1. Reference problem#

1.1. Geometry#

The pipe is modelled by a hollow circular section 762mm in diameter and 22mm thick (S1) or 813mm in diameter and 23mm thick (S2). The modeling is done with SEG2 (element POU_D_T) only.

_images/1000020100000284000001F447BF3B6482197C1E.png

Symbol

Description
_images/1000020100000025000000191095571F33A0D4BC.png

Point mass
_images/100002010000001F0000001DA492A6014E26BE4E.png _images/10000201000000130000001116F2DD9430B470A4.png

0D spring in translation and/or rotation

Figure 1: Benchmark 6 diagram

The following table shows the coordinates of each of the points in the pipe:

Knot

X (m)

Y (m)

Z (m)

PT_1

3.20

12.29

17.93

PT_2

3.20

12.29

17.90

PT_3

3.20

13.44

16.75

PT_4

3.20

14.43

16.75

PT_5

3.20

16.56

16.75

PT_6

3.20

18.69

16.75

PT_7

3.20

20.39

16.75

PT_8

3.20

22.08

16.75

PT_9

3.20

23.30

16.75

PT_10

3.20

24.52

16.75

PT_11

3.20

24.59

16.75

PT_12

4.31

25.74

16.50

PT_13

4.42

25.74

16.48

PT_14

5.84

25.74

16.03

PT_15

7.21

25.74

15.46

PT_16

8.53

25.74

14.77

PT_17

9.79

25.74

13.97

PT_18

10.97

25.74

13.07

PT_19

12.07

25.74

12.06

PT_20

13.08

25.74

10.96

PT_21

13.98

25.74

9.78

PT_22

14.78

25.74

8.52

PT_23

15.47

25.74

7.20

PT_24

16.04

25.74

5.83

PT_25

16.49

25.74

4.41

PT_26

16.81

25.74

2.95

PT_27

17.00

25.74

1.48

PT_28

17.07

25.74

-0.01

PT_29

17.00

25.74

-1.50

PT_30

16.81

25.74

-2.97

PT_31

16.49

25.74

-4.43

PT_32

16.04

25.74

-5.85

PT_33

15.47

25.74

-7.22

PT_34

14.78

25.74

-8.54

PT_35

13.99

25.74

-9.79

PT_36

9.53

25.74

-11.35

PT_37

8.78

25.74

-11.09

PT_38

6.66

25.74

-10.36

PT_39

5.63

25.74

-10.00

PT_40

4.55

24.59

-9.63

PT_41

4.55

24.59

-9.63

Table 1: Coordinates of pipe nodes

The following table shows the types of elements that make up the pipe:

Element

Node 1

Node 2

Type

Section

EL_1

PT_1

PT_2

Tangent

1

EL_2

PT_2

PT_3

Bend

1

EL_3

PT_3

PT_4

Tangent

1

EL_4

PT_4

PT_5

Tangent

1

EL_5

PT_5

PT_6

Tangent

1

EL_6

PT_6

PT_7

Tangent

1

EL_7

PT_7

PT_8

Tangent

1

EL_8

PT_8

PT_9

Tangent

1

EL_9

PT_9

PT_10

Tangent

1

EL_10

PT_10

PT_11

Tangent

1

EL_11

PT_11

PT_12

Bend

1

EL_12

PT_12

PT_13

Tangent

1

EL_13

PT_13

PT_14

Tangent

1

EL_14

PT_14

PT_15

Tangent

1

EL_15

PT_15

PT_16

Tangent

1

EL_16

PT_16

PT_17

Tangent

1

EL_17

PT_17

PT_18

Tangent

1

EL_18

PT_18

PT_19

Tangent

1

EL_19

PT_19

PT_20

Tangent

1

EL_20

PT_20

PT_21

Tangent

1

EL_21

PT_21

PT_22

Tangent

1

EL_22

PT_22

PT_23

Tangent

1

EL_23

PT_23

PT_24

Tangent

1

EL_24

PT_24

PT_25

Tangent

1

EL_25

PT_25

PT_26

Tangent

1

EL_26

PT_26

PT_27

Tangent

1

EL_27

PT_27

PT_28

Tangent

1

EL_28

PT_28

PT_29

Tangent

1

EL_29

PT_29

PT_30

Tangent

1

EL_30

PT_30

PT_31

Tangent

1

EL_31

PT_31

PT_32

Tangent

1

EL_32

PT_32

PT_33

Tangent

1

EL_33

PT_33

PT_34

Tangent

1

EL_34

PT_34

PT_35

Tangent

1

EL_35

PT_35

PT_36

Bend

1

EL_36

PT_36

PT_37

Tangent

1

EL_37

PT_37

PT_38

Tangent

1

EL_38

PT_38

PT_39

Tangent

1

EL_39

PT_39

PT_40

Bend

2

EL_40

PT_40

PT_41

Tangent

2

Table 2: Type of pipe elements

1.2. Material properties#

The characteristics are as follows:

  • \(\mathit{YOUNG}=206000\mathit{MPa}\)

  • \(\mathit{NU}=0.30\)

  • \(\mathit{RHO}=0\mathit{kg}/m3\)

The mass of the pipe is not considered in this test case.

1.3. Boundary conditions and loads#

1.3.1. Boundary conditions#

In accordance with Figure, this study does not include fixed supports. On the other hand, some points are elastic supports whose characteristics are specified in the following tables:

Knot

X (m)

Y (m)

Z (m)

Type

RESS_PT10_42_BASE

0.00

0.00

0.00

-0.19

K_T_D_L

RESS_PT10_43_BASE

1.83

3.69

-0.03

K_T_D_L

RESS_PT30_50_BASE

2.78

3.69

3.69

0.92

K_T_D_L

RESS_PT34_51_BASE

2.75

3.71

3.00

K_T_D_L

RESS_PT1_BASE

3.20

12.29

12.29

17.93

K_ TR_D_L

RESS_PT20_BASE

13.08

25.74

25.74

10.96

K_ TR_D_L

RESS_PT26_BASE

16.81

25.74

2.95

K_ TR_D_L

RESS_PT41_BASE

4.55

24.59

-9.63

K_ TR_D_L

Table 3: Coordinates and type of elastic supports

Node

K local (N/m)

K X (N/m)

K Y (N/m)

K Z (N/m)

K RX (N/ rad )) **

K RY (N/ rad )) **

K RZ (N/ rad )

RESS_PT10_42_BASE

1.75E+08

RESS_PT10_43_BASE

1.75E+08

RESS_PT30_50_BASE

3.50E+08

RESS_PT34_51_BASE

1.40E+08

RESS_PT1_BASE

1.75E+21

1.75E+21

1.75E+21

1.75E+21

1.75E+21

1.75E+21

1.75E+21

RESS_PT20_BASE

4.37E+07

4.37E+07

3.50E+08

4.37E+07

RESS_PT26_BASE

7.87E+07

3.50E+07

3.50E+08

7.87E+07

RESS_PT41_BASE

1.75E+11

1.75E+11

1.75E+11

1.13E+16

1.13E+16

1.13E+16

1.13E+16

1.13E+16

Table 4: Stiffers of elastic supports

1.3.2. Loads#

The loads applied to the pipe are as follows:

  • Point masses in different nodes (identical in all 3 directions);

  • Earthquake in X, Y, and Z directions. The spectrum is weighted by 1 in all three directions;

Knot

M ( kg )

PT_4

1 738.13

PT_5

954.97

PT_6

856.02

PT_7

1 031.15

PT_9

940.96

PT_11

691.75

PT_12

425.56

PT_13

690.17

PT_15

1 332.54

PT_17

1 332.54

PT_19

1 333.07

PT_21

1 332.89

PT_23

1 332.89

PT_25

1 332.89

PT_27

1 332.89

PT_29

1 332.89

PT_31

1 332.89

PT_33

1 331.14

PT_35

1 802.58

PT_36

1 316.60

PT_37

678.97

PT_38

1 843.74

Table 5: Values and locations of point masses

The spectra used for modal analysis are shown in the following figure:

_images/100002010000078C000004F58CA9D8C038C4CAA7.png

Figure 2: Computational spectrum — X and Z

_images/100002010000078C000004F5119E9C2D83E20D8C.png

Figure 3: Computational spectrum - Y