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Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
1/8
Organization (S): EDF-R & D/AMA
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
Document: V2.01.022
SDLD22 - Transitoire of a system mass-arises
to 8 ddl with viscous damping device
Summary:
The mechanical structure considered is made up of a linear one-way whole of mass-springs
with damping devices viscous and subjected to a transitory excitation of crenel type.
Two modelings are developed. The first retains only the degree of freedom in axial translation of
masses, the second considers the axial translation and rotation.
This problem makes it possible to test:
·
discrete elements (masses, springs, damping devices) in translation-rotation,
·
the definition of a force of specific excitation transitory,
·
the operator of transitory calculation of response by modal recombination (DYNA_TRAN_MODAL
[U4.53.21]), as well as the recovery with initial conditions (modeling A),
·
the operator of calculation of direct transitory response with the diagram to step of adaptive time
(DYNA_LINE_TRAN [U4.53.02]) (modeling B).
In addition, several operators of postprocessing are tested: RECU_FONCTION [U4.32.03], TEST_FONCTION
[U4.92.02], RECU_CHAMP [U4.71.01].
The results obtained (field of displacements, speeds) are in concord with the results of the guide
VPCS, taken for reference solution.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
2/8
1
Problem of reference
1.1 Geometry
U1
U2
U3
U8
K
K
K
K
With
m
m
m
m
B
X, U
P1
P2
P3
P8
C
C
C
C
Specific masses:
mP = m = m = ...... = m = m
1
P2
P3
P8
Stiffnesses of connection:
kAP1 = kP1P2 = kP2P3 = ...... = kP8B = K
Viscous damping:
cAP1 = cP1P2 = cP2P3 = ...... = cP8B = C
1.2
Material properties
Comes out from linear elastic translation
K =
105 NR/m
Specific mass
m =
10 kg
One-way viscous damping
C =
50 NR/(m/s)
1.3
Boundary conditions and loadings
Boundary conditions: embedded points A and B (U = 0).
Loading: force concentrated at the P4 point in the shape of crenel:
Not P
=
=
4
F
F (T)
0 T1 S F (T) 1 NR
x4
T > 1s F (T) = 0.
Other points P
F = 0.
I
xi
1.4 Conditions
initial
For T = 0, in any point, U = 0 and
= 0.
dt
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
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2
Reference solution
The reference solution is from guide VPCS.
2.1
Method of calculation used for the reference solution
Numerical integration selected to obtain this solution rests on a diagram of integration by
finished differences, of the method type - Newmark improved, with step of time of 0.001s [bib2].
1
1
1
1
M +
C +
K un+2 = (N
F +2 + N
F 1 +
+
N
F)
2
T
2 T
3
3
2
1
1
1
1
+
M
K U
+
+
M +
C
K U
2
T
3
N 1
2
T
2 T
3
N
The displacement of item 4 according to time takes the following form:
Appear 2.1-a: Point 4: displacement according to time
2.2
Results of reference
Displacement according to X of the P4 point.
2.3
Uncertainty on the solution
Precision of the diagram of Newmark.
2.4 References
bibliographical
[1]
Card-index SDLD22/90 of commission VPCS.
[2]
NEWMARK NR. Mr.: “A method off computation for structural dynamics”, proceeding ASCE
J. Eng. Mech. Div E-3, July 1959, p 67-94.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
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3 Modeling
With
3.1
Characteristics of modeling
This modeling allows the validation of integration by modal recombination.
Discrete element of rigidity in translation
y
With
P
P
B
X
1
2
P3
P4
P5
P6
P7
P8
Characteristics of the elements
DISCRET with
nodal masses
M_T_D_N
M_T_N
matrices of rigidity
K_T_D_L
K_T_L
matrices
of damping
A_T_D_L A_T_L
Blocking of the DDL in Y and Z of all the nodes
DDL_IMPO: (TOUT:“YES” DY: 0. , DZ: 0. )
Boundary conditions with the extreme nodes
(GROUP_NO: AB DX: 0. )
Names of the nodes:
Not A = N1
P1 = N2
Not B = N10
P2 = N3
.............
P8 = N9
Modal recombination with all the modes (either 8),
diagram of EULER, resumption of the first calculation with T = 0.455 S
no time used: T = 1. E3 S.
3.2
Characteristics of the grid
A number of nodes: 10
A number of meshs and types: 9 SEG2
3.3 Functionalities
tested
Commands
DISCRETE AFFE_CARA_ELEM GROUP_MA “K_T_D_L'
GROUP_MA
“A_T_D_L'
GROUP_NO
“M_T_D_N'
“MECHANICAL” AFFE_MODELE VERY
“DIS_T'
GROUP_NO
“DIS_T'
AFFE_CHAR_MECA DDL_IMPO GROUP_NO
FORCE_NODALE
NOEUD
MODE_ITER_INV ADJUSTS
DYNA_TRAN_MODAL MATR_AMOR EULER
PAS
0.001
DEFI_LIST_REEL BEGINNING
INTERVALLE
RECU_FONCTION LIST_INST
REST_BASE_PHYS INTERPOL “FLAX”
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
5/8
4
Results of modeling A
4.1 Values
tested
Time Reference Aster %
Difference
0.09
4.02 E5
4.022 E5
0.05
0.18
4.22 E6
3.973 E6
5.8
0.27
3.89 E5
3.902 E5
0.32
0.37
5.98 E6
5.750 E6
3.83
0.46
3.73 E5
3.746 E5
0.43
0.54
7.14 E6
6.977 E6
2.27
0.63
3.64 E5
3.646 E5
0.16
0.72
8.07 E6
7.923 E6
1.81
0.81
3.58 E5
3.586 E5
0.18
0.9
8.76 E6
8.861 E6
1.12
0.99
3.52 E5
3.531 E5
0.317
1.08
3.08 E5
3.072 E5
0.23
1.18
3.02 E5
3.014 E5
0.17
1.27
2.88 E5
2.878 E5
0.06
1.36
2.80 E5
2.791 E5
0.31
1.45
2.65 E5
2.652 E5
0.09
4.2 Remarks
Relative minima (T = 0.18, 0.54,…) do not have a very good precision during the phase of excitation
with a step T = 0.001.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
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5 Modeling
B
5.1
Characteristics of modeling
This modeling allows, in addition to a new use of the modal recombination, the validation of
direct integration with adaptive step.
Discrete element of rigidity in translation and rotation
y
With
P
P
B
X
1
2
P3
P4
P5
P6
P7
P8
Characteristics of the elements:
DISCRET:
with nodal masses
M_TR_D_N
M_TR_N
and matrices of rigidity
K_TR_D_L
K_TR_L
and matrices of damping
A_TR_D_L A_TR_L
Boundary conditions and directions blocked:
in all the nodes
DDL_IMPO:
(TOUT:“YES” DY: 0. , DZ: 0. )
(TOUT:“YES” DRX: 0. DRY: 0 DRZ: 0)
with the nodes ends
(GROUP_NO: AB DX: 0. )
Direct integration by DYNA_LINE_TRAN, algorithm ADAPT, not of time max 103 S.
Integration by modal recombination on all the modes, diagram of Euler.
5.2
Characteristics of the grid
A number of nodes: 10
A number of meshs and types: 9 SEG2
5.3 Functionalities
tested
Commands
DISCRETE AFFE_CARA_ELEM GROUP_MA
“K_TR_D_L'
GROUP_MA
“A_TR_D_L'
GROUP_MA
“M_TR_D_N'
“MECHANICAL” AFFE_MODELE VERY
“DIS_T'
GROUP_NO
“DIS_T'
AFFE_CHAR_MECA DDL_IMPO GROUP_NO
FORCE_NODALE
NOEUD
CALC_MATR_ELEM OPTION
“MASS_MECA_DIAG”
MODE_ITER_INV ADJUSTS
DYNA_TRAN_MODAL MATR_AMOR
PAS
0.001
RECU_FONCTION LIST_INST
REST_BASE_PHYS INTERPOL “FLAX”
DYNA_LINE_TRAN ADAPT
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
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6
Results of modeling B
6.1 Values
tested
Transient by modal recombination
Time Reference Aster %
Difference
0.09
4.02 E5
4.022 E5
0.05
0.18
4.22 E6
3.973 E6
5.8
0.27
3.89 E5
3.902 E5
0.32
0.37
5.98 E6
5.750 E6
3.83
0.46
3.73 E5
3.746 E5
0.43
0.54
7.14 E6
6.977 E6
2.27
0.63
3.64 E5
3.646 E5
0.16
0.72
8.07 E6
7.923 E6
1.81
0.81
3.58 E5
3.586 E5
0.18
0.9
8.76 E6
8.861 E6
1.12
0.99
3.52 E5
3.531 E5
0.317
1.08
3.08 E5
3.072 E5
0.23
1.18
3.02 E5
3.014 E5
0.17
1.27
2.88 E5
2.878 E5
0.06
1.36
2.80 E5
2.791 E5
0.31
1.45
2.65 E5
2.652 E5
0.09
Direct transient
Time Reference Aster %
Difference
0.09
4.02 E5
4.022 E5
0.06
0.18
4.22 E6
4.000 E6
5.19
0.27
3.89 E5
3.900 E5
0.27
0.37
5.98 E6
5.764 E5
3.60
0.46
3.73 E5
3.743 E5
0.36
0.54
7.14 E6
6.990 E6
2.10
0.63
3.64 E5
3.645 E5
0.14
0.72
8.07 E6
7.936 E6
1.64
0.81
3.58 E5
3.586 E5
0.17
0.9
8.76 E6
8.663 E6
1.09
0.99
3.52 E5
3.531 E5
0.32
1.08
3.08 E5
3.078 E5
0.04
1.18
3.02 E5
3.023 E5
0.11
1.27
2.88 E5
2.884 E5
0.15
1.36
2.80 E5
2.798 E5
0.03
1.45
2.65 E5
2.657 E5
0.28
6.2 Remarks
Modelings A and B lead to the same results.
Relative minima (T = 0.18, 0.54,…) do not have a very good precision during the phase
of excitation with a step T = 0.001.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Code_Aster ®
Version
6.0
Titrate:
SDLD22 - Transitoire of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE Key
:
V2.01.022-C Page:
8/8
7
Summary of the results
This test is to be supplemented while using:
·
a step of time T = 1. E 4,
·
other diagrams of integration.
Handbook of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
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