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.