Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
1/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
Organization (S):
EDF/AMA, DeltaCAD
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
Document: V2.03.502
SDLS502 - Square plate “solid” simply
supported
Summary:
This test simply represents a calculation in dynamic modal analysis of a thick square plate
supported. This test makes it possible to validate:
·
modelings finite elements DST, DKT, COQUE_3D with meshs QUAD4 and TRIA3,
QUAD8 and TRIA6, and 3D with meshs HEXA20,
·
the taking into account of rigidity in transverse shearing.
The frequencies and the modes obtained are compared with a reference solution, suggested by NAFEMS,
obtained with a calculation finite elements of voluminal type.
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
2/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
L
X, U
Z, W
y, v
L = 10.0 m
H = 1.0m
With
B
D
C
H
1.2
Properties of material
The properties of material constituting the plate are:
E
= 2. 10
11
AP Modulus Young
= 0.3
Poisson's ratio
= 8000. Kg/m
3
Mass
voluminal
1.3
Boundary conditions and loadings
- C.L. : plate simply supported on its contour
1.4 Conditions
initial
Without object
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
3/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
the reference solution suggested by NAFEMS [bib1] was obtained to leave a calculation finite elements
3D with elements bricks with 20 nodes and with a mesh 4x4 (xy plan) and 1 following element
the thickness.
2.2
Results of reference
the first 7 nonnull frequencies and the associated clean modes, the first three modes are
those of rigid bodies:
·
Frequency (mode 4 except plan)
: 44.762
Hz
·
Frequency (modes 5 & 6 except plan)
: 110.52
Hz
·
Frequency (mode 7 except plan)
: 169.08
Hz
·
Frequency (Mode 8 in the plan)
: 193.93
Hz
·
Frequency (mode 9 & 10 in the plan): 206.64
Hz
2.3
Uncertainties on the solution
< 2% for a mesh identical to that of [§2.1], i.e. with few elements.
2.4 References
bibliographical
[1]
NAFEMS: Standard The NAFEMS Benchmarks, TNSB, rev. 3, October 5, 1990.
mode 4 except plan
5&6 mode except plan
mode 7 except plan
mode 8 in the plan
9&10 mode in the plan
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
4/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
- The plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling DST (TRIA3)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
3.2
Characteristics of the mesh
A number of nodes: 122
A number of meshs and types: 200 TRIA3
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING: `DST
AFFE_CARA_ELEM
HULL
THICK
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
4
Results of modeling A
4.1 Values
tested
Identification Moments
Reference Aster %
difference
Frequency
(mode 4 except plan)
44.762
44.989
0.507
Frequency
(modes 5 & 6 except plan)
110.52
107.608
107.880
2.634
2.388
Frequency
(mode 7 except plan)
169.08 165.454 2.144
Frequency
(Mode 8 in the plan)
193.93
196.089
1.114
Frequency
(mode 9 & 10 in the plan)
206.64
211.658
212.000
2.428
2.594
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
5/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
4.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending enters modes 8 and 9 of reference: these modes are them
modes 6 and 7 of Code_Aster.
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 44,98
2 107.61
3 107.88
4 165.45
5 196.09
6 202.80
7 203.54
8 211.66
9 212.00
10 222.53
11 254.74
12 255.62
13 264.73
14 289.85
4.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 4.62 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
6/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
- The plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling DST (QUAD4)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
5.2
Characteristics of the mesh
A number of nodes: 122
A number of meshs and types: 100 QUAD4
5.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING: `DST
AFFE_CARA_ELEM
HULL
THICK
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
6
Results of modeling B
6.1 Values
tested
Identification Moments
Reference
Aster %
difference
Frequency
(mode 4 except plan)
44.762
44.64
0.273
Frequency
(modes 5 & 6 except plan)
110.52
108.04
108.26
2.247
2.041
Frequency
(mode 7 except plan)
169.08
162.86
3.681
Frequency
(Mode 8 in the plan)
193.93
195.70
0.912
Frequency
(mode 9 & 10 in the plan)
206.64
208.89
208.89
1.088
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
7/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
6.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending enters modes 8 and 9 of reference: these modes are them
modes 6 and 7 of Code_Aster.
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 44.64
2 108.04
3 108.26
4 162.86
5 195.70
6 203.97
7 206.08
8 208.89
9 208.89
10 220.92
11 248.12
12 250.10
13 252.49
14 289.79
6.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 4.81 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
8/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
- The plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling DKT (TRIA6)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
7.2
Characteristics of the mesh
A number of nodes: 122
A number of meshs and types: 200 TRIA3
7.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING: “DKT”
AFFE_CARA_ELEM
HULL
THICK
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
8
Results of modeling C
8.1 Values
tested
Identification Moments
Reference
Aster %
difference
Frequency
(mode 4 except plan)
44.762
47.358
5.799
Frequency
(modes 5 & 6 except plan)
110.52
118.029
118.059
6.795
6.822
Frequency
(mode 7 except plan)
169.08
187.504
10.897
Frequency
(Mode 8 in the plan)
193.93
196.089
1.114
Frequency
(mode 9 & 10 in the plan)
206.64
211.658
212.000
2.428
2.594
- To validate modeling cf page4
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
9/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
8.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending after mode 11 of reference (mode 8 of Code_Aster), of
the same form as those appeared in DST modeling enters modes 8 and 9 of reference
(modes 6 and 7 of Code_Aster).
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 47.358
2 118.03
3 118.06
4 187.50
5 196.09
6 211.66
7 212.00
8 222.53
9 235.41
10 235.56
11 264.73
12 289.85
13 302.84
14 303.15
8.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 3.97 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
10/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
9 Modeling
D
9.1
Characteristics of modeling
- The plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling DKT (QUAD4)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
9.2
Characteristics of the mesh
A number of nodes: 122
A number of meshs and types: 100 QUAD4
9.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING: “DKT”
AFFE_CARA_ELEM
HULL
THICK
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
10 Results of modeling D
10.1 Values
tested
Identification Moments
Reference
Aster %
difference
Frequency
(mode 4 except plan)
44.762
47.182
5.408
Frequency
(modes 5 & 6 except plan)
110.52
117.463
6.283
Frequency
(mode 7 except plan)
169.08
184.746
9.266
Frequency
(Mode 8 in the plan)
193.93
195.699
0.912
Frequency
(mode 9 & 10 in the plan)
206.64
208.887
1.088
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
11/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
10.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending after mode 11 of reference (mode 8 of Code_Aster), of
the same form as those appeared in DST modeling enters modes 8 and 9 of reference
(modes 6 and 7 of Code_Aster).
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 47.183
2 117.46
3 117.46
4 184.75
5 195.70
6 208.89
7 208.89
8 220.92
9 234.74
10 234.74
11 252.49
12 289.79
13 297.27
14 297.27
10.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 4.02 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
12/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
11 Modeling
E
11.1 Characteristics of modeling
- The plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling COQUE_3D (TRIA6)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
11.2 Characteristics of the mesh
A number of nodes: 122
A number of meshs and types: 200 TRIA6
11.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING:
“hull-3D”
AFFE_CARA_ELEM
HULL
THICK
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
12 Results of modeling E
12.1 Values
tested
Identification Moments
Reference
Aster %
difference
Frequency
(mode 4 except plan)
44.762
43.867
2.00
Frequency
(modes 5 & 6 except plan)
110.52
106.058
106.066
4.037
4.029
Frequency
(mode 7 except plan)
169.08
160.010
5.305
Frequency
(Mode 8 in the plan)
193.93
193.600
0.170
Frequency
(mode 9 & 10 in the plan)
206.64
206.209
206.211
0.208
0.207
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
13/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
12.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending enters modes 8 and 9 of reference: they are modes 6 and
7 of Code_Aster.
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 43,867
2 106.06
3 106.07
4 160.11
5 186,72
6 193.60
7 199.76
8 200.23
9 206.21
10 206.21
11 219.28
12 245.91
13 245.94
14 249.27
12.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 10.97 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
14/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
13 Modeling
F
13.1 Characteristics of modeling
- The plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling COQUE_3D (QUAD8)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
13.2 Characteristics of the mesh
A number of nodes: 122
A number of meshs and types: 100 QUAD8
13.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING:
“COQUE_3D”
AFFE_CARA_ELEM
HULL
THICK
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
14 Results of modeling F
14.1 Values
tested
Identification Moments
Reference
Aster %
difference
Frequency
(mode 4 except plan)
44.762
43.870
1.993
Frequency
(modes 5 & 6 except plan)
110.52
106.041
4.052
Frequency
(mode 7 except plan)
169.08
160.055
5.337
Frequency
(Mode 8 in the plan)
193.93
193.588
0.176
Frequency
(mode 9 & 10 in the plan)
206.64
206.192
0.216
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
15/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
14.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending enters modes 8 and 9 of reference: they are modes 6 and
7 of Code_Aster.
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 43.87
2 106.04
3 106.04
4 160.06
5 193.59
6 199.64
7 200.13
8 206.19
9 206.19
10 219.26
11 245.68
12 245.68
13 249.20
14 287.99
14.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 9.99 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
16/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
15 Modeling
G
15.1 Characteristics of modeling
- The average plan of the plate is located in the plan Z= 2.3
- Not O: (0. ;0. ;2.3)
Modeling 3D (HEXA20)
X
Y
With
B
D
C
15°5
O
Boundary conditions:
- Dimensioned AB, BC, CD, DA: w=0
X
Z
O
15.2 Characteristics of the mesh
A number of nodes: 1266
A number of meshs and types: 200 HEXA20
15.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING: “3D”
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHOD:
“SORENSEN”
OPTION: “TAPE”
16 Results of modeling G
16.1 Values
tested
Identification Moments
Reference
Aster %
difference
Frequency
(mode 4 except plan)
44.762
43.862
2.009
Frequency
(modes 5 & 6 except plan)
110.52
105.953
4.132
Frequency
(mode 7 except plan)
169.08
159.749
5.518
Frequency
(Mode 8 in the plan)
193.93
193.590
0.175
Frequency
(mode 9 & 10 in the plan)
206.64
199.410
199.903
3.498
3.260
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
17/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
16.2 Remarks
·
In Aster, the calculated modes are those of rigid body: the fourth mode of reference is it
first mode calculated by Code_Aster.
·
Appearance of two modes of bending enters modes 8 and 9 of reference: they are modes 6 and
7 of Code_Aster.
In the table below we deferred the first 14 found Eigen frequencies.
N° mode
Frequency (Hz)
1 43.86
2 105.95
3 105.95
4 159.75
5 193.59
6 199.41
7 199.90
8 206.16
9 206.16
10 219.27
11 245.07
12 245.07
13 249.13
14 287.75
16.3 Parameters
of execution
Version:
NEW 5.04.17
Machine:
SGI-Origin2000 R12000
Overall dimension memory: 16 megabytes
Time CPU To use: 24.77 seconds
Code_Aster
®
Version
5.0
Titrate:
SDLS502 - Square plate “solid” simply supported
Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER
Key
:
V2.03.502-A
Page:
18/18
Manual of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A
17 Summary of the results
Taking into account the nature of the numerical solution (voluminal finite elements), the results obtained
are satisfactory for:
·
modeling A and B (DST) the maximum change is less than 4% for the first 5 modes,
·
modeling E and F (COQUE_3D), the maximum change is approximately 5% for the 5 first
modes,
·
modeling G (3D), the maximum change is approximately 5% for the first 5 modes,
·
the modes of reference 5&6 except plan have symmetry different from those
met in modelings E, F and G, but they are equivalent because it is about
modal recombinations.
Modelings C and D (DKT) are less satisfactory with relative variations reaching 10% on
mode 7 except plan, this due to is not taken into account of transverse shearing for this plate
relatively thick.
Moreover one observes the appearance of modes of bending and membrane for all these modelings, y
included/understood voluminal modeling 3D G. When one refines sufficiently the mesh, this
tendency is confirmed and the relative variations regress. Calculation 3D in addition showed that in on this side
of a mesh 6x6 in plan (XY), the modes of bending and membrane were not detected.