B modeling
==============


Characteristics of modeling
-----------------------------------

Modeling COQUE_3D (QUAD9)


Characteristics of the mesh
----------------------------

Number of knots: 5400

Number of meshes and types: 1340 QUAD9

(The circle is cut into 20 segments)


Tested sizes and results
------------------------------

Tab. 3. B modeling results


+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**m=1**|**FF**                      |**SF**                       |**SS**                      |
+       +---------+-------+----------+---------+--------+----------+---------+-------+----------+
|       |**Aster**|**Ref**|**%** diff|**Aster**|**Ref** |**%** diff|**Aster**|**Ref**|**%** diff|
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=2**|660,729  |654,216|1.00      |661,256  |657,308 |0.6       |670,323  |663,543|1.02      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=3**|1865,28  |1850,29|0.81      |1866,01  |1851,81 |0.77      |1872.62  |1855,44|0.93      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=4**|3573,33  |3547.66|0.72      |3573,86  |3549,113|0.70      |3584,50  |3552.95|0.89      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=5**|5786,88  |5737.23|0.87      |5787,12  |5738.70 |0.84      |5804,33  |5742,74|1.07      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=6**|8562,17  |8416.32|1.73      |8532.92  |8417.79 |1.37      |8558,68  |8421.97|1.62      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+


+-------+---------+-------+----------+---------+-------+----------++++
|**m=1**|**SC**                      |**CC**                      |  |
+       +---------+-------+----------+---------+-------+----------++++
|       |**Aster**|**Ref**|**%** diff|**Aster**|**Ref**|**%** diff||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=2**|678.72   |671,113|1.13      |692,930  |687,249|0.83      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=3**|1873,76  |1856,45|0.93      |1875,31  |1858,30|0.92      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=4**|3584,91  |3553,29|0.89      |3585,38  |3553,91|0.89      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=5**|5804,53  |5742,87|1.07      |5804,76  |5743,21|1.07      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=6**|8558,81  |8422.00|1.62      |8558,95  |8422,24|1.62      ||||
+-------+---------+-------+----------+---------+-------+----------++++


notes
---------

We couldn't find the clean mode for :math:`n=1` and :math:`m=1`.

Thanks to the symmetry of the pipe structure, we observe that the natural modes of :math:`n=2-6` and :math:`m=1` always appear in pairs.

Comparing with modeling A, we observe less accurate results in COQUE_3D (mesh with 3030 nodes, 30 points on the circle) than those in DKT (mesh with 5400 nodes, 40 points on the circle).