SDLL132 - Clean modes of a frame in multifibre beams

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Titrate:

SDLL132 - Clean modes of a frame

Date:

15/04/03

Author (S):

J-L. FLEJOU

Key

V2.02.132-A

Page:

1/8

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HR-17/02/019/A

Organization (S):

EDF-R & D/TESE

Manual of Validation
V2.02 booklet: Linear dynamics of the beams
Document: V2.02.132

SDLL132 - Clean modes of a frame in
multifibre beams

Summary:

This test relates to the validation of the option

MASS_INER

, as well as calculation of the clean modes of the frame

when the model contains

POU_D_TGM

(multifibre beams). The results of the reference solution are

obtained by making the same study but with a model of beams based on

POU_D_E

This test makes it possible to validate, by making a modal analysis of the structure:

linear finite elements of type

POU_D_TGM

results of the controls:

POST_ELEM

NORM_MODE

EXTR_MODE

results of

MACRO_MODE_MECA

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Titrate:

SDLL132 - Clean modes of a frame

Date:

15/04/03

Author (S):

J-L. FLEJOU

Key

V2.02.132-A

Page:

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Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HR-17/02/019/A

Problem of reference

1.1 Geometry

The case test is a metal frame made up of beams and posts.

Co-ordinates of the main nodes of the mesh:

Not

Coord. X

(in m)

Coord. Y

(in m)

Coord. Z

(in m)

To 2.0

2.5

0.0

B 4.0

0.0

C 2.0

 2.5

0.0

D 0.0

0.0

E 2.0

2.5

3.0

F 4.0

0.0

3.0

G 2.0

 2.5

3.0

H 0.0

0.0

3.0

I 2.0

0.0 3.0

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Titrate:

SDLL132 - Clean modes of a frame

Date:

15/04/03

Author (S):

J-L. FLEJOU

Key

V2.02.132-A

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Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HR-17/02/019/A

1.2

Mechanical characteristics of the beams

The beams of the case test are standard sections of the steel construction. Units of theirs
mechanical characteristics are homogeneous with [m].

HEA200 IPE220 IPE160 HEA140 IPE120

Beams

BF, DH

I.E.(INTERNAL EXCITATION), CG

FG, GH

With 5.39E03

3.34E03

2.01E03 3.14E03 1.32E03

IY 3.69E05

2.77E05

8.70E06 1.03E05 3.18E06

IZ 1.34E05

2.05E06

6.83E07 3.89E06 2.77E07

1.474994 1.789865 1.792884 1.464032 1.774392

4.466038 2.633754 2.586199 4.464173 2.590182

JX 1.97E07

8.66E08

3.37E08 7.76E08 1.63E08

JG 1.06E07

2.23E08

3.89E09 1.47E08 8.73E10

Sizes EY, EZ, IYR2, IZR2 are null for all the beams.

1.3

Properties of material

Only one material is used:

Young 2.10e+11

Rho 7.85e+03

kg/m

1.4

Boundary conditions

The points A, B, C, D are embedded.

DX = 0

DY = 0

DZ = 0

DRX = 0

DRY = 0

DRZ = 0

Code_Aster

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Titrate:

SDLL132 - Clean modes of a frame

Date:

15/04/03

Author (S):

J-L. FLEJOU

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V2.02.132-A

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Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HR-17/02/019/A

Reference solution

2.1

Method of calculation used for the reference solution

The values of the reference solution are obtained with the frame, produced with a model with
base

POU_D_E

2.2

Results of reference

Values obtained by the control

POST_ELEM

, with the key word

MASS_INER

Sizes Value

MASS

5.85759E+02

CDG_X

2.00000E+00

CDG_Z

2.03968E+00

IX_PRIN_G

1.56562E+03

IY_PRIN_G

1.81822E+03

IZ_PRIN_G

2.23486E+03

The table below gives the clean modes calculated with a model of

POU_D_E

. Modes

are filtered by the control

EXTR_MODE

with the criterion

MASS_EFFE_UN

and a threshold of 5.0E-04.

NUME
MODE

FREQUENCY MASS_EFFE_UN

CUMUL_DX MASS_EFFE_UN

CUMUL_DY MASS_EFFE_UN

CUMUL_DZ

1 1.00E+01 2.41E01 2.41E01

1.69E26 1.69E26

7.04E30 7.04E30

2 1.24E+01 4.33E01 6.74E01

3.99E24 4.01E24

2.64E27 2.65E27

3 1.31E+01 3.84E24 6.74E01

5.29E01 5.29E01

4.13E04 4.13E04

4 1.75E+01 7.73E04 6.74E01

4.54E26 5.29E01

2.74E28 4.13E04

5 1.91E+01 7.92E02 7.54E01

1.88E27 5.29E01

4.25E28 4.13E04

6 2.24E+01 6.29E27 7.54E01

1.38E01 6.67E01

2.22E04 6.35E04

7 2.69E+01 1.21E29 7.54E01

6.00E02 7.27E01

1.50E07 6.35E04

10 3.36E+01 2.42E30 7.54E01

6.37E04 7.27E01

6.26E06 6.41E04

13 3.53E+01 1.67E03 7.55E01

7.43E30 7.27E01

1.13E29 6.41E04

14 3.70E+01 1.21E02 7.68E01

9.09E30 7.27E01

2.84E33 6.41E04

2.3

Uncertainty on the solution

Without object.

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SDLL132 - Clean modes of a frame

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3 Modeling

With

3.1

Characteristics of modeling and the mesh

The model is composed of

POU_D_TGM

(multifibre beams). All the sections, are in form of

“I” and are described with 30 fibers: 1 in the sole and web thickness, 10 in the width of
soles and 10 in the height of the core.

3.2 Functionalities

tested

The case test comprises three stages:

the first calculates the structural features with the control

post_elem

the second stage consists in calculating the clean modes of the structures using
controls

calc_matr_elem

nume_ddl

asse_matrice

mode_iter_simult

and with

to normalize with the result of the concept

post_elem

the third stage calculates the clean modes of the structure with the macro-control

MACRO_MODE_MECA

by normalizing the modes with the result of the concept

POST_ELEM

Controls

AFFE_CARA_ELEM BEAM

AFFE_FIBER

POST_ELEM MASS_INER

CALC_MATR_ELEM OPTION

“RIGI_MECA”
“MASS_MECA”

MODE_ITER_SIMULT TYPE_RESU

CALC_FREQ

“DYNAMIC”
BANDAGE

NORM_MODE NORMALIZES

“MASS_GENE”

MACRO_MODE_MECA NORMALIZES

“MASS_GENE”

3.3

Sizes tested and results

The table below summarizes the results obtained by the controls

POST_ELEM

, with the key word

MASS_INER

, for the model

POU_D_TGM

and compares them with the values of reference obtained with one

model of

POU_D_E

Sizes Values

References

Values

POU_D_TGM

Error

Relative

MASS

5.8576E+02 5.8576E+02 7.04E07

CDG_X

2.0000E+00 2.0000E+00 0.00E+00

CDG_Z

2.0397E+00 2.0397E+00 2.16E06

IX_PRIN_G

1.5656E+03 1.5656E+03 1.11E06

IY_PRIN_G

1.8182E+03 1.8182E+03 1.80E07

IZ_PRIN_G

2.2349E+03 2.2349E+03 4.72E07

In this test, the authorized maximum relative error is fixed at 2.0E-05.

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Titrate:

SDLL132 - Clean modes of a frame

Date:

15/04/03

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Key

V2.02.132-A

Page:

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Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HR-17/02/019/A

The table below gives the clean modes calculated with a model of

POU_D_TGM

. Modes

are filtered by the control

EXTR_MODE

with the criterion

MASS_EFFE_UN

and a threshold of 5.0E-04.

The maximum relative error authorized on the calculation of the frequencies is fixed at 2.0E-02. The absolute error
maximum authorized on the calculation of

MASS_EFFE_UN

is fixed at 1.0E-02.

NUME
MODE

FREQUENCY MASS_EFFE_UN

CUMUL_DX MASS_EFFE_UN

CUMUL_DY MASS_EFFE_UN

CUMUL_DZ

1 1.00E+01 2.45E01 2.45E01

1.38E27 1.38E27

7.12E31 7.12E31

2 1.23E+01 4.30E01 6.75E01

1.28E25 1.30E25

7.59E29 7.66E29

3 1.29E+01 1.10E25 6.75E01

5.35E01 5.35E01

4.02E04 4.02E04

4 1.73E+01 1.90E03 6.77E01

4.08E28 5.35E01

5.99E31 4.02E04

5 1.91E+01 7.67E02 7.54E01

2.18E27 5.35E01

3.36E30 4.02E04

6 2.21E+01 7.04E28 7.54E01

1.40E01 6.75E01

2.28E04 6.30E04

7 2.68E+01 7.31E28 7.54E01

5.57E02 7.31E01

1.34E07 6.30E04

8 3.49E+01 2.32E03 7.56E01

5.33E29 7.31E01

2.56E31 6.30E04

9 3.76E+01 1.72E02 7.73E01

1.77E29 7.31E01

8.92E34 6.30E04

The table below compares the results obtained with the model

LOUSE

TGM

and values of

reference obtained with a model of

POU_D_E

(

NUME_MODE

1, 2, 3, 5, 6, 7), for which there is not

no particular remarks.

NUME
MODE

FREQUENCY MASS_EFFE_UN

MASS_EFFE_UN

MASS_EFFE_UN_DZ

Values references

10.0386 2.4062E01

1.6855E26 7.0440E30

POU_D_TGM

1 10.0299

2.4507E01

1.3770E27

7.1158E31

Relative error

 8.7E04

1.8E02

---

Absolute error

 8.7E03

4.4E03

---

Values references

12.3631 4.3310E01

3.9884E24 2.6399E27

POU_D_TGM

2 12.2722

4.3008E01

1.2845E25

7.5937E29

Relative error

 7.4E03

 7.0E03

---

Absolute error

 9.1E02

 3.0E03

---

Values references

13.0613 3.8389E24

5.2880E01 4.1267E04

POU_D_TGM

3 12.8877

1.1018E25

5.3471E01

4.0172E04

Relative error

 1.3E02

---

1.1E02

 2.7E02

Absolute error

 1.7E01 --- 5.9E03

 1.1E05

Values references

19.1421 7.9213E02

1.8759E27 4.2482E28

POU_D_TGM

5 19.0752

7.6706E02

2.1807E27

3.3632E30

Relative error

 3.5E03

 3.3E02

---

Absolute error

 6.7E02

 2.5E03

---

Values references

22.359 6.2877E27

1.3777E01

2.2223E04

POU_D_TGM

6 22.1023

7.0371E28

1.4041E01

2.2790E04

Relative error

 1.2E02

---

1.9E02

2.5E02

Absolute error

 2.6E01 --- 2.6E03

5.7E06

Values references

26.9214 1.2099E29

6.0029E02 1.5014E07

POU_D_TGM

7 26.7993

7.3140E28

5.5675E02

1.3418E07

Relative error

 4.6E03

---

 7.8E02

---

Absolute error

 1.2E01

---

 4.4E03

---

Code_Aster

Version

6.0

Titrate:

SDLL132 - Clean modes of a frame

Date:

15/04/03

Author (S):

J-L. FLEJOU

Key

V2.02.132-A

Page:

7/8

Manual of Validation

V2.02 booklet: Linear dynamics of the beams

HR-17/02/019/A

The table below compares the results obtained with the model

POU_D_TGM

and values of

reference obtained with a model of

POU_D_E

(

NUME_MODE

4, 8, 9) for which some

remarks are necessary.

NUME
MODE

FREQUENCY MASS_EFFE_UN

MASS_EFFE_UN

MASS_EFFE_UN_DZ

Values references

17.5316 7.7262E04 4.5440E26 2.7423E28

POU_D_TGM

4 17.3126

1.9020E03

4.0831E28

5.9912E31

Relative error

 1.3E02

5.9E01

---

Absolute error

 2.2E01

1.1E03

---

Values references

35.2798 1.6712E03 7.4262E30 1.1337E29

POU_D_TGM

8 34.9301

2.3155E03

5.3345E29

2.5636E31

Relative error

 1.0E02

2.8E01

---

Absolute error

 3.5E01

6.4E04

---

Values references

37.0148 1.2125E02 9.0891E30 2.8395E33

POU_D_TGM

9 37.6334

1.7201E02

1.7660E29

8.9176E34

Relative error

1.6E02

3.0E01

---

Absolute error

6.2E01

5.1E03

---

For

NUME_MODE

4, the frequency is correct, on the other hand there is a relative error of 59% on

MASS_EFFE_UN_DX

(1.9E-03 to be compared with 7.7E-04), and an absolute error of 1.1E-03. The value of

MASS_EFFE_UN_DX

indicate a weak participation of this mode to the dynamic response of

structure. The two analyzes are thus in agreement, there is well a mode in the vicinity of 17.5Hz, and its
contribution is very weak with respect to the dynamic response of the structure.

After analysis of the results, calculated mode with 34.9Hz (

NUME_MODE

8 for the model

POU_D_TGM

)

corresponds to the mode of reference to 35.3Hz (

NUME_MODE

13). On the other hand there is a relative error

from 28% on

MASS_EFFE_UN_DX

(2.3E-03 to be compared with 1.7E-03) and an absolute error of 6.4E-04.

The value of

MASS_EFFE_UN_DX

indicate a weak participation of this mode to the dynamic response

structure, the two analyzes are thus in agreement.

After analysis of the results, calculated mode with 37.6Hz (

NUME_MODE

9 for the model

POU_D_TGM

)

corresponds to the mode of reference to 37.0Hz (

NUME_MODE

14). On the other hand there is a relative error

from 30% on

MASS_EFFE_UN_DX

(1.7E-02 to be compared with 1.2E-02) and an absolute error of 5.1E-03.

The value of

MASS_EFFE_UN_DX

indicate a weak participation of this mode to the dynamic response

structure, the two analyzes are thus in agreement.

Mode, of the reference solution, which corresponds to the frequency of 33.6Hz (

NUME_MODE

10) is not

not found by modeling in

POU_D_TGM

MASS_EFFE_UN_DY

, corresponding to this mode

is of 6.37E-04, lower than 0.1%. This value indicates a weak participation of this mode to
dynamic response of the structure. The fact that one does not find this mode, with a modeling
of

POU_D_TGM

, thus will not influence the dynamic analysis which one could make thereafter.

3.4 Parameters

of execution

Version:

6.0

Machine:

IRIX64

Overall dimension memory: 16Mo
Time CPU To use

: 9.0sec