Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
1/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
Document: V2.01.022
SDLD22 - Transient of a system mass-arises
to 8 ddl with viscous shock absorber
Summary:
The mechanical structure considered is made up of a linear one-way whole of mass-springs
with shock absorbers viscous and subjected to a transitory excitation of square pulse 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, shock absorbers) 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 pitch 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.
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
2/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
X, U
P1
U1
With
C
m
C
K
K
m
P2
U2
m
C
K
P3
U3
m
C
K
P8
B
U8
Specific masses:
m
P1
= m
P2
= m
P3
= ...... = m
P8
= m
Stiffnesses of connection:
K
AP1
= K
P1P2
= K
P2P3
= ...... = K
P8B
= K
Viscous damping:
C
AP1
= C
P1P2
= C
P2P3
= ...... = C
P8B
= C
1.2
Material properties
Comes out from linear elastic translation
K =
10
5
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 point P
4
in the shape of square pulse:
()
()
()
Not P
1 NR
Other points P
4
I
F
F T
T
S F T
T
S F T
F
X
X
I
4
0
1
1
0
0
=
=
>
=
=
.
.
1.4 Conditions
initial
For T = 0, in any point, U = 0 and
dt = 0
.
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
3/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
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 pitch of time of 0.001s [bib2].
(
)
1
1
2
1
3
1
3
2
1
3
1
1
2
1
3
2
2
2
1
2
1
2
T
T
T
T
T
N
N
N
N
N
N
M
C
K U
F
F
F
M
K U
M
C
K U
+
+
=
+
+
+
+
+
+
+
+
+
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 point P
4
.
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.
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
4/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
This modeling allows the validation of integration by modal recombination.
Discrete element of rigidity in translation
With
B
P
1
y
X
P
2
P
3
P
4
P
5
P
6
P
7
P
8
Characteristics of the elements
DISCRETE
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: (ALL:“YES” DY: 0. , DZ: 0. )
Boundary conditions with the extreme nodes
(GROUP_NO: AB DX: 0. )
Names of the nodes:
Not A = N1
P
1
= N2
Not B = N10
P
2
= N3
.............
P
8
= 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 mesh
A number of nodes: 10
A number of meshs and types: 9 SEG2
3.3 Functionalities
tested
Controls
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
NODE
MODE_ITER_INV ADJUSTS
DYNA_TRAN_MODAL MATR_AMOR EULER
NOT
0.001
DEFI_LIST_REEL BEGINNING
INTERVAL
RECU_FONCTION LIST_INST
REST_BASE_PHYS INTERPOL “FLAX”
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
5/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
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 pitch
T =
0.001
.
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
6/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
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 pitch.
Discrete element of rigidity in translation and rotation
With
B
P
1
y
X
P
2
P
3
P
4
P
5
P
6
P
7
P
8
Characteristics of the elements:
DISCRETE
:
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 locked:
in all the nodes
DDL_IMPO:
(ALL:“YES” DY: 0. , DZ: 0. )
(ALL:“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 10
3
S.
Integration by modal recombination on all the modes, diagram of Euler.
5.2
Characteristics of the mesh
A number of nodes: 10
A number of meshs and types: 9 SEG2
5.3 Functionalities
tested
Controls
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
NODE
CALC_MATR_ELEM OPTION
“MASS_MECA_DIAG”
MODE_ITER_INV ADJUSTS
DYNA_TRAN_MODAL MATR_AMOR
NOT
0.001
RECU_FONCTION LIST_INST
REST_BASE_PHYS INTERPOL “FLAX”
DYNA_LINE_TRAN ADAPT
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
7/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
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 pitch
T =
0.001
.
Code_Aster
®
Version
6.0
Titrate:
SDLD22 - Transient of a system mass-arises to 8 ddl
Date:
17/02/04
Author (S):
E. BOYERE
Key
:
V2.01.022-C
Page:
8/8
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
7
Summary of the results
This test is to be supplemented while using:
·
a pitch of time
T =
1. E 4
,
·
other diagrams of integration.