5. C modeling#
5.1. Characteristics of modeling#
Same as modeling A with the following changes:
mesh in TRIA6,
free refinement-deraffination (MACR_ADAP_MAIL option LIBRE =” RAFF_DERA “) driven by the component NUEST of ERRE_ELGA_NORE (relative component of the residual indicator). With the criteria CRIT_RAFF_PE = CRIT_DERA_PE =0.2 (we refine 20% of the worst elements and we deraffine 20% of the best).
5.2. Characteristics of the mesh#
Initially: 61 TRIA6, 15 SEG3, 156 knots
After free refinement: 107 TRIA6, 19 SEG3, 256 knots
After two free refinements: 212 TRIA6, 26 SEG3, 479 knots
After three free refinements: 404 TRIA6, 33 SEG3, 879 knots
After four free refinements: 786 TRIA6, 39 SEG3, 1671 knots
5.3. 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 |
||||
\({E}_{p}(4)\) |
1.245370 10— 2% |
same |
10— 4% |
—2.27 10—12 |
||
~ 0% « |
|
eren4 |
||||
Arrow (0) |
0.106929% |
same |
10— 6% |
1.6 10—12 |
||
~ 0% « |
|
erfl0 |
||||
Arrow (4) |
1.074923 10— 2% |
same |
10— 4% |
—2.34 10—12 ~ 0% |
|
erfl4 |
5.4. What to remember from this part of the TP…#
The « thermo-mechanical operators/ MACR_ADAP_MAIL OPTION “LIBRE” » sequence allows the mesh to converge optimally.
The quality of the elements is little affected by the refinement/deraffination process. Given the choices made in HOMARD, it can even improve in 3D!
The type of indicator and how it is normalized has a big impact on the final mesh. Taking into account the type of standardization adopted for mechanical indicators,
(in%)
On problems with singularities (embedment, curvature discontinuity, recessed corner, crack…), it is better to use the absolute component of these indicators. Because as for « our good old embedded beam »:
% when
(near the embed)
% when
(near the arrow)
regardless of the true values of the absolute indicator
This does not at all call into question the great usefulness of these indicators. You just have to take these elements into account to refine your diagnosis and possibly « juggle » these two components to refine in the areas of interest.
The thermal problem does not occur, because the residual indicator for the thermal problem is normalized differently. However, we can deal with the components of the thermal indicator and boundary conditions, « fictitious » or not, to guide the construction of a refined or unrefined mesh by zones (cf. [§6.3] [R4.10.03] and modeling A, _ TP21 _] and modeling A, _ _, from the documentation [V6.03.120]).