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Version
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Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
1/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA, (*) CS IF
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
V2.01.030 document
SDLD30 - Spectral seismic response of one
system 2 masses and 3 springs multimedia
Summary:
The problem consists in calculating the spectral response of a system 2 masses - 3 springs subjected to one
multiple seismic excitation.
One tests the discrete element in traction, the calculation of the clean modes, the static modes and the answer
spectral by modal superposition via operator COMB_SISM_MODAL. Various office pluralities are tested at the time of
calculation of the answers of supports.
The results obtained are in very good agreement with the analytical results of reference.
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
2/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
The structure is modelized by a unit of 3 springs and 2 specific masses.
1.2
Material properties
Stiffness of connection: K
1
= K
2
= K = 1000 NR/m; K
3
= 10 K = 10000 NR/m
specific mass: m
2
= m
3
= m = 10 kg.
1.3
Boundary conditions and loadings
· boundary conditions
Only authorized displacements are the translations according to axis X.
Points NO1 and NO4 are embedded: DX=DY=DZ=DRX=DRY=DRZ=0.
The other points are free in translation according to direction X: DY=DZ=DRX=DRY=DRZ=0.
· loading
The structure is subjected to a multiple spectral seismic excitation and displacements
differentials.
The spectra of answers of oscillator in pseudo acceleration are simplified. Only them
values corresponding to the 2 Eigen frequencies of the system are mentioned. They
do not depend on damping:
with node NO1:
SRO
NO1
(F
1
) = A
11
= 7 m/s
2
SRO
NO1
(F
2
) = A
12
= 5 m/s
2
DDS
NO1
= D
1
= - 0.04 m
with node NO4:
SRO
NO4
(F
1
) = A
21
= 12 m/s
2
SRO
NO4
(F
2
) = A
22
= 6 m/s
2
DDS
NO4
= D
2
= 0.06 m
1.4 Conditions
initial
The system is initially at rest.
m
3
m
2
X
K
1
K
2
K
3
NO1
NO2
NO3
NO4
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
3/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One calculates the spectral response by modal superposition of a system masses spring subjected to two
distinct excitations. One determines the displacement of the masses and the reactions of support to the nodes
NO1 and NO4 following axis X.
One calculates analytically:
·
Eigen frequencies F
I
,
·
associated clean vectors
Ni
standardized compared to the modal mass,
·
static modes of supports
J
system,
·
factors of modal participation P
ij
relating to the supports,
·
Rm
ij
the maximum of the response of each mode starting from the spectra of excitation,
·
Re
J
the contribution of the movement of drive of each support starting from displacements
differentials,
·
Rc
J
the static term of correction,
·
primary and secondary components of the response according to the rules of office plurality
adopted.
2.2
Results of reference
· stamp rigidity K
-
-
-
-
-
-
=
K
K
K
K
K
K
K
K
K
K
K
10
10
0
0
10
11
0
0
2
0
0
· stamp of mass M
=
0
0
0
0
0
0
0
0
0
0
0
0
0
0
m
m
M
· modal calculation in embedded base
(
)
0
=
-
I
I
M
K
2
I
I
=
(
)
85
13
2
1
-
= mk
(
)
85
13
2
2
+
= mk
- Eigen frequencies:
2
/
2
/
2
2
1
1
=
=
F
F
Code_Aster
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Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
4/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
- not normalized clean modes:
(
)
+
-
=
0
2
85
9
1
0
1
(
)
+
-
=
0
2
85
9
1
0
2
- generalized modal masses
I
I
T
I
M
µ
=
:
(
)
85
18
170
4
1
-
= m
µ
(
)
85
18
170
4
2
+
= m
µ
- clean modes normalized with the unit generalized modal mass
Ni
:
1
1
1
µ
=
NR
2
2
2
µ
=
NR
- modal reactions Fm
I
:
(
)
-
-
=
=
85
9
5
0
0
1
1
1
1
µ
K
K
Fm
NR
(
)
+
-
=
=
85
9
5
0
0
1
2
2
2
µ
K
K
Fm
NR
- factors of modal participation
J
I
T
ij
M
P
=
:
- contribution of the dynamic mode 1 to the movement imposed on node NO1:
(
)
85
13
42
1
1
1
11
+
=
=
µ
m
M
P
T
- contribution of the dynamic mode 1 to the movement imposed on node NO4:
(
)
85
8
21
10
1
2
1
12
+
-
=
=
µ
m
M
P
T
- contribution of the dynamic mode 2 to the movement imposed on node NO1:
(
)
85
13
42
2
1
2
21
+
-
=
=
µ
m
M
P
T
- contribution of the dynamic mode 2 to the movement imposed on node NO4:
(
)
85
8
21
10
2
2
2
22
+
=
=
µ
m
M
P
T
- factor of participation of the dynamic mode 1 in direction X:
12
11
1
P
P
P
X
+
=
- factor of participation of the dynamic mode 2 in direction X:
22
21
2
P
P
P
X
+
=
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
5/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
· static modes of supports
J
- static solution with a unit displacement of node NO1:
displacements:
=
0
1
11
21
21
1
1
nodal reactions:
-
=
=
1
0
0
1
21
10
1
1
K
K
Fs
- static solution with a unit displacement of node NO4:
displacements:
=
21
20
10
0
21
1
2
nodal reactions:
-
=
=
1
0
0
1
21
10
2
2
K
K
Fs
· response of mode I to the movement of the support J
2
I
ij
ij
I
ij
With
P
R
Rm
=
with
I
Ni
I
Fm
R
or
=
· static correction
- static modes
J
U
solution of
J
J
M
Ku
=
:
displacements:
=
0
13
122
0
441
1
K
m
U
nodal reactions:
-
-
=
130
21
231
122
441
1
m
Fu
displacements:
=
0
50
130
0
441
2
K
m
U
nodal reactions:
-
-
=
500
420
210
130
441
2
m
Fu
- static correction relating to the movement of the support J if mode 2 is not retained:
J
J
J
J
With
R
P
Ru
Rc
2
2
1
1
1
-
=
with:
J
J
J
Fu
U
Ru
or
=
and
1
1
1
Fm
R
NR
or
=
· contribution of the support J to the movement of drive
J
J
J
D
R
=
Re
with
J
J
J
Fs
R
or
=
2.3
Uncertainty on the solution
No (exact analytical solution).
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
6/16
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
The system is modelized by:
·
3 discrete elements K_T_D_L,
·
2 discrete elements M_T_D_N.
3.2
Characteristics of the mesh
The mesh consists of 3 meshs SEG2.
3.3 Functionalities
tested
Controls
AFFE_MODELE GROUP_MA
“MECHANICAL”
“DIS_T'
DISCRETE AFFE_CARA_ELEM
NODE
M_T_D_N
NET
K_T_D_L
AFFE_CHAR_MECA DDL_IMPO
MACRO_MATR_ASSE
MODE_ITER_SIMULT CALC_FREQ
METHOD
“SORENSEN”
NORM_MODE NORMALIZES
“MASS_GENE”
MODE_STATIQUE MODE_STAT
PSEUDO_MODE
COMB_SISM_MODAL MODE_CORR
EXCIT
COMB_MODE
“SRSS”
COMB_MULT_APPUI
“QUAD”
“LINE”
DEPL_MULT_APPUI
COMB_DEPL_APPUI
“QUAD”
“LINE”
“ABS”
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
7/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
4
Results of modeling A
4.1 Frequencies
clean
MODE
Reference
Code_Aster
Relative error (%)
1
2,18815E+00 2,18815E+00 0,000
2
5,30484E+00 5,30484E+00 0,000
4.2
Total response on complete modal basis
Modes 1 and 2 are taken into account. Components inertial (primary education) and statics (secondary)
response are directly cumulated to the level of the supports.
·
calculation n°1
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
2
1
2
1
1
Re
+
= Rm
R
with
2
21
2
11
1
Rm
Rm
Rm
+
=
- response of the support j=2 (node NO4)
:
2
2
2
2
2
Re
+
= Rm
R
with
2
22
2
12
2
Rm
Rm
Rm
+
=
- total answer:
2
2
2
1
R
R
R
+
=
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02 0,000
NO2
5,43820E-02 5,43820E-02 0,000
NO3
5,75544E-02 5,75544E-02 0,000
NO4
6,00000E-02 6,00000E-02 0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
5,36769E+01 5,36769E+01
0,000
NO4
7,44120E+01 7,44120E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
8/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
·
calculation n°2
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' LINE'
- response of the support j=1 (node NO1):
2
1
2
1
1
Re
+
= Rm
R
with
2
21
2
11
1
Rm
Rm
Rm
+
=
- response of the support j=2 (node NO4)
:
2
2
2
2
2
Re
+
= Rm
R
with
2
22
2
12
2
Rm
Rm
Rm
+
=
- total answer:
2
1
R
R
R
+
=
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
7,48259E-02 7,48259E-02
0,000
NO3
6,03377E-02 6,03377E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
7,34576E+01 7,34576E+01
0,000
NO4
9,72617E+01 9,72617E+01
0,000
4.3 Total response on incomplete modal basis without correction
statics
Only mode 1 is taken into account. Components inertial (primary education) and statics (secondary) of
response are directly cumulated to the level of the supports.
·
calculation n°1
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
2
1
2
1
1
Re
+
= Rm
R
with
11
1
Rm
Rm
=
- response of the support j=2 (node NO4):
2
2
2
2
2
Re
+
= Rm
R
with
12
2
Rm
Rm
=
- total answer:
2
2
2
1
R
R
R
+
=
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
5,43794E-02 5,43794E-02
0,000
NO3
5,73536E-02 5,73536E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
5,36743E+01 5,36743E+01
0,000
NO4
5,68312E+01 5,68312E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
9/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
·
calculation n°2
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' LINE'
- response of the support j=1 (node NO1):
2
1
2
1
1
Re
+
= Rm
R
with
11
1
Rm
Rm
=
- response of the support j=2 (node NO4):
2
2
2
2
2
Re
+
= Rm
R
with
12
2
Rm
Rm
=
- total answer:
2
1
R
R
R
+
=
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
7,48229E-02 7,48229E-02
0,000
NO3
6,01363E-02 6,01363E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
7,34546E+01 7,34546E+01
0,000
NO4
7,76841E+01 7,76841E+01
0,000
4.4 Total response on incomplete modal basis with correction
statics
Only mode 1 intervenes in the calculation of the answer. The static contribution of neglected mode 2 is
taking into account.
·
calculation n°1
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
2
1
2
1
2
1
1
Re
+
+
=
Rc
Rm
R
with
11
1
Rm
Rm
=
- response of the support j=2 (node NO4):
2
2
2
2
2
2
2
Re
+
+
=
Rc
Rm
R
with
12
2
Rm
Rm
=
- total answer:
2
2
2
1
R
R
R
+
=
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
5,43820E-02 5,43820E-02
0,000
NO3
5,75544E-02 5,75544E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
5,36769E+01 5,36769E+01
0,000
NO4
7,44120E+01 7,44120E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
10/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
·
calculation n°2
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' LINE'
- response of the support j=1 (node NO1):
2
1
2
1
2
1
1
Re
+
+
=
Rc
Rm
R
with
11
1
Rm
Rm
=
- response of the support j=2 (node NO4):
2
2
2
2
2
2
2
Re
+
+
=
Rc
Rm
R
with
12
2
Rm
Rm
=
- total answer:
2
1
R
R
R
+
=
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
7,48259E-02 7,48259E-02
0,000
NO3
6,03377E-02 6,03377E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
7,34576E+01 7,34576E+01
0,000
NO4
9,72617E+01 9,72617E+01
0,000
4.5
Partition of the components primary and secondary of the answer
The components inertial (primary education) and statics (secondary) are treated separately.
· calculation n°1
- primary response on modal basis supplements (modes 1 and 2)
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
2
21
2
11
1
Rm
Rm
IH
+
=
- response of the support j=2 (node NO4):
2
22
2
12
2
Rm
Rm
IH
+
=
- primary answer:
2
2
2
1
IH
IH
IH
+
=
relative displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
0,00000E+00 0,00000E+00
-
NO2
4,12562E-02 4,12562E-02
0,000
NO3
6,60152E-03 6,60152E-03
0,000
NO4
0,00000E+00 0,00000E+00
-
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,12562E+01 4,12562E+01
0,000
NO4
6,60152E+01 6,60152E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
11/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
-
secondary answer
COMB_DEPL_APPUI=' QUAD'
- secondary answer:
2
2
2
1
Re
Re
+
=
RII
displacements of drive: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
3,54306E-02 3,54306E-02
0,000
NO3
5,71746E-02 5,71746E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
3,43386E+01 3,43386E+01
0,000
NO4
3,43386E+01 3,43386E+01
0,000
·
calculation n°2
- primary response on incomplete modal basis without static correction
Only mode 1 intervenes in the calculation of the answer
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
11
1
Rm
IH
=
- response of the support j=2 (node NO4):
12
2
Rm
IH
=
- primary answer:
2
2
2
1
IH
IH
IH
+
=
relative displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
0,00000E+00 0,00000E+00
-
NO2
4,12528E-02 4,12528E-02
0,000
NO3
4,52841E-03 4,52841E-03
0,000
NO4
0,00000E+00 0,00000E+00
-
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,12528E+01 4,12528E+01
0,000
NO4
4,52841E+01 4,52841E+01
0,000
- secondary answer
COMB_DEPL_APPUI=' LINE'
- secondary answer:
2
1
Re
Re
+
=
RII
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
12/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
displacements of drive: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
- 4,00000E-02 - 4,00000E-02
0,000
NO2
7,61905E-03 7,61905E-03
0,000
NO3
5,52381E-02 5,52381E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
- 4,76190E+01 - 4,76190E+01
0,000
NO4
4,76190E+01 4,76190E+01
0,000
·
calculation n°3
- primary response on incomplete modal basis with static correction
Only mode 1 intervenes in the calculation of the answer
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
2
1
2
11
1
Rc
Rm
IH
+
=
- response of the support j=2 (node NO4):
2
2
2
12
2
Rc
Rm
IH
+
=
- primary answer:
2
2
2
1
IH
IH
IH
+
=
relative displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
0,00000E+00 0,00000E+00
-
NO2
4,12562E-02 4,12562E-02
0,000
NO3
6,60152E-03 6,60152E-03
0,000
NO4
0,00000E+00 0,00000E+00
-
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,12562E+01 4,12562E+01
0,000
NO4
6,60152E+01 6,60152E+01
0,000
- secondary answer
COMB_DEPL_APPUI=' ABS'
- secondary answer:
2
1
Re
Re
+
=
RII
displacements of drive: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
4,95238E-02 4,95238E-02
0,000
NO3
5,90476E-02 5,90476E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
13/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,76190E+01 4,76190E+01
0,000
NO4
4,76190E+01 4,76190E+01
0,000
·
calculation n°4
- primary response on incomplete modal basis with static correction
Only mode 1 intervenes in the calculation of the answer.
COMB_MODE=' SRSS'
COMB_MULT_APPUI=' QUAD'
- response of the support j=1 (node NO1):
2
1
2
11
1
Rc
Rm
IH
+
=
- response of the support j=2 (node NO4):
2
2
2
12
2
Rc
Rm
IH
+
=
- primary answer:
2
2
2
1
IH
IH
IH
+
=
- secondary answer: test office plurality of DDSs
5 loading cases are defined. The 5 associated elementary static answers are:
- case a: DDSa
NO1
=-0.04
Ra=r
1
×DDSa
NO1
- case b: DDSb
NO4
=0.06
Rb=r
2
×DDSb
NO4
- case C: DDSc
NO4
=0.03
Rc=r
2
×DDSc
NO4
- case D: DDSd
NO1
=-0.07
Rd=r
1
×DDSd
NO1
- case E: DDSe
NO4
=0.05
Re=r
2
×DDSe
NO4
4 combinations are calculated:
·
combination n°1
linear office plurality of the cases has and b: TYPE_COMBI=' LINE' NUME_ORDRE=200
secondary answer:
Rb
Ra
RII
+
=
1
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
- 4,00000E-02 - 4,00000E-02
0,000
NO2
7,61905E-03 7,61905E-03
0,000
NO3
5,52381E-02 5,52381E-02
0,000
NO4
6,00000E-02 6,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
- 4,76190E+01 - 4,76190E+01
0,000
NO4
4,76190E+01 4,76190E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
14/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
·
combination n°2
absolute office plurality of the cases has and C: TYPE_COMBI=' ABS' NUME_ORDRE=201
secondary answer:
Rc
Ra
RII
+
=
2
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,00000E-02 4,00000E-02
0,000
NO2
3,52381E-02 3,52381E-02
0,000
NO3
3,04762E-02 3,04762E-02
0,000
NO4
3,00000E-02 3,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
3,33333E+01 3,33333E+01
0,000
NO4
3,33333E+01 3,33333E+01
0,000
·
combination n°3
quadratic office plurality of the cases D and E: TYPE_COMBI=' QUAD' NUME_ORDRE=202
secondary answer:
2
2
3
Re
+
= Rd
RII
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
7,00000E-02 7,00000E-02
0,000
NO2
4,37189E-02 4,37189E-02
0,000
NO3
4,77356E-02 4,77356E-02
0,000
NO4
5,00000E-02 5,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
4,09635E+01 4,09635E+01
0,000
NO4
4,09635E+01 4,09635E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
15/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
·
combination n°4
linear office plurality of the cases has and E: TYPE_COMBI=' LINE' NUME_ORDRE=203
secondary answer:
Re
4
+
= Ra
RII
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
- 4,00000E-02 - 4,00000E-02
0,000
NO2
2,85714E-03 2,85714E-03
0,000
NO3
4,57143E-02 4,57143E-02
0,000
NO4
5,00000E-02 5,00000E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
- 4,28571E+01 - 4,28571E+01
0,000
NO4
4,28571E+01 4,28571E+01
0,000
The total secondary answer is established by the quadratic office plurality of the 4 combinations precedents:
2
4
2
3
2
2
2
1
RII
RII
RII
RII
RII
+
+
+
=
NUME_ORDRE=204
absolute displacements: DEPL
NODE
Reference
Code_Aster
Relative error (%)
NO1
9,84886E-02 9,84886E-02
0,000
NO2
5,67386E-02 5,67386E-02
0,000
NO3
9,13703E-02 9,13703E-02
0,000
NO4
9,74679E-02 9,74679E-02
0,000
nodal reactions: REAC_NODA
NODE
Reference
Code_Aster
Relative error (%)
NO1
8,30266E+01 8,30266E+01
0,000
NO4
8,30266E+01 8,30266E+01
0,000
Code_Aster
®
Version
6.4
Titrate:
SDLD30 - Spectral seismic response of a system 2 masses 3 springs
Date:
05/03/04
Author (S):
Y. PONS, D. NUNEZ *, L. VIVAN *
Key
:
V2.01.030-A
Page:
16/16
Manual of Validation
V2.01 booklet: Linear dynamics of the discrete systems
HT-66/04/005/A
5
Summary of the results
The results obtained with Code_Aster are in conformity with the analytical results of reference.