3. Modellations#
Depending on the models, the objects are meshed with different elements:
Modeling A: cube: 1 HEXA8 element with 8 nodes
faces: 1 QUAD4 element with 4 knots
Modeling B: cube: 6 elements TETRA4 with 4 nodes
faces: 2 TRIA3 elements with 3 knots
C modeling: same modeling as in A with quadratic elements
D modeling: same modeling as in B with quadratic elements
3.1 Tested quantities and results of modeling A
Modeling A consists of a CUB8 element for the cube and a QUA4 element for each face. The behavior is elastic (commands MECA_STATIQUE then STAT_NON_LINE (check)).
The values given by EPSI_ELGA; EPSI_ELNO, SIEF_ELGA, SIEF_ELNO,,,, SIEF_ELGA, SIGM_ELNO are tested at various points in the main directions of the reinforcement plies, obtained respectively with the commands MECA_STATIQUE and STAT_NON_LINE.
For MECA_STATIQUE:
Integration points |
EPSI_ELGA (in the main direction of the reinforcing sheet) |
SIEF_ELGA (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA3 — Point 1 (tablecloth GEOY) |
1.8264 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA4 — Point 1 (tablecloth GEOY) |
1.8264 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA5 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA6 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
Bow |
EPSI_ELNO (in the main direction of the reinforcing sheet) |
SIGM_ELNO (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
NO1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
NO1 (tablecloth GEOY) |
1.8264 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
NO1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
For STAT_NON_LINE
Integration points |
EPSI_ELGA (in the main direction of the reinforcing sheet) |
SIEF_ELGA (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA3 — Point 1 (tablecloth GEOY) |
1.8264 |
1.8263 |
0.003 |
3.6527E11 |
3.6527E11 |
0 |
MA4 — Point 1 (tablecloth GEOY) |
1.8264 |
1.8263 |
0.003 |
3.6527E11 |
3.6527E11 |
0 |
MA5 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA6 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
Bow |
EPSI_ELNO (in the main direction of the reinforcing sheet) |
SIEF_ELNO (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 - NO1 (GEOZ tablecloth) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 - NO1 (GEOY tablecloth) |
1.8264 |
1.8263 |
0.003 |
3.6527E11 |
3.6527E11 |
0 |
MA3 - NO1 (GEOX tablecloth) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
The total potential energy value is also tested using calculation STAT_NON_LINE. The analytical solution is calculated from all the uniaxial deformations in the grids, from the equation:
where \(A\) refers to the elasticity tensor.
The results obtained are as follows:
Code_Aster |
Analytical reference |
Variance |
|
Total potential energy (\(J\)) |
2.8173E10 |
2.8173E10 |
0 |
3.2 Tested quantities and B modeling results
Model B consists of six TETRA4 elements for the cube and two TRIA3 elements for each face.
The behavior is elastic using the MECA_STATIQUE command and then the STAT_NON_LINE command (check).
The values given by EPSI_ELGA; EPSI_ELNO, SIEF_ELGA, SIEF_ELNO;;;; SIEF_ELGA; SIGM_ELNO are tested at various points in the main directions of the reinforcement plies, obtained respectively with the commands MECA_STATIQUE and STAT_NON_LINE.
For MECA_STATIQUE:
Integration points |
EPSI_ELGA (in the main direction of the reinforcing sheet) |
SIEF_ELGA (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA3 — Point 1 (tablecloth GEOZ) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA4 — Point 1 (tablecloth GEOZ) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA5 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA6 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA11 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA21 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA31 — Point 1 (tablecloth GEOY) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA41 — Point 1 (tablecloth GEOY) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA51 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA61 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
Bow |
EPSI_ELNO (in the main direction of the reinforcing sheet) |
SIGM_ELNO (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 - NO1 (GEOZ tablecloth) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 - NO1 (GEOY tablecloth) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA3 - NO1 (GEOX tablecloth) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA11 - NO1 (GEOZ tablecloth) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA21 - NO1 (GEOY tablecloth) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA31 - NO1 (GEOX tablecloth) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
For STAT_NON_LINE
Integration points |
EPSI_ELGA (in the main direction of the reinforcing sheet) |
SIEF_ELGA (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA3 — Point 1 (tablecloth GEOY) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA4 — Point 1 (tablecloth GEOY) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA5 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA6 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA11 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA21 — Point 1 (tablecloth GEOZ) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA31 — Point 1 (tablecloth GEOY) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA41 — Point 1 (tablecloth GEOY) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA51 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA61 — Point 1 (tablecloth GEOX) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
Bow |
EPSI_ELNO (in the main direction of the reinforcing sheet) |
SIEF_ELNO (in the main direction of the reinforcing sheet) |
||||
Aster_code |
Reference |
Gap (\(\text{\%}\)) |
Aster_code |
Reference |
Ecart |
|
MA1 - NO1 (GEOZ tablecloth) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA2 - NO1 (GEOY tablecloth) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA3 - NO1 (GEOX tablecloth) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |
MA11 - NO1 (GEOZ tablecloth) |
1.067 |
1.067 |
0.001 |
2.13397E11 |
2.13397E11 |
0 |
MA21 - NO1 (GEOY tablecloth) |
1.8263 |
1.8263 |
0 |
3.6527E11 |
3.6527E11 |
0 |
MA31 - NO1 (GEOX tablecloth) |
2 |
2 |
0 |
4E11 |
4E11 |
0 |