8. F modeling#
8.1. Characteristics of modeling#
This modeling is strictly identical to the previous ones. In order to test that the HM-XFEM model is functional with PYRAM13, we choose to subdivide the 5 HEXA20 of the C modeling, each into 6 PYRAM13. This makes a total of 30 quadratic pyramidal elements. As before, the pyramidal elements contained in the extreme hexahedra are not enriched. On the contrario those contained in the 3 central hexahedra are enriched by the Heaviside function.
8.2. Characteristics of the mesh#
The mesh consists of 30 quadratic pyramidal cells (PYRAM13).
8.3. Tested sizes and results#
The results obtained with*Code_Aster* (resolution with STAT_NON_LINE) are summarized in the tables below. To test all the nodes in the column at the same time, we calculate MIN and MAX.
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DZ (below) MIN |
“ANALYTIQUE” |
-4.323558729E-03 |
0.1 |
DZ (below) MAX |
“ANALYTIQUE” |
-4.323558729E-03 |
0.1 |
DZ (above) MIN |
“ANALYTIQUE” |
4.297130927-03 |
0,1 |
DZ (above) MAX |
“ANALYTIQUE” |
4.297130927-03 |
0,1 |
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DX (below) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DX (below) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
DX (above) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DX (above) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DY (below) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DY (below) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
DY (above) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DY (above) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
Note:
The tolerance for the on DZ test is higher, we go from \({10}^{\text{-6}}\) to \({10}^{\text{-3}}\). In fact, the shape functions of pyramids are not polynomials but rational fractions. This explains the lower precision obtained for this linear problem compared to previous models.
Figure 8.3-a : Field of movement by direction (Oz)
A second modeling is then carried out which uses the same parameters as the previous one, but this time by conducting the calculation XFEM (which is then a pure mechanical calculation) with the operator MECA_STATIQUE instead of the operator STAT_NON_LINE in the case HM-XFEM. The results obtained are strictly identical to the previous ones.