13. K modeling#
13.1. Characteristics of modeling#
Same as E modeling with DKQG elements (DKTG modeling).
The purpose of this modeling is to test the consideration of temperature for elements DKQG.
Plate elements DKQG: QUAD4
Discretized geometry is shown above.
point |
knot |
\(K\) |
|
\(L\) |
|
\(M\) |
|
\(N\) |
|
\(P\) |
|
\(Q\) |
|
13.2. Characteristics of the mesh#
Number of knots: 231
Number of meshes and types: 200 QUAD4 + 80 SEG2
13.3. Boundary conditions in movement and rotation#
13.3.1. 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 \(\mathrm{MN}\).
13.3.2. 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 \(\mathrm{METN}\).
13.3.3. 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 \(\mathrm{METN}\).
13.4. K 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 |
|
\(K(181)\) |
\(\mathrm{NYY}(N)\) |
8.00000 10—4 |
|
\(N(\mathrm{M200})\) |
\(\mathrm{NYY}(N)\) |
8.00000 10—4 |
|
Dilation case 1 |
\(L(\mathrm{M1})\) |
\(\mathrm{MYY}(\mathrm{N.mm})\) |
—2.38095 10—1 |
\(M(\mathrm{M20})\) |
\(\mathrm{MYY}(\mathrm{N.mm})\) |
—2.38095 10—1 |
|
Dilation case 2 |
\(L\) |
\(\mathrm{DX}(\mathrm{mm})\) |
26.0000 10—6 |
\(M\) |
\(\mathrm{DY}(\mathrm{mm})\) |
26.0000 10—6 |
|
\(L(\mathrm{M1})\) |
\(\mathrm{NYY}(N)\) |
—2.00000 10—1 |
|
\(M(\mathrm{M20})\) |
\(\mathrm{NYY}(N)\) |
—2.00000 10—1 |