4. B modeling#

4.1. Characteristics of modeling#

Modeling COQUE_3D (QUAD9)

4.2. Characteristics of the mesh#

Number of knots: 5400

Number of meshes and types: 1340 QUAD9

(The circle is cut into 20 segments)

4.3. 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 |||| +——-+———+——-+———-+———+——-+———-++++

4.4. notes#

We couldn’t find the clean mode for \(n=1\) and \(m=1\).

Thanks to the symmetry of the pipe structure, we observe that the natural modes of \(n=2-6\) and \(m=1\) 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).