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SDLL132 - Modes clean of a frame
Date:
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Author (S):
J-L. Key FLEJOU
:
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Organization (S): EDF-R & D/TESE
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
Document: V2.02.132
SDLL132 - Modes clean of a frame in
multifibre beams
Summary:
This test relates to the validation of 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 commands: POST_ELEM, NORM_MODE, EXTR_MODE.
· results of MACRO_MODE_MECA.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
Code_Aster ®
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Titrate:
SDLL132 - Modes clean of a frame
Date:
15/04/03
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:
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1
Problem of reference
1.1 Geometry
The case test is a metal frame made up of beams and posts.
Co-ordinates of the principal nodes of the grid:
Coord. X
Coord. Y
Coord. Z
Not
(in m)
(in m)
(in m)
To 2.0
2.5
0.0
B 4.0
0.0
0.0
C 2.0
2.5
0.0
D 0.0
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
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
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SDLL132 - Modes clean of a frame
Date:
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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
HF
I.E.(INTERNAL EXCITATION), CG
AE
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
AY
1.474994 1.789865 1.792884 1.464032 1.774392
AZ
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
Pa
Rho 7.85e+03
kg/m3
1.4
Boundary conditions
The points A, B, C, D are embedded.
DX = 0
DY = 0
DZ = 0
DRX = 0
DRY = 0
DRZ = 0
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
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Titrate:
SDLL132 - Modes clean of a frame
Date:
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2
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 command POST_ELEM, with key word MASS_INER:
Sizes Value
MASSE
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 command EXTR_MODE with criterion MASS_EFFE_UN and a threshold of 5.0E-04.
NUME FREQUENCY MASS_EFFE_UN CUMUL_DX MASS_EFFE_UN CUMUL_DY MASS_EFFE_UN CUMUL_DZ
MODE
DX
DY
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.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
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3 Modeling
With
3.1
Characteristics of modeling and the grid
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 command post_elem,
· the second stage consists in calculating the clean modes of the structures using
commands 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-command
MACRO_MODE_MECA by normalizing the modes with the result of concept POST_ELEM.
Commands
AFFE_CARA_ELEM BEAM
AFFE_FIBER
POST_ELEM MASS_INER
CALC_MATR_ELEM OPTION
“RIGI_MECA”
“MASS_MECA”
MODE_ITER_SIMULT TYPE_RESU
“DYNAMIQUE”
CALC_FREQ
BANDE
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 commands POST_ELEM, with the key word
MASS_INER, for model POU_D_TGM and compares them with the values of reference obtained with one
model of POU_D_E.
Sizes Values Values
Error
References
POU_D_TGM
Relative
MASSE
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.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
Code_Aster ®
Version
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Titrate:
SDLL132 - Modes clean of a frame
Date:
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Author (S):
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:
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The table below gives the clean modes calculated with a model of POU_D_TGM. Modes
are filtered by command EXTR_MODE with 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 the MASS_EFFE_UN is fixed at 1.0E-02.
NUME FREQUENCY MASS_EFFE_UN CUMUL_DX MASS_EFFE_UN CUMUL_DY MASS_EFFE_UN CUMUL_DZ
MODE
DX
DY
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 model POU_D_TGM and the 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
FREQUENCY MASS_EFFE_UN
MASS_EFFE_UN MASS_EFFE_UN_DZ
MODE
DX
DY
Values references
1
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
2
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
3
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
5
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
6
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
7
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
---
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
Code_Aster ®
Version
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Titrate:
SDLL132 - Modes clean of a frame
Date:
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:
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The table below compares the results obtained with model POU_D_TGM and the values of
reference obtained with a model of POU_D_E (NUME_MODE 4, 8, 9) for which some
remarks are necessary.
NUME
FREQUENCY MASS_EFFE_UN MASS_EFFE_UN MASS_EFFE_UN_DZ
MODE
DX
DY
Values references
4
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
13
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
14
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 the 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 indicates 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 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 the 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 indicates 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 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 the 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 indicates 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. The 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
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
Obstruction memory: 16Mo
Time CPU To use
: 9.0sec
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
Code_Aster ®
Version
6.0
Titrate:
SDLL132 - Modes clean of a frame
Date:
15/04/03
Author (S):
J-L. Key FLEJOU
:
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4
Summary of the results
The results of reference are obtained with a model of POU_D_E.
The analyzes carried out with a modeling in POU_D_TGM are in agreement with the solution of
reference.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HR-17/02/019/A
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