Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
1/18

Organization (S): EDF/AMA, DeltaCAD

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
Document: V2.03.502

SDLS502 - Square Plaque “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.

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
2/18

1
Problem of reference

1.1 Geometry

B
C
H
Z, W
L
y, v
L = 10.0 m
H = 1.0m
With
D
X, U


1.2
Properties of material

The properties of material constituting the plate are:

E = 2. 1011
Pa Module of Young
= 0.3
Poisson's ratio
= 8000. Kg/m3 Masses
voluminal

1.3
Boundary conditions and loadings

- C.L. : plate simply supported on its contour

1.4 Conditions
initial

Without object

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A



Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
3/18

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 grid 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




mode 4 except plan
5&6 mode except plan


mode 7 except plan

mode 8 in the plan

9&10 mode in the plan



2.3
Uncertainties on the solution

< 2% for a grid 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.

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
4/18

3 Modeling
With

3.1
Characteristics of modeling

Y
C
Modeling DST (TRIA3)
- The plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
- 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
D
to change the Eigen frequencies
obtained.
With


3.2
Characteristics of the grid

A number of nodes: 122
A number of meshs and types: 200 TRIA3

3.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION: `DST
AFFE_CARA_ELEM
COQUE
EPAIS
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

4
Results of modeling A

4.1 Values
tested

Identification Moments
Reference Aster %
difference
Frequency
44.762
44.989
0.507
(mode 4 except plan)
Frequency
110.52
107.608
­ 2.634
(modes 5 & 6 except plan)
107.880
­ 2.388
Frequency

169.08 165.454 ­ 2.144
(mode 7 except plan)
Frequency
193.93
196.089
1.114
(Mode 8 in the plan)
Frequency
206.64
211.658
2.428
(mode 9 & 10 in the plan)
212.000
2.594

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
5/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 4.62 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
6/18

5 Modeling
B

5.1
Characteristics of modeling

Y
C
Modeling DST (QUAD4)
- The plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
D
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
With


5.2
Characteristics of the grid

A number of nodes: 122
A number of meshs and types: 100 QUAD4

5.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION: `DST
AFFE_CARA_ELEM
COQUE
EPAIS
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

6
Results of modeling B

6.1 Values
tested

Identification Moments
Reference
Aster %
difference
Frequency
44.762
44.64
­ 0.273
(mode 4 except plan)
Frequency
110.52
108.04
­ 2.247
(modes 5 & 6 except plan)
108.26
­ 2.041
Frequency
169.08
162.86
­ 3.681
(mode 7 except plan)
Frequency
193.93
195.70
0.912
(Mode 8 in the plan)
Frequency
206.64
208.89
1.088
(mode 9 & 10 in the plan)
208.89
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
7/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 4.81 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
8/18

7 Modeling
C

7.1
Characteristics of modeling

Y
C
Modeling DKT (TRIA6)
- The plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
- To validate modeling cf page4
D
With


7.2
Characteristics of the grid

A number of nodes: 122
A number of meshs and types: 200 TRIA3

7.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION: “DKT”
AFFE_CARA_ELEM
COQUE
EPAIS
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

8
Results of modeling C

8.1 Values
tested

Identification Moments
Reference
Aster %
difference
Frequency
44.762
47.358
5.799
(mode 4 except plan)
Frequency
110.52
118.029
6.795
(modes 5 & 6 except plan)
118.059
6.822
Frequency
169.08
187.504
10.897
(mode 7 except plan)
Frequency
193.93
196.089
1.114
(Mode 8 in the plan)
Frequency
206.64
211.658
2.428
(mode 9 & 10 in the plan)
212.000
2.594
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
9/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 3.97 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
10/18

9 Modeling
D

9.1
Characteristics of modeling

Y
C
Modeling DKT (QUAD4)
- The plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
D
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
With



9.2
Characteristics of the grid

A number of nodes: 122
A number of meshs and types: 100 QUAD4

9.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION: “DKT”
AFFE_CARA_ELEM
COQUE
EPAIS
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

10 Results of modeling D

10.1 Values
tested

Identification Moments
Reference
Aster %
difference
Frequency
44.762
47.182
5.408
(mode 4 except plan)
Frequency
110.52
117.463
6.283
(modes 5 & 6 except plan)
Frequency
169.08
184.746
9.266
(mode 7 except plan)
Frequency
193.93
195.699
0.912
(Mode 8 in the plan)
Frequency
206.64
208.887
1.088
(mode 9 & 10 in the plan)
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
11/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 4.02 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
12/18

11 Modeling
E

11.1 Characteristics of modeling

Y
C
Modeling COQUE_3D (TRIA6)
- The plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
- To validate modeling in
a reference mark different from the reference mark
total, the plate is turned of
D
15,5 degrees. This does not have
to change the Eigen frequencies
obtained.
With


11.2 Characteristics of the grid

A number of nodes: 122
A number of meshs and types: 200 TRIA6

11.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION:
“hull-3D”
AFFE_CARA_ELEM
COQUE
EPAIS
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

12 Results of modeling E

12.1 Values
tested

Identification Moments
Reference
Aster %
difference
Frequency
44.762
43.867
2.00
(mode 4 except plan)
Frequency
110.52
106.058
­ 4.037
(modes 5 & 6 except plan)
106.066
­ 4.029
Frequency
169.08
160.010
­ 5.305
(mode 7 except plan)
Frequency
193.93
193.600
­ 0.170
(Mode 8 in the plan)
Frequency
206.64
206.209
0.208
(mode 9 & 10 in the plan)
206.211
0.207
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
13/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 10.97 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
14/18

13 Modeling
F

13.1 Characteristics of modeling

Y
C
Modeling COQUE_3D (QUAD8)
- The plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
- 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
D
to change the Eigen frequencies
obtained.
With


13.2 Characteristics of the grid

A number of nodes: 122
A number of meshs and types: 100 QUAD8

13.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION:
“COQUE_3D”
AFFE_CARA_ELEM
COQUE
EPAIS
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

14 Results of modeling F
14.1 Values
tested

Identification Moments
Reference
Aster %
difference
Frequency
44.762
43.870
­ 1.993
(mode 4 except plan)
Frequency
110.52
106.041
­ 4.052
(modes 5 & 6 except plan)
Frequency
169.08
160.055
­ 5.337
(mode 7 except plan)
Frequency
193.93
193.588
­ 0.176
(Mode 8 in the plan)
Frequency
206.64
206.192
­ 0.216
(mode 9 & 10 in the plan)
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
15/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 9.99 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
16/18

15 Modeling
G

15.1 Characteristics of modeling

Y
C
Modeling 3D (HEXA20)
- The average plan of the plate is located in the plan Z= 2.3
B
- Not O: (0. ;0. ;2.3)
Boundary conditions:
15°5
O
X
- Dimensioned AB, BC, CD, DA: w=0
Z
D
X
With
O


15.2 Characteristics of the grid

A number of nodes: 1266
A number of meshs and types: 200 HEXA20

15.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION: “3D”
CALC_MATR_ELEM
OPTION: “RIGI_MECA”
OPTION: “MASS_MECA”
MODE_ITER_SIMULT
CALC_FREQ
METHODE:
“SORENSEN”
OPTION: “BANDE”

16 Results of modeling G

16.1 Values
tested

Identification Moments
Reference
Aster %
difference
Frequency
44.762
43.862
­ 2.009
(mode 4 except plan)
Frequency
110.52
105.953
­ 4.132
(modes 5 & 6 except plan)
Frequency
169.08
159.749
­ 5.518
(mode 7 except plan)
Frequency
193.93
193.590
­ 0.175
(Mode 8 in the plan)
Frequency
206.64
199.410
­ 3.498
(mode 9 & 10 in the plan)
199.903
­ 3.260
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
17/18

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 inflection 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
Obstruction memory: 16 megabytes
Time CPU To use: 24.77 seconds

Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SDLS502 - Square Plaque “solid” simply supported

Date:
04/09/02
Author (S):
P. MASSIN, F. LEBOUVIER Key
:
V2.03.502-A Page:
18/18

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 inflection and membrane for all these modelings, y
included/understood voluminal modeling 3D G. Lorsque one refines sufficiently the grids, this
tendency is confirmed and the relative variations regress. Calculation 3D in addition showed that in on this side
of a grid 6x6 in plan (XY), the modes of inflection and membrane were not detected.
Handbook of Validation
V2.03 booklet: Linear dynamics of the hulls and plates
HT-66/02/001/A

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