10. H modeling#
10.1. Characteristics of modeling#
10.2. Characteristics of the mesh#
Number of knots: 33
Number of meshes and type: 20 QUAD4, 2 SEG2
10.3. Tested sizes and results#
10.3.1. Tested values#
The calculation strategy used is divided into two steps:
Imposed load: a disruptive load of \(1\mathrm{/}1000\) of the critical load following \(X\) is imposed to reveal the buckling mode. This load is applied for \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}0.95\) and up to \(P\mathrm{/}{P}_{\mathit{cr}}\mathrm{=}1.015\).
Imposed displacement: clear of 0.947, the structure begins to undergo a strong lateral displacement for a very small increase in load, so the structure is controlled in arc length to determine the post-buckling behavior.
The calculations no longer converge clear of ETA_PILOTAGE = 3.73969. The evolution of movements as a function of load is shown in the figure below. The critical load is well detected. In the post-buckling part, a maximum difference of 10% in the critical load with the analytical solution is observed.
Using the arc-length technique makes it difficult to define the reference value to be entered in the TEST_RESU command, since these values cannot be imposed. To define the reference values, we looked for the values of DZ that were as close as possible to those listed in the table in [§2.2] and we reported the values of the control parameter and of DX that we had to obtain for the values of DZ in question.
DZ |
Identification |
Instants |
Instants |
Reference Value |
Tolerance (%) |
—0.0150 |
DX |
0.995 |
“ANALYTIQUE” |
0.110 |
2.0 |
DZ |
0.995 |
“ANALYTIQUE” |
—0.015 |
2.5 |
|
ETA_PILOTAGE |
0.995 |
“ANALYTIQUE” |
1.015 |
1.5 |
|
—0.1295 |
DX |
1.10671 |
“ANALYTIQUE” |
0.2965 |
0.7 |
DZ |
1.10671 |
“ANALYTIQUE” |
—0.1295 |
1.0 |
|
ETA_PILOTAGE |
1.10671 |
“ANALYTIQUE” |
1.152 |
5.0 |
|
—0.3255 |
DX |
1.22068 |
“ANALYTIQUE” |
0.396 |
0.5 |
DZ |
1.22068 |
“ANALYTIQUE” |
—0.3255 |
0.7 |
|
ETA_PILOTAGE |
1.22068 |
“ANALYTIQUE” |
1.518 |
8.0 |
|
—0.5535 |
DX |
1.34521 |
“ANALYTIQUE” |
0.375 |
0.1 |
DZ |
1.34521 |
“ANALYTIQUE” |
—0.5535 |
0.5 |
|
ETA_PILOTAGE |
1.34521 |
“ANALYTIQUE” |
2.541 |
10.0 |
