3. Modeling A#
3.1. Characteristics of modeling#
Discrete elements of stiffness, damping and mass.
Characteristics of the elements:
DISCRET: |
nodal masses |
M_ TR_D_N |
linear stiffness |
K_ TR_D_L |
|
linear amortization |
A_ TR_D_L |
No boundary conditions, in all nodes: \(\mathrm{DX},\mathrm{DY},\mathrm{DZ},\mathrm{DRX},\mathrm{DRY},\mathrm{DRZ}\) free.
Node names: \({P}_{1}=\mathrm{N1}\), \({P}_{2}=\mathrm{N2}\), \({P}_{3}=\mathrm{N3}\).
Calculation method:
Full modal integration with Newmark (\(\alpha =\mathrm{0,25}\), \(\delta =\mathrm{0,5}\)),
No time: \(\Delta t={10}^{-\mathrm{4s}}\) then modal recombination.
Observation time: \(\mathrm{5s}\).
3.2. Characteristics of the mesh#
Number of knots: 3
Number of meshes and type: 2 meshes SEG2
3.3. Tested sizes and results#
Move point \({P}_{3}\)
Time |
Move |
Move |
Difference |
(\(s\)) |
Reference (\(m\)) |
Aster (\(m\)) |
(%) |
0.09 |
6.7395 E-6 |
6.73326 E-6 |
-0.093 |
0.32 |
1.1019 E-5 |
1.10002 E-6 |
-0.171 |
1.18 |
3.6683 E-5 |
3.66122-5 |
-0.193 |
4.92 |
1.6615 E-4 |
1.65849 E-4 |
-0.181 |
Point \({P}_{3}\) speed
Time |
Speed |
Speed |
Speed |
Difference |
(\(s\)) |
Reference (\({\mathrm{m.s}}^{-1}\)) |
Aster (\({\mathrm{m.s}}^{-1}\)) |
(%) |
|
0.05 |
1.3425 E-4 |
1.34131 E-4 |
-0.088 |
|
0.32 |
-6.4111 E-5 |
-6.41097 E-4 |
-0.002 |
|
1.18 |
1.6104 E-5 |
1.60598 E-5 |
-0.274 |
|
3.55 |
4.4262 E-5 |
4.41720 E-5 |
-0.203 |
Acceleration of point \({P}_{3}\)
Time |
Acceleration |
Acceleration |
Difference |
(\(s\)) |
Reference (\({\mathrm{m.s}}^{-2}\)) |
Aster (\({\mathrm{m.s}}^{-2}\)) |
(%) |
0.09 |
-3.5694 E-3 |
-3.56634 E-3 |
-0.086 |
0.18 |
-4.3924 E-3 |
-4.38933 E-3 |
-0.070 |
0.55 |
4.3766 E-3 |
4.37283 E-3 |
-0.086 |
1.18 |
4.2459 E-3 |
4.24264 E-3 |
-0.077 |
4.92 |
-4,2233 E-3 |
-4,21962 E-3 |
-0.087 |
Relative displacement of point \({P}_{3}\) in relation to point \({P}_{1}\)
Time |
\({u}_{3}-{u}_{1}\) |
|
Difference |
(\(s\)) |
Reference (\(m\)) |
Aster (\(m\)) |
(%) |
0.18 |
8.0987 E-6 |
8.04800 E-6 |
-0.626 |
0.55 |
-6,2246 E-6 |
-6,21194 E-6 |
-0.203 |
0.82 |
5.3064 E-6 |
5.34121 E-6 |
0.656 |
1.18 |
-4.5552 E-6 |
-4.52071 E-6 |
-0.757 |
1.92 |
-3.0416 E-6 |
-3.04417 E-6 |
0.085 |
3.55 |
1.8448 E-6 |
1.82742 E-6 |
-0.942 |
4.92 |
1.4832 E-6 |
1.47526 E-6 |
-0.535 |
3.4. notes#
In addition to the comparison for the values tested, it is checked that the kinematic variables other than those related to the following translation \(x\) remain zero.