3. Modeling A#
3.1. Characteristics of the mesh#
The mesh is composed of a QUAD4 mesh with four nodes (\(\mathit{N1}\), \(\mathit{N2}\), \(\mathit{N3}\) and \(\mathit{N4}\)).
For each mesh, there are 4 integration points
Node group \(\mathit{ENC}\) is composed of nodes \(\mathit{N1}\) and \(\mathit{N2}\)
Node group \(\mathit{CHA}\) is composed of nodes \(\mathit{N3}\) and \(\mathit{N4}\)
3.2. Characteristics of modeling#
Modeling:
MO= AFFE_MODELE (MAILLAGE =MA,
AFFE =_F (TOUT =” OUI “, PHENOMENE =” MECANIQUE”,
MODELISATION =” DKT “,),
)
Boundary conditions:
BLOCAGE = AFFE_CHAR_MECA (MODELE =MO,
DDL_IMPO =_F (GROUP_NO =” ENC “,
DX=0.0, DY=0.0, DZ=0.0, DRX =0.0, =0.0, DRY =0.0, DRZ =0.0,),
)
Mechanical loading:
CHARGE = AFFE_CHAR_MECA (MODELE =MO,
FORCE_NODALE =_F (GROUP_NO =” CHA “, FX=0, FX=0, FZ=-100. ),
)
Assignment of the characteristics of the elements:
PLAQUE = AFFE_CARA_ELEM (MODELE =MO,
COQUE =_F (GROUP_MA =( “PLA”), EPAIS = 0.5, COQUE_NCOU = 4,),
)
3.3. Tested values and results#
Coordinated mesh QUA1 |
Point integration |
sub-point |
Reference |
|
COOR_X |
1 |
1 |
1 |
0.204941012 |
COOR_X |
1 |
2 |
0.232004306 |
|
COOR_X |
1 |
3 |
3 |
0.2590676 |
COOR_X |
1 |
4 |
0.2590676 |
|
COOR_X |
1 |
5 |
5 |
0.286130894 |
COOR_X |
1 |
6 |
6 |
0.313194187 |
COOR_X |
1 |
7 |
7 |
0.313194187 |
COOR_X |
1 |
8 |
8 |
0.340257481 |
COOR_X |
1 |
9 |
9 |
0.367320775 |
COOR_X |
1 |
10 |
0.367320775 |
|
COOR_X |
1 |
11 |
0.394384069 |
|
COOR_X |
1 |
12 |
0.421447363 |
|
COOR_Y |
1 |
1 |
1 |
0.490331216 |
COOR_Y |
1 |
2 |
2 |
0.443456216 |
COOR_Y |
1 |
3 |
3 |
0.396581216 |
COOR_Y |
1 |
4 |
4 |
0.396581216 |
COOR_Y |
1 |
5 |
5 |
0.349706216 |
COOR_Y |
1 |
6 |
6 |
0.302831216 |
COOR_Y |
1 |
7 |
7 |
0.302831216 |
COOR_Y |
1 |
8 |
8 |
0.255956216 |
COOR_Y |
1 |
9 |
9 |
0.209081216 |
COOR_Y |
1 |
10 |
0.209081216 |
|
COOR_Y |
1 |
11 |
0.162206216 |
|
COOR_X |
1 |
12 |
0.115331216 |
|
COOR_Z |
1 |
1 |
1 |
0.058012702 |
COOR_Z |
1 |
2 |
0.089262702 |
|
COOR_Z |
1 |
3 |
3 |
0.120512702 |
COOR_Z |
1 |
4 |
4 |
0.120512702 |
COOR_Z |
1 |
5 |
5 |
0.151762702 |
COOR_z |
1 |
6 |
6 |
0.183012702 |
COOR_Z |
1 |
7 |
7 |
0.183012702 |
COOR_Z |
1 |
8 |
8 |
0.214262702 |
COOR_z |
1 |
9 |
0.245512702 |
|
COOR_Z |
1 |
10 |
0.245512702 |
|
COOR_Z |
1 |
11 |
0.276762702 |
|
COOR_Z |
1 |
12 |
0.308012702 |
Tolerance is \(1.0E-03\) for all tests.