked on the group of nodes \(\mathrm{KETL}\).
The \(\mathrm{DZ}\) movement and the rotation around the \(X\) axis are blocked on the group of nodes \(\mathrm{METN}\).
5.3.3. Thermal expansion case no. 1#
The \(\mathrm{DZ}\) movement as well as the rotations around the \(X\) and \(Y\) axes are blocked on the node groups \(\mathrm{KNSANSKN}\) and \(\mathrm{LMSANSLM}\).
The movement \(\mathrm{DY}\) as well as the rotations around the axes \(X\) and \(Z\) are blocked on the group of nodes \(\mathrm{KL}\).
The movement \(\mathrm{DX}\) as well as the rotations around the axes \(Y\) and \(Z\) are blocked on the group of nodes \(\mathrm{MN}\).
The \(\mathrm{DZ}\) movement and the rotation around the \(Y\) axis are blocked on the group of nodes \(\mathrm{KETL}\).
The \(\mathrm{DZ}\) movement and the rotation around the \(X\) axis are blocked on the group of nodes \(\mathrm{METN}\).
5.3.4. Thermal expansion case no. 2#
The \(\mathrm{DZ}\) movement as well as the rotations around the \(X\) and \(Y\) axes are blocked on the node groups \(\mathrm{KNSANSKN}\) and \(\mathrm{LMSANSLM}\).
The movement \(\mathrm{DY}\) as well as the rotations around the axes \(X\) and \(Z\) are blocked on the group of nodes \(\mathrm{KL}\).
The movement \(\mathrm{DX}\) as well as the rotations around the axes \(Y\) and \(Z\) are blocked on the group of nodes \(\mathrm{MN}\).
The \(\mathrm{DZ}\) movement and the rotation around the \(Y\) axis are blocked on the group of nodes \(\mathrm{KETL}\).
The \(\mathrm{DZ}\) movement and the rotation around the \(X\) axis are blocked on the group of nodes \(\mathrm{METN}\).
5.4. C modeling results#
Identification |
Knot (mesh) |
Value tested |
Reference |
Gravity |
\(K\) |
\(\mathrm{DX}\) \((\mathrm{mm})\) |
—2.40000 10—8 |
\(N\) |
\(\mathrm{DY}\) \((\mathrm{mm})\) |
—2.40000 10—8 |
|
\(P\) |
\(\mathrm{DZ}\) \((\mathrm{mm})\) |
5.00000 10—9 |
|
\(Q\) |
\(\mathrm{DZ}\) \((\mathrm{mm})\) |
5.00000 10—9 |
|
\(P\) |
\(\mathrm{DRY}\) |
2.40000 10—9 |
|
\(Q\) |
\(\mathrm{DRX}\) |
2.40000 10—9 |
|
\(K(\mathrm{M4})\) |
\(\mathrm{NYY}\) \((N)\) |
8.00000 10—4 |
|
\(N(\mathrm{M32})\) |
\(\mathrm{NYY}\) \((N)\) |
8.00000 10—4 |
|
\(K(\mathrm{M4})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
8.00000 10—4 |
|
\(N(\mathrm{M32})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
8.00000 10—4 |
|
Rotation — centrifugal force |
\(L\) |
\(\mathrm{DX}\) \((\mathrm{mm})\) |
2.91200 10—7 |
\(M\) |
\(\mathrm{DY}\) \((\mathrm{mm})\) |
2.91200 10—7 |
|
\(L(\mathrm{M1})\) |
\(\mathrm{NYY}\) \((N)\) |
9.60000 10—4 |
|
\(M(\mathrm{M29})\) |
\(\mathrm{NYY}\) \((N)\) |
9.60000 10—4 |
|
\(L(\mathrm{M1})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
9.84600 10—4 |
|
\(M(\mathrm{M29})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
9.84600 10—4 |
|
Dilation case 1 |
\(L(\mathrm{M1})\) |
\(\mathrm{MYY}\) \((\mathrm{N.mm})\) |
—2.38095 10—1 |
\(M(\mathrm{M29})\) |
\(\mathrm{MYY}\) \((\mathrm{N.mm})\) |
—2.38095 10—1 |
|
\(L(\mathrm{M1})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
1.428571 |
|
\(M(\mathrm{M29})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
1.428571 |
|
Dilation case 2 |
\(L\) |
\(\mathrm{DX}\) \((\mathrm{mm})\) |
25.9946 10—6 |
\(M\) |
\(\mathrm{DY}\) \((\mathrm{mm})\) |
25.9946 10—6 |
|
\(L(\mathrm{M1})\) |
\(\mathrm{NYY}\) \((N)\) |
—2.00000 10—1 |
|
\(M(\mathrm{M29})\) |
\(\mathrm{NYY}\) \((N)\) |
—2.00000 10—1 |
|
\(L(\mathrm{M1})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
—1.97800 10—1 |
|
\(M(\mathrm{M29})\) Inner skin |
\(\mathrm{SIYY}\) \((\mathrm{MPa})\) |
—2.97800 10—1 |
5.5. notes#
Satisfactory and identical results for calculations with MECA_STATIQUE and STAT_NON_LINE.