9. G modeling#
9.1. Characteristics of modeling#
Modeling of a quarter cylinder.
Plate elements DKT: TRIA3. The modeling uses a bi-layer plate whose orthotropy characteristics are those of the material defined in \(\S 1.2\).
Discretized geometry is shown above.
point |
knot |
\(K\) |
|
\(L\) |
|
\(M\) |
|
\(N\) |
|
\(P\) |
|
\(Q\) |
|
9.2. Characteristics of the mesh#
Number of knots: 231
Number of meshes and types: 400 TRIA3 + 80 SEG2
9.3. Boundary conditions in movement and rotation#
9.3.1. 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 \(\mathrm{MN}\).
9.3.2. 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 \(\mathrm{METN}\).
9.3.3. 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 \(\mathrm{METN}\).
9.4. G modeling results#
Identification |
Knot (mesh) |
Value tested |
Reference |
Gravity |
\(K\) |
\(\mathrm{DX}\) |
—2.40000 10—8 |
\(N\) |
\(\mathrm{DY}\) |
—2.40000 10—8 |
|
\(P\) |
\(\mathrm{DZ}\) |
5.0 10—9 |
|
\(Q\) |
\(\mathrm{DZ}\) |
5.0 10—9 |
|
\(P\) |
\(-\mathrm{DRY}\) |
2.40000 10—9 |
|
\(Q\) |
\(\mathrm{DRX}\) |
2.40000 10—9 |
|
\(K(\mathrm{M362})\) |
\(\mathrm{NYY}\) |
8.00000 10—4 |
|
\(N(\mathrm{M400})\) |
\(\mathrm{NYY}\) |
8.00000 10—4 |
|
\(K(\mathrm{M362})\) |
\(\mathrm{SIYY}\) |
8.00000 10—4 |
|
\(N(\mathrm{M400})\) |
\(\mathrm{SIYY}\) |
8.00000 10—4 |
|
Dilation case 1 |
\(L(\mathrm{M1})\) |
\(\mathrm{MYY}\) |
—2.38095 10—1 |
\(M(\mathrm{M39})\) |
\(\mathrm{MYY}\) |
—2.38095 10—1 |
|
\(L(\mathrm{M1})\), inner skin |
\(\mathrm{SIXX}\) |
1.428571 |
|
\(L(\mathrm{M1})\), outer skin |
\(\mathrm{SIXX}\) |
— 1.428571 |
|
\(M(\mathrm{M39})\), inner skin |
\(\mathrm{SIXX}\) |
1.428571 |
|
\(M(\mathrm{M39})\), outer skin |
\(\mathrm{SIXX}\) |
— 1.428571 |
|
Dilation case 2 |
\(L\) |
\(\mathrm{DX}\) |
26.0 10—6 |
\(M\) |
\(\mathrm{DY}\) |
26.0 10—6 |
|
\(L(\mathrm{M1})\) |
\(\mathrm{NYY}\) |
—2.00000 10—1 |
|
\(M(\mathrm{M39})\) |
\(\mathrm{NYY}\) |
—2.00000 10—1 |
|
\(L(\mathrm{M1})\) |
\(\mathrm{SIYY}\) |
—2.00000 10—1 |
|
\(M(\mathrm{M39})\) |
\(\mathrm{SIYY}\) |
—2.00000 10—1 |