B modeling
====


Characteristics of modeling
----

Same as modeling A, but in TRIA6.


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


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. [:ref:`§2.2 <§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).


.. csv-table::

    "**Identification**", "**Values**
    **Code_Aster**", "**Values of**
    **reference**", "**Tolerance**", "**Relative variance**"
    **(in%)**", "**Variable**
    **ASTER**", "**Variable PYTHON**"
    ":math:`{E}_{p}(0)` ", "0.125637%", "same", "10— 6% ", "—2.65 10—12"
    ~ 0% "," ERREEN0 ", "eren0"
    ":math:`{E}_{p}(4)` ", "7.015631 10— 4% ", "same", "10— 4% ", "4.71 10—13"
    ~ 0% "," ERREEN4 ", "eren4"
    "", "", "", "", "", "", ""
    "Arrow (0)", "0.106929%", "same", "10— 6% ", "1.6 10—12"
    ~ 0% "," ERREFL0 ", "erfl0"
    "Arrow (4)", "1.546674 10— 4% ", "same", "10— 4% ", "—3.3 10—13
    ~ 0% "," ERREFL4 ", "erfl4"



What to remember from this part of the TP...
----

Elements :math:`{P}_{1}` are not recommended in mechanics. **Best practice is rather:** :math:`{P}_{1}` **plugged in thermics and** :math:`{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.