v6.08.102 SSND102 – Loi de comportement cinématique non-linéaire pour des éléments discrets#
Résumé:
Le problème est quasi-statique non-linéaire en mécanique des structures. Il s’agit d’une loi avec écrouissage cinématique non-linéaire. On analyse la réponse d’éléments discrets supportant une loi de comportement cinématique non-linéaire sous un chargement cyclique.
Les éléments discrets testés sont:
\(\mathrm{3D}\) (K_T_D_L, K_TR_D_L, K_T_D_N, K_TR_D_N);
\(\mathrm{2D}\) (K_T_D_L, K_TR_D_L, K_T_D_N, K_TR_D_N).
Tous les degrés de liberté sont testés, les paramètres du chargement en déplacements et ceux de la loi cinématique sont différents pour tous les degrés de liberté de façon à couvrir différentes situations.
Les solutions de référence sont obtenues de façon analytique ou par comparaison avec une application extérieure.
Solution de référence#
Méthode de calcul utilisée pour la solution de référence#
Dans le cas général, la forme complexe de la loi ne permet pas de calculer une solution de référence.
Pour valider la loi, on se place dans le cas d’un écrouissage cinématique linéaire (la puissance et l’effort limite cinématique ne sont pas donnés). Les efforts ainsi que l’énergie dissipée peuvent être calculés analytiquement.
|
Les données sont:
|
Figure 2.1.a: cycle de chargement.
Pour un cycle stabilisé (déplacement allant de 0 à
à
à
) l’énergie dissipée est
.
Dans le cas général de la loi puissance, un programme extérieur a permis de valider les réponses en efforts.
Résultats de référence#
Les tests sont réalisés sur:
l’effort à chaque inversion de chargement;
l’énergie dissipée en fin de chargement.
Pour les deux modélisations un tableau présente les paramètres de la loi ainsi que les valeurs des efforts et de l’énergie dissipée en fin de cycle.
Incertitude sur la solution#
Pour le cas de l’écrouissage cinématique linéaire il n’y a aucune incertitude, la solution est analytique, aussi bien pour les efforts que pour l’énergie.
Pour le cas de l’écrouissage non linéaire la solution de référence est donnée par un programme extérieur.
Modélisation A#
Caractéristiques de la modélisation#
Modélisation DISCRET (en 3D)
Figure 3.1.a: géométrie.
Caractéristiques des éléments discrets
Modélisation en 3D GROUP_MA
Maille \(\mathrm{M1}\) : Nœud \(\mathrm{N1}\) à \(\mathrm{N2}\) DIS_T DL_T
Maille \(\mathrm{M2}\) : Nœud \(\mathrm{N1}\) à \(\mathrm{N3}\) DIS_TR DL_TR
Maille \(\mathrm{M3}\) : Nœud \(\mathrm{N4}\) DIS_T DN_T
Maille \(\mathrm{M4}\) : Nœud \(\mathrm{N5}\) DIS_TR DN_TR
Maille \(\mathrm{M10}\) : Nœud \(\mathrm{N1}\) à \(\mathrm{N20}\) DIS_T DL_T0
Maille \(\mathrm{M30}\) : Nœud \(\mathrm{N40}\) DIS_T DN_T0
Le discret dl_t0 à les mêmes caractéristiques que dl_t, par contre son orientation est différente.
CARA=”ANGL_NAUT”, VALE=(90.0,-90.0,0.0)
L’effort \(N\) est donc suivant l’axe \(Z\) , l’effort \(\mathrm{VY}\) suivant l’axe \(Z\) et l’effort \(\mathrm{VZ}\) suivant \(X\) .
Caractéristiques du maillage#
Nombre de nœuds: 7, Nombre de mailles: 6, Éléments SEG2: 3, Éléments POI1: 3
Définition de la fonction de chargement#
instants |
valeurs |
0.0 |
0.000 |
30.0 |
1.000 |
90.0 |
-1.000 |
145.0 |
0.800 |
180.0 |
-0.450 |
230.0 |
1.150 |
250.0 |
0.500 |
280.0 |
1.450 |
Le pas choisi est de \(1.s\) .
Propriétés des discrets#
Le tableau ci-dessous donne pour toutes les directions sollicitées les caractéristiques des discrets.
LIMY_* |
K_T* |
LIMU_* |
KCIN_* |
PUIS_* |
||
DL_T |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
DL_T0 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
dz |
2000.0 |
2500000.0 |
800.0 |
700000.0 |
2.25 |
|
DN_T |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
dz |
2000.0 |
2500000.0 |
800.0 |
700000.0 |
2.25 |
|
DL_TR |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
dz |
2000.0 |
2500000.0 |
800.0 |
700000.0 |
2.25 |
|
rx |
3000.0 |
3000000.0 |
1000.0 |
600000.0 |
2.00 |
|
ry |
3500.0 |
2700000.0 |
1800.0 |
800000.0 |
1.50 |
|
rz |
2500.0 |
3200000.0 |
1400.0 |
850000.0 |
2.25 |
|
DN_TR |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
dz |
2000.0 |
2500000.0 |
800.0 |
700000.0 |
2.25 |
|
rx |
3000.0 |
3000000.0 |
1000.0 |
600000.0 |
2.00 |
|
ry |
3500.0 |
2700000.0 |
1800.0 |
800000.0 |
1.50 |
|
rz |
2500.0 |
3200000.0 |
1400.0 |
850000.0 |
2.25 |
|
DN_T0 |
dx |
1000.0 |
3400000.0 |
700000.0 |
||
dy |
1500.0 |
2000000.0 |
900000.0 |
|||
dz |
2000.0 |
2500000.0 |
700000.0 |
Grandeurs testées et résultats#
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DN_TR |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DN_TR |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DN_TR |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DN_TR |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DN_TR |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DN_TR |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DN_TR |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DN_TR |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DN_TR |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DN_TR |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DN_TR |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DN_TR |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DN_TR |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DN_TR |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DN_TR |
VZ |
30.000 |
2767.252580 |
2767.252580 |
-7.5200e-11 |
DN_TR |
VZ |
90.000 |
-2767.252580 |
-2767.252580 |
-7.5200e-11 |
DN_TR |
VZ |
145.000 |
2740.932239 |
2740.932239 |
1.8200e-10 |
DN_TR |
VZ |
180.000 |
-2547.183658 |
-2547.183658 |
2.5800e-11 |
DN_TR |
VZ |
230.000 |
2777.276300 |
2777.276300 |
-1.5700e-10 |
DN_TR |
VZ |
250.000 |
-1243.236082 |
-1243.236082 |
-9.2100e-11 |
DN_TR |
VZ |
280.000 |
2787.481342 |
2787.481342 |
7.7000e-11 |
DN_TR |
MFY |
30.000 |
5022.231028 |
5022.231028 |
9.6800e-11 |
DN_TR |
MFY |
90.000 |
-5022.231028 |
-5022.231028 |
9.6800e-11 |
DN_TR |
MFY |
145.000 |
4911.499221 |
4911.499221 |
8.9600e-11 |
DN_TR |
MFY |
180.000 |
-4443.221450 |
-4443.221450 |
-4.3200e-12 |
DN_TR |
MFY |
230.000 |
5075.752629 |
5075.752629 |
3.5200e-12 |
DN_TR |
MFY |
250.000 |
-2025.828992 |
-2025.828992 |
-8.7200e-11 |
DN_TR |
MFY |
280.000 |
5143.339483 |
5143.339483 |
-4.7600e-11 |
DN_TR |
MFZ |
30.000 |
3773.863680 |
3773.863680 |
4.0200e-11 |
DN_TR |
MFZ |
90.000 |
-3773.863680 |
-3773.863680 |
4.0200e-11 |
DN_TR |
MFZ |
145.000 |
3686.099695 |
3686.099695 |
-2.8500e-11 |
DN_TR |
MFZ |
180.000 |
-3236.583886 |
-3236.583886 |
1.3700e-10 |
DN_TR |
MFZ |
230.000 |
3810.233618 |
3810.233618 |
6.2600e-11 |
DN_TR |
MFZ |
250.000 |
-1262.367026 |
-1262.367026 |
5.6200e-11 |
DN_TR |
MFZ |
280.000 |
3849.201624 |
3849.201624 |
-1.8600e-12 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DN_T |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DN_T |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DN_T |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DN_T |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DN_T |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DN_T |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DN_T |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DN_T |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DN_T |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DN_T |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DN_T |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DN_T |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DN_T |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DN_T |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DN_T |
VZ |
30.000 |
2767.252580 |
2767.252580 |
-7.5200e-11 |
DN_T |
VZ |
90.000 |
-2767.252580 |
-2767.252580 |
-7.5200e-11 |
DN_T |
VZ |
145.000 |
2740.932239 |
2740.932239 |
1.8200e-10 |
DN_T |
VZ |
180.000 |
-2547.183658 |
-2547.183658 |
2.5800e-11 |
DN_T |
VZ |
230.000 |
2777.276300 |
2777.276300 |
-1.5700e-10 |
DN_T |
VZ |
250.000 |
-1243.236082 |
-1243.236082 |
-9.2100e-11 |
DN_T |
VZ |
280.000 |
2787.481342 |
2787.481342 |
7.7000e-11 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DL_TR |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DL_TR |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DL_TR |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DL_TR |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DL_TR |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DL_TR |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DL_TR |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DL_TR |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DL_TR |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DL_TR |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DL_TR |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DL_TR |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DL_TR |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DL_TR |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DL_TR |
VZ |
30.000 |
2767.252580 |
2767.252580 |
-7.5200e-11 |
DL_TR |
VZ |
90.000 |
-2767.252580 |
-2767.252580 |
-7.5200e-11 |
DL_TR |
VZ |
145.000 |
2740.932239 |
2740.932239 |
1.8200e-10 |
DL_TR |
VZ |
180.000 |
-2547.183658 |
-2547.183658 |
2.5800e-11 |
DL_TR |
VZ |
230.000 |
2777.276300 |
2777.276300 |
-1.5700e-10 |
DL_TR |
VZ |
250.000 |
-1243.236082 |
-1243.236082 |
-9.2100e-11 |
DL_TR |
VZ |
280.000 |
2787.481342 |
2787.481342 |
7.7000e-11 |
DL_TR |
MFY |
30.000 |
5022.231028 |
5022.231028 |
9.6800e-11 |
DL_TR |
MFY |
90.000 |
-5022.231028 |
-5022.231028 |
9.6800e-11 |
DL_TR |
MFY |
145.000 |
4911.499221 |
4911.499221 |
8.9600e-11 |
DL_TR |
MFY |
180.000 |
-4443.221450 |
-4443.221450 |
-4.3200e-12 |
DL_TR |
MFY |
230.000 |
5075.752629 |
5075.752629 |
3.5200e-12 |
DL_TR |
MFY |
250.000 |
-2025.828992 |
-2025.828992 |
-8.7200e-11 |
DL_TR |
MFY |
280.000 |
5143.339483 |
5143.339483 |
-4.7600e-11 |
DL_TR |
MFZ |
30.000 |
3773.863680 |
3773.863680 |
4.0200e-11 |
DL_TR |
MFZ |
90.000 |
-3773.863680 |
-3773.863680 |
4.0200e-11 |
DL_TR |
MFZ |
145.000 |
3686.099695 |
3686.099695 |
-2.8500e-11 |
DL_TR |
MFZ |
180.000 |
-3236.583886 |
-3236.583886 |
1.3700e-10 |
DL_TR |
MFZ |
230.000 |
3810.233618 |
3810.233618 |
6.2600e-11 |
DL_TR |
MFZ |
250.000 |
-1262.367026 |
-1262.367026 |
5.6200e-11 |
DL_TR |
MFZ |
280.000 |
3849.201624 |
3849.201624 |
-1.8600e-12 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DL_T |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DL_T |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DL_T |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DL_T |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DL_T |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DL_T |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DL_T |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DL_T |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DL_T |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DL_T |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DL_T |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DL_T |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DL_T |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DL_T |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DL_T |
VZ |
30.000 |
2767.252580 |
2767.252580 |
-7.5200e-11 |
DL_T |
VZ |
90.000 |
-2767.252580 |
-2767.252580 |
-7.5200e-11 |
DL_T |
VZ |
145.000 |
2740.932239 |
2740.932239 |
1.8200e-10 |
DL_T |
VZ |
180.000 |
-2547.183658 |
-2547.183658 |
2.5800e-11 |
DL_T |
VZ |
230.000 |
2777.276300 |
2777.276300 |
-1.5700e-10 |
DL_T |
VZ |
250.000 |
-1243.236082 |
-1243.236082 |
-9.2100e-11 |
DL_T |
VZ |
280.000 |
2787.481342 |
2787.481342 |
7.7000e-11 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DL_T0 |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DL_T0 |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DL_T0 |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DL_T0 |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DL_T0 |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DL_T0 |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DL_T0 |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DL_T0 |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DL_T0 |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DL_T0 |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DL_T0 |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DL_T0 |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DL_T0 |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DL_T0 |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DL_T0 |
VZ |
30.000 |
2767.252580 |
2767.252580 |
-7.5200e-11 |
DL_T0 |
VZ |
90.000 |
-2767.252580 |
-2767.252580 |
-7.5200e-11 |
DL_T0 |
VZ |
145.000 |
2740.932239 |
2740.932239 |
1.8200e-10 |
DL_T0 |
VZ |
180.000 |
-2547.183658 |
-2547.183658 |
2.5800e-11 |
DL_T0 |
VZ |
230.000 |
2777.276300 |
2777.276300 |
-1.5700e-10 |
DL_T0 |
VZ |
250.000 |
-1243.236082 |
-1243.236082 |
-9.2100e-11 |
DL_T0 |
VZ |
280.000 |
2787.481342 |
2787.481342 |
7.7000e-11 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DN_T0 |
N |
30.000 |
1823.529412 |
1823.529412 |
3.5500e-11 |
DN_T0 |
N |
90.000 |
-1823.529412 |
-1823.529412 |
3.5500e-11 |
DN_T0 |
N |
145.000 |
1823.529412 |
1823.529412 |
3.5500e-11 |
DN_T0 |
VY |
30.000 |
4200.000000 |
4200.000000 |
2.1700e-16 |
DN_T0 |
VY |
90.000 |
-4200.000000 |
-4200.000000 |
-4.3300e-16 |
DN_T0 |
VY |
145.000 |
4200.000000 |
4200.000000 |
-2.1700e-16 |
DN_T0 |
VZ |
30.000 |
4240.000000 |
4240.000000 |
0.0000e+00 |
DN_T0 |
VZ |
90.000 |
-4240.000000 |
-4240.000000 |
-2.1500e-16 |
DN_T0 |
VZ |
145.000 |
4240.000000 |
4240.000000 |
2.1500e-16 |
GROUP_MA |
Direction |
Énergie Référence |
Énergie Code_Aster |
Erreur |
DN_TR |
DX |
9.083900 |
9.083899 |
-1.1600e-07 |
DN_TR |
DY |
35.563390 |
35.563387 |
-9.4500 10-8 |
DN_TR |
DZ |
51.155440 |
51.155445 |
9.2600 10-8 |
DN_TR |
RX |
96.706530 |
96.706529 |
-1.5000 10-8 |
DN_TR |
RY |
144.155340 |
144.155339 |
-4.8400 10-9 |
DN_TR |
RZ |
61.549450 |
61.549446 |
-5.8100 10-8 |
DN_T |
DX |
9.083900 |
9.083899 |
-1.1600e-07 |
DN_T |
DY |
35.563390 |
35.563387 |
-9.4500 10-8 |
DN_T |
DZ |
51.155440 |
51.155445 |
9.2600 10-8 |
DL_TR |
DX |
9.083900 |
9.083899 |
-1.1600e-07 |
DL_TR |
DY |
35.563390 |
35.563387 |
-9.4500 10-8 |
DL_TR |
DZ |
51.155440 |
51.155445 |
9.2600 10-8 |
DL_TR |
RX |
96.706530 |
96.706529 |
-1.5000 10-8 |
DL_TR |
RY |
144.155340 |
144.155339 |
-4.8400e-09 |
DL_TR |
RZ |
61.549450 |
61.549446 |
-5.8100 10-8 |
DL_T |
DX |
9.083900 |
9.083899 |
-1.1600e-07 |
DL_T |
DY |
35.563390 |
35.563387 |
-9.4500 10-8 |
DL_T |
DZ |
51.155440 |
51.155445 |
9.2600 10-8 |
DL_T0 |
DX |
9.083900 |
9.083899 |
-1.1600e-07 |
DL_T0 |
DY |
35.563390 |
35.563387 |
-9.4500 10-8 |
DL_T0 |
DZ |
51.155440 |
51.155445 |
9.2600 10-8 |
DN_T0 |
DX |
5.055974 |
5.055974 |
-5.5200e-12 |
DN_T0 |
DY |
14.602500 |
14.602500 |
0.0000 |
DN_T0 |
DZ |
25.620480 |
25.620480 |
1.3900e-16 |
Modélisation B#
Caractéristiques de la modélisation#
Modélisation 2D_DISCRET
Figure 5.1.a: géométrie.
Caractéristiques des éléments discrets
Modélisation \(\mathrm{2D}\) GROUP_MA
Maille \(\mathrm{M1}\) : Nœud \(\mathrm{N1}\) à \(\mathrm{N2}\) 2D_DIS_T DL_T
Maille \(\mathrm{M2}\) : Nœud \(\mathrm{N1}\) à \(\mathrm{N3}\) 2D_DIS_TR DL_TR
Maille \(\mathrm{M3}\) : Nœud \(\mathrm{N4}\) 2D_DIS_T DN_T
Maille \(\mathrm{M4}\) : Nœud \(\mathrm{N5}\) 2D_DIS_TR DN_TR
Caractéristiques du maillage#
Nombre de nœuds: 5, Nombre de mailles: 4, Élément SEG2 : 2, Élément POI1 : 2
Propriétés des discrets#
Le tableau ci-dessous donne pour toutes les directions sollicitées les caractéristiques des discrets.
|
|
|
|
|
||
DL_T |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
DN_T |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
DL_TR |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
rz |
2500.0 |
3200000.0 |
1400.0 |
850000.0 |
2.25 |
|
DN_TR |
dx |
1000.0 |
3400000.0 |
1000.0 |
700000.0 |
2.00 |
dy |
1500.0 |
2000000.0 |
800.0 |
900000.0 |
1.50 |
|
rz |
2500.0 |
3200000.0 |
1400.0 |
850000.0 |
2.25 |
Grandeurs testées et résultats#
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DN_TR |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DN_TR |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DN_TR |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DN_TR |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DN_TR |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DN_TR |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DN_TR |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DN_TR |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DN_TR |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DN_TR |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DN_TR |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DN_TR |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DN_TR |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DN_TR |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DN_TR |
MFZ |
30.000 |
3773.863680 |
3773.863680 |
4.0200e-11 |
DN_TR |
MFZ |
90.000 |
-3773.863680 |
-3773.863680 |
4.0200e-11 |
DN_TR |
MFZ |
145.000 |
3686.099695 |
3686.099695 |
-2.8500e-11 |
DN_TR |
MFZ |
180.000 |
-3236.583886 |
-3236.583886 |
1.3700e-10 |
DN_TR |
MFZ |
230.000 |
3810.233618 |
3810.233618 |
6.2600e-11 |
DN_TR |
MFZ |
250.000 |
-1262.367026 |
-1262.367026 |
5.6200e-11 |
DN_TR |
MFZ |
280.000 |
3849.201624 |
3849.201624 |
-1.8600e-12 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DN_T |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DN_T |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DN_T |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DN_T |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DN_T |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DN_T |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DN_T |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DN_T |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DN_T |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DN_T |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DN_T |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DN_T |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DN_T |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DN_T |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DL_TR |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DL_TR |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DL_TR |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DL_TR |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DL_TR |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DL_TR |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DL_TR |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DL_TR |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DL_TR |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DL_TR |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DL_TR |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DL_TR |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DL_TR |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DL_TR |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
DL_TR |
MFZ |
30.000 |
3773.863680 |
3773.863680 |
4.0200e-11 |
DL_TR |
MFZ |
90.000 |
-3773.863680 |
-3773.863680 |
4.0200e-11 |
DL_TR |
MFZ |
145.000 |
3686.099695 |
3686.099695 |
-2.8500e-11 |
DL_TR |
MFZ |
180.000 |
-3236.583886 |
-3236.583886 |
1.3700e-10 |
DL_TR |
MFZ |
230.000 |
3810.233618 |
3810.233618 |
6.2600e-11 |
DL_TR |
MFZ |
250.000 |
-1262.367026 |
-1262.367026 |
5.6200e-11 |
DL_TR |
MFZ |
280.000 |
3849.201624 |
3849.201624 |
-1.8600e-12 |
GROUP_MA |
Effort |
Instant |
Effort Référence |
Effort Code_Aster |
Erreur |
DL_T |
N |
30.000 |
1635.707253 |
1635.707253 |
-8.4900e-11 |
DL_T |
N |
90.000 |
-1635.707253 |
-1635.707253 |
-8.4900e-11 |
DL_T |
N |
145.000 |
1525.492881 |
1525.492881 |
-1.8200e-10 |
DL_T |
N |
180.000 |
-1249.231871 |
-1249.231871 |
1.4500e-11 |
DL_T |
N |
230.000 |
1699.177353 |
1699.177353 |
-1.6000e-10 |
DL_T |
N |
250.000 |
-415.381013 |
-415.381013 |
-1.1200e-10 |
DL_T |
N |
280.000 |
1789.595108 |
1789.595108 |
-4.9600e-11 |
DL_T |
VY |
30.000 |
2224.098875 |
2224.098875 |
-4.9400e-12 |
DL_T |
VY |
90.000 |
-2224.098875 |
-2224.098875 |
-4.9400e-12 |
DL_T |
VY |
145.000 |
2190.040518 |
2190.040518 |
-1.0900e-10 |
DL_T |
VY |
180.000 |
-2017.290415 |
-2017.290415 |
-1.5500e-10 |
DL_T |
VY |
230.000 |
2239.745512 |
2239.745512 |
-6.2600e-12 |
DL_T |
VY |
250.000 |
-790.397664 |
-790.397663 |
-3.5800e-11 |
DL_T |
VY |
280.000 |
2258.782745 |
2258.782745 |
1.0400e-10 |
GROUP_MA |
Direction |
Énergie Référence |
Énergie Code_Aster |
Erreur |
DN_TR |
DX |
12.862800 |
12.862836 |
2.8000 10-6 |
DN_TR |
DY |
49.538500 |
49.538536 |
7.3200e-07 |
DN_TR |
RZ |
84.921900 |
84.921949 |
5.8100e-07 |
DN_T |
DX |
12.862800 |
12.862836 |
2.8000 10-6 |
DN_T |
DY |
49.538500 |
49.538536 |
7.3200e-07 |
DL_TR |
DX |
12.862800 |
12.862836 |
2.8000 10-6 |
DL_TR |
DY |
49.538500 |
49.538536 |
7.3200e-07 |
DL_TR |
RZ |
84.921900 |
84.921949 |
5.8100e-07 |
DL_T |
DX |
12.862800 |
12.862836 |
2.8000 10-6 |
DL_T |
DY |
49.538500 |
49.538536 |
7.3200e-07 |
Synthèse des résultats#
Ces tests permettent de vérifier le bon fonctionnement des éléments discrets \(\mathrm{2D}\) et \(\mathrm{3D}\) avec le comportement DIS_ECRO_CINE et l’utilisation de STAT_NON_LINE.