2. Benchmark solution#
2.1. Calculation method#
The total surface is \(\mathrm{12m²}\).
The area opposite the nodes is given in the following table:
Knots |
X [m] |
Y [m] |
Y [m] |
Z [m] |
Z [m] |
Z [m] |
Z [m] |
Z [m] |
Area [m²] |
|||
1 |
2.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.2500 |
11 |
2.00 |
3.00 |
0.00 |
0.6667 |
|
2 |
3.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.5000 |
12 |
3.00 |
3.00 |
0.00 |
0.00 |
0.9167 |
3 |
4.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.5000 |
13 |
4.00 |
3.00 |
0.00 |
0.00 |
0.8333 |
4 |
5.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.5000 |
14 |
5.00 |
3.00 |
0.00 |
0.00 |
1.0833 |
5 |
6.00 |
1.00 |
0.00 |
0.00 |
0.00 |
0.2500 |
15 |
6.00 |
3.00 |
0.00 |
0.5000 |
|
6 |
2.00 |
2.00 |
0.00 |
0.00 |
0.00 |
0.4167 |
16 |
2.00 |
4.00 |
0.00 |
0.00 |
0.1667 |
7 |
3.00 |
2.00 |
0.00 |
0.00 |
0.00 |
1.0833 |
17 |
3.00 |
4.00 |
0.00 |
0.00 |
0.5000 |
8 |
4.00 |
2.00 |
0.00 |
0.00 |
0.00 |
1.0000 |
18 |
4.00 |
0.00 |
0.00 |
0.6667 |
|
9 |
5.00 |
2.00 |
0.00 |
0.00 |
0.00 |
1.0833 |
19 |
5.00 |
4.00 |
0.00 |
0.00 |
0.3333 |
10 |
6.00 |
2.00 |
0.00 |
0.00 |
0.00 |
0.4167 |
20 |
6.00 |
4.00 |
0.00 |
0.00 |
0.3333 |
For a mass to be distributed over a surface, the POI1 cells are affected by the mass:
\({\mathit{Masse}}_{\mathit{POI1}}=\frac{{\mathit{Masse}}_{\mathit{Totale}}\ast {\mathit{Surface}}_{\mathit{Noeud}}}{{\mathit{Surface}}_{\mathit{Totale}}}\)
For a surface mass to be distributed over a surface, the POI1 cells are affected by the mass:
\({\mathit{Masse}}_{\mathit{POI1}}={\mathit{Masse}}_{\mathit{Surfacique}}\ast {\mathit{Surface}}_{\mathit{Noeud}}\)
If a distribution function is given, the mass (surface or linear) is weighted by the value of the function calculated at the center of gravity of the mesh (surface or linear). This weighted mass is then distributed over the POI1 cells.
2.2. Reference quantities and results#
All the masses assigned to GROUP_MA_POI1.
2.3. Uncertainties about the solution#
None.