4. B modeling#
4.1. Characteristics of modeling#
Same as modeling A, but in TRIA6.
4.2. Characteristics of the mesh#
Initially: 61 TRIA6, 15 SEG3, 156 knots
After uniform refinement: 244 TRIA6, 30 SEG3, 555 knots
After two uniform refinements: 976 TRIA6, 60 SEG3, 2085 knots
After three uniform refinements: 3904 TRIA6, 120 SEG3, 8073 knots
After four uniform refinements: 15616 TRIA6, 240 SEG3, 31761 knots
4.3. Tested sizes and results#
We test the values of the relative errors in deflection and in potential deformation energy with respect to the reference solutions (cf. [§2.2]). And this, on the initial mesh and after four uniform refinements. Since the tests must be multi-platform, the relative tolerance, which is on initial errors set at 10—6%, is deliberately relaxed on errors after four refinements: 10— 4%.
These tests are carried out on variables PYTHON (via TEST_FONCTION) previously inserted into functions ASTER (via FORMULE).
Identification |
Values Code_Aster |
Values of reference |
Tolerance |
Relative variance |
||
(in%) » |
Variable ASTER |
Variable PYTHON |
||||
\({E}_{p}(0)\) |
0.125637% |
same |
10— 6% |
—2.65 10—12 |
||
~ 0% « |
|
eren0 |
||||
\({E}_{p}(4)\) |
7.015631 10— 4% |
same |
10— 4% |
4.71 10—13 |
||
~ 0% « |
|
eren4 |
||||
Arrow (0) |
0.106929% |
same |
10— 6% |
1.6 10—12 |
||
~ 0% « |
|
erfl0 |
||||
Arrow (4) |
1.546674 10— 4% |
same |
10— 4% |
—3.3 10—13 ~ 0% |
|
erfl4 |
4.4. What to remember from this part of the TP…#
Elements \({P}_{1}\) are not recommended in mechanics. Best practice is rather: \({P}_{1}\) plugged in thermics and \({P}_{2}\) (possibly under-integrated) mechanics (in order not to artificially favor the thermal component of the deformation field and try to avoid space-time oscillations in the temperature field and its violation of the principle of maximum).
The choice of the type of finite element takes precedence over the quality of the meshes on which this element is based.