Modeling A
==============


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

Modeling DKT (QUAD4)


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

Number of knots: 3030

Number of meshes and types: 3000 QUAD4

(The circle is cut into 30 segments)


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

Tab. 2. Results of modeling A


+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**m=1**|**FF**                      |**SF**                       |**SS**                      |
+       +---------+-------+----------+---------+--------+----------+---------+-------+----------+
|       |**Aster**|**Ref**|**%** diff|**Aster**|**Ref** |**%** diff|**Aster**|**Ref**|**%** diff|
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=2**|657,335  |654,216|0.48      |657,938  |657,308 |0.10      |667,023  |663,543|0.52      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=3**|1858.85  |1850,29|0.46      |1859,73  |1851,81 |0.43      |1865,40  |1855,44|0.54      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=4**|3564,70  |3547.66|0.48      |3565.61  |3549,113|0.46      |3572.44  |3552.95|0.55      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=5**|5767,42  |5737.23|0.53      |5768,30  |5738.70 |0.52      |5775,67  |5742,74|0.57      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+
|**n=6**|8466,42  |8416.32|0.60      |8467,30  |8417.79 |0.59      |8474.04  |8421.97|0.62      |
+-------+---------+-------+----------+---------+--------+----------+---------+-------+----------+


+-------+---------+-------+----------+---------+-------+----------++++
|**m=1**|**SC**                      |**CC**                      |  |
+       +---------+-------+----------+---------+-------+----------++++
|       |**Aster**|**Ref**|**%** diff|**Aster**|**Ref**|**%** diff||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=2**|675.59   |671,113|0.67      |690,073  |687,249|0.41      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=3**|1866,57  |1856,45|0.54      |1868,14  |1858,30|0.53      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=4**|3572,85  |3553,29|0.55      |3573,32  |3553,91|0.55      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=5**|5775,87  |5742,87|0.57      |5776,09  |5743,21|0.57      ||||
+-------+---------+-------+----------+---------+-------+----------++++
|**n=6**|8474.16  |8422.00|0.62      |8474,27  |8422,24|0.62      ||||
+-------+---------+-------+----------+---------+-------+----------++++


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.