3. Modeling A#

3.1. Characteristics of modeling#

The straight elements are modeled by POU_D_T elements.

Curved elements are also modeled by POU_D_T elements (20 elements per bend).

_images/1000200E000019380000196DD0736C1CFFD4EEF2.svg

3.2. Characteristics of the mesh#

Number of knots:

51

Number of stitches and types:

50 POU_D_T (10 for the parts straight)

3.3. notes#

The modes are standardized as follows: largest component (degree of freedom of translation or rotation) to one.

The overall response is obtained by quadratic combination of the directions of the excitations.

3.4. Tested sizes and results#

Structure frequencies (full mass matrix).

Natural Frequencies

Reference

Fashion 1

10.39

2

20.02

3

25.45

4

48.32

5

52.60

6

84.81

7

87.16

8

129.31

9

131.69

Structure frequencies (diagonal mass matrix).

Natural Frequencies

Reference

1

10.18

2

19.54

3

25.47

4

48.09

5

52.86

6

75.94

7

80.11

8

122.34

9

123.15

3.4.1. Single-press spectral response (calculation 1)#

The correction of frequencies due to damping is not taken into account (option CORR_FREQ to NON in operator COMB_SISM_MODAL)

Displacement

Identifier

cation

Reference

DEPL

\(N300\)

DX

4.84710—3

DY

2.19210—3

DZ

2.73510—6

\(N500\)

DX

4.80810—3

DY

2.91410—3

DZ

6.50710—4

\(N700\)

DX

3.5810—3

DY

2.91410—3

DZ

8.59910—4

\(N900\)

DX

2.34210—3

DY

2.91310—3

DZ

1.02710—3

\(N1100\)

DX

3.00910—6

DY

9.37510—4

DZ

3.36410—4

Nodal reaction

Identifier

cation

Reference

REAC

\(N100\)

DX

2132.0

DY

1241.0

DZ

564.6

DRX

2352.0

DRY

4746.0

DRZ

937.3

\(N1500\)

DX

1653.0

DY

3354.0

DZ

893.7

DRX

170.8

DRY

1668.0

DRZ

4903.0

Generalized efforts

Identifier

cation

Reference

EFGE

\(N300\)

N

559.9

VY

430.8

VZ

914.9

MT

932.5

MFY

587.3

MFZ

620.4

N700

N

1625.0

VY

1367.0

VZ

225.4

MT

649.6

MFY

499.8

MFZ

908.7

N1100

N

1652.0

VY

3177.0

VZ

795.7

MT

170.6

MFY

924.7

MFZ

2150.0

3.4.2. Single-press spectral response with static correction (calculation 2)#

Same as § 3.4.1, but taking into account static correction and removing contributions from the last two modes. We test the total (NOM_CAS =” TOTA “), dynamic (NOM_CAS =” PART_DYNA”), which must correspond to the contribution of the first 7 modes without static correction, and static (NOM_CAS =” PART_QS “) components, which must correspond to the quadratic difference between the total and dynamic components.

Travel:

Nodal reactions:

Generalized constraints:

3.4.3. Single-press spectral response with correction of damping frequencies (calculation 3)#

The correction of frequencies due to damping is taken into account (option CORR_FREQ to OUI in operator COMB_SISM_MODAL)

Nodal Displacement and Reaction

Identifier

cation

Reference type

Reference

Tolerance

DEPL

\(N300\)

DX

SOURCE_EXTERNE

4.84710—3

7,3E-3

DY

SOURCE_EXTERNE

2.19210—3

3,5E-3

\(N700\)

DX

SOURCE_EXTERNE

3.5810

4.4E-3

DY

SOURCE_EXTERNE

2.91410—3

3,5E-3

DRY

SOURCE_EXTERNE

1.43610-3

1,0E-2

\(N100\)

DX

SOURCE_EXTERNE

8,0E-3

DY

SOURCE_EXTERNE

1,0E-2

DZ

SOURCE_EXTERNE

564.6

3,5E-2

\(N1500\)

DRX

SOURCE_EXTERNE

170.8

2,5E-2

DRY

SOURCE_EXTERNE

1668

1,5E-2

DRZ

SOURCE_EXTERNE

4903.0

8,1E-3

Identifier

cation

Reference type

Reference

Tolerance

REAC_NODA

\(N100\)

N

SOURCE_EXTERNE

564.6

3,5E-3

VY

SOURCE_EXTERNE

1241.0

1.0e-2

VZ

SOURCE_EXTERNE

2132.0

1,0e-2

\(N200\)

MT

SOURCE_EXTERNE

936.2

1,4e-2

MFY

SOURCE_EXTERNE

1857.0

1,4e-2

MFZ

SOURCE_EXTERNE

759.6

7,6e-3

\(N1000\)

N

SOURCE_EXTERNE

2454.0

1,7e-2

VY

SOURCE_EXTERNE

1997.0

1,4e-2

VZ

SOURCE_EXTERNE

505.0

2,8e-2

\(N1100\)

MT

SOURCE_EXTERNE

170.6

0.23

MFY

SOURCE_EXTERNE

925.1

1,2e-3

MFZ

SOURCE_EXTERNE

2151.0

2,5e-3

3.4.4. Spectral response in correlated multi-support (calculation 4)#

The command COMB_SISM_MODAL is then tested in multi-press mode with three-dimensional excitation by duplicating the previous single-press calculation. These are computer tests.

The first calculation validates the correlated multi-support calculation.

The same excitations are imposed on the two supports in order to comply with the single-support calculation.

Nodal Displacement and Reaction

Identifier

cation

Reference type

Reference

Tolerance

DEPL

\(N300\)

DX

SOURCE_EXTERNE

4.84710—3

7, 5E-3

DY

SOURCE_EXTERNE

2.19210—3

4,1-3

\(N700\)

DX

SOURCE_EXTERNE

3.58810

4, 8E-3

DY

SOURCE_EXTERNE

2.91410—3

3, 7E-3

DRY

SOURCE_EXTERNE

1.43610

1, 1E-2

REAC_NODA

\(N100\)

DX

SOURCE_EXTERNE

2,0E-3

DY

SOURCE_EXTERNE

2,0E-3

DZ

SOURCE_EXTERNE

564.6

3, 0E-2

\(N1500\)

DRX

SOURCE_EXTERNE

170.8

3, 1E-2

DRY

SOURCE_EXTERNE

1668

5,0E-2

DRZ

SOURCE_EXTERNE

4903.0

8, 6E-3

Identifier

cation

Reference type

Reference

Tolerance

effort

\(N100\)

N

SOURCE_EXTERNE

564.6

3,0e-2

VY

SOURCE_EXTERNE

1241.0

2,0e-3

VZ

SOURCE_EXTERNE

2132.0

2,0e-3

\(N200\)

MT

SOURCE_EXTERNE

936.2

1,4e-2

MFY

SOURCE_EXTERNE

1857.0

1,7e-2

MFZ

SOURCE_EXTERNE

759.6

1,4e-2

\(N1000\)

N

SOURCE_EXTERNE

2454.0

2, e-2

VY

SOURCE_EXTERNE

1997.0

1,2e-2

VZ

SOURCE_EXTERNE

505.0

8,0e-2

\(N1100\)

MT

SOURCE_EXTERNE

170.6

0.24

MFY

SOURCE_EXTERNE

925.1

1,0e-2

MFZ

SOURCE_EXTERNE

2151.0

3,0e-3

3.4.5. Spectral response in multi-support correlated with static correction (calculation 5)#

Same as § 3.4.4, but taking into account static correction and removing contributions from the last two modes. We test the total (NOM_CAS =” TOTA “), dynamic (NOM_CAS =” PART_DYNA”), which must correspond to the contribution of the first 7 modes without static correction, and static (NOM_CAS =” PART_QS “) components, which must correspond to the quadratic difference between the total and dynamic components.

Travel:

Nodal reactions:

Generalized constraints:

3.4.6. Spectral response in uncorrelated multi-support (calculation 6)#

The multi-direction uncorrelated multi-support calculation is validated.

It should be noted that putting the same excitement to the different supports is not a good practice in uncorrelated multi-support, but the aim of this test is only to verify that things work computationally. It is a non-regression test.

Nodal Displacement and Reaction

Identifier

cation

Reference type

Reference

Tolerance

DEPL

\(N300\)

DX

NON_REGRESSION

DY

NON_REGRESSION

\(N700\)

DX

NON_REGRESSION

DY

NON_REGRESSION

DRY

NON_REGRESSION

REAC_NODA

\(N100\)

DX

NON_REGRESSION

DY

NON_REGRESSION

DZ

NON_REGRESSION

\(N1500\)

DRX

NON_REGRESSION

DRY

NON_REGRESSION

DRZ

NON_REGRESSION

Identifier

cation

Reference type

Reference

Tolerance

effort

\(N100\)

N

NON_REGRESSION

VY

NON_REGRESSION

VZ

NON_REGRESSION

\(N200\)

MT

NON_REGRESSION

MFY

NON_REGRESSION

MFZ

NON_REGRESSION

\(N1000\)

N

NON_REGRESSION

VY

NON_REGRESSION

VZ

NON_REGRESSION

\(N1100\)

MT

NON_REGRESSION

MFY

NON_REGRESSION

MFZ

NON_REGRESSION

Calculation 8:

Nodal Displacement and Reaction

Identifier

cation

Reference type

Reference

Tolerance

DEPL

\(N300\)

DX

NON_REGRESSION

DY

NON_REGRESSION

\(N700\)

DX

NON_REGRESSION

DY

NON_REGRESSION

DRY

NON_REGRESSION

REAC_NODA

\(N100\)

DX

NON_REGRESSION

DY

NON_REGRESSION

DZ

NON_REGRESSION

\(N1500\)

DRX

NON_REGRESSION

DRY

NON_REGRESSION

DRZ

NON_REGRESSION

Identifier

cation

Reference type

Reference

Tolerance

effort

\(N100\)

N

NON_REGRESSION

VY

NON_REGRESSION

VZ

NON_REGRESSION

\(N200\)

MT

NON_REGRESSION

MFY

NON_REGRESSION

MFZ

NON_REGRESSION

\(N1000\)

N

NON_REGRESSION

VY

NON_REGRESSION

VZ

NON_REGRESSION

\(N1100\)

MT

NON_REGRESSION

MFY

NON_REGRESSION

MFZ

NON_REGRESSION

3.4.7. Spectral response in uncorrelated multi-support with static correction (calculation 7)#

Same as § 3.4.6, but taking into account static correction and removing contributions from the last two modes. We test the total (NOM_CAS =” TOTA “), dynamic (NOM_CAS =” PART_DYNA”), which must correspond to the contribution of the first 7 modes without static correction, and static (NOM_CAS =” PART_QS “) components, which must correspond to the quadratic difference between the total and dynamic components.

Travel:

Nodal reactions:

Generalized constraints:

3.5. notes#

Spectrum values (interpolation).

Mode

1, 2, 3

4

4

5

7

7

8, 9

Next acceleration \(x\) and \(y\)

19.620

8.06148

8.06148

6.72586

3.38994

3.04168

1.9620

Next acceleration \(z\)

9.810

4.03074

4.03074

3.36293

1.69497

1.52084

0.9810

0.9810