Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
1/22

Organization (S): EDF-R & D/AMA, SAMTECH

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
Document: V3.03.101

SSLS101 - Circular Plaque posed subjected
with a uniform pressure

Summary:

One treats the case of a circular plate posed on the edge in linear elasticity under 3 loadings (weight
clean, pressure, effort distributed constant) which gives the same deformation.

The first two modelings make it possible to evaluate the influence of the grid.

The test gathers 9 modelings (model Coils-Kirchhoff, Mindlin-Reissner and COQUE_3D and SHB8).

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
2/22

1
Problem of reference

1.1 Geometry

y
C
B
E
F
O
D
With
X
1/4 of plate
Radius
R = 1 m
Thickness
T = 0.1 m


Co-ordinates of the points:


O WITH B C D E F
X 0.
1.
2/2
0. 0.5
0. 0.4
y 0.
0.
2/2
1. 0. 0.5
0.4
Z
0. 0. 0. 0. 0. 0. 0.

1.2
Material properties

E = 1. Pa
= 0.3
= 1. kg/m3

1.3
Boundary conditions and loadings

Simple support on the edge of the plate:
in all the points P such as COp = R: U = v = W = 0

FORCE_COQUE
Uniform pressure
P = 1 NR/M2
FORCE_COQUE
Charge distributed normal
F3 = ­ 1 NR/m2
PESANTEUR
G = 10 m/s2 according to Z from where
FZ = WP = ­ 1 NR/m2

These three loadings lead to the same solution.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
3/22

2
Reference solution

2.1
Method of calculation used for the reference solution

Two reference solutions are usable, for the calculation of the deformation, according to the theory of plate
used:

· the theory of Coils-Kirchhoff, usually used for the plates known as “thin”, that one
will retain for modelings A, B and E,
· the theory of Reissner, including the effects of shearing for the plates known as “thick”,
that one will retain for modelings F, G and H.

In any distant point of R of the center of the plate (R R), one has for the calculation of the arrow:
(
W R)
4
PR
2
R


2
R
(23+)
3
=

And
1

1+
-
- with D =

2

64
2
D
R
R
1+





12 (1 - 2)
16 T 2 1
and = 0 (Love -
or

Kirchhoff)
=
(Reissner).
5 R 1

For the calculation of the moments the two theories lead to the same expressions:
P R2
R 2
P R2

1+ 3 R 2
Mrr (R) =
(3+)

1
M (R)

=
(3+) 1

16


-

R -
16

3 +
R





In the center of the plate:
(
4
4
PR
PR
W 0)
5 +
=
(
5

Coil - Kirchhoff)
or

(
W 0)
+
=
+ (


Reissner)
64D 1+
64D 1+


M rr (
2
PR
0) =M (0) =
(3+)
16
Note:

Code_Aster calculates the moments with the nodes of each finite element in the reference mark of
reference defined by the external normal and the reference axes defined on the hull (see
AFFE_CARA_ELEM in the documentation of use).
The value of moment Mxx (or M yy), extracted field “EFGE_ELNO_DEPL”, in a node
belonging to several finite elements can be regarded as being the average of
computed values on the elements which have this joint node. This average can be
obtained by procedure POST_RELEVE [U4.74.03].

For each node, one a: (M + M) = (M + M) = Sm
rr
xx
yy

for the point O
M
= M
= M
= M
xx
yy
rr

for the points A and D
M
= M
and
M
= M
xx
rr
yy

for the points C and E
M
= M
and
M

= M
xx
yy
rr
for the points B and F
M
= M
xx
yy
= (M + M
rr
)/2

2.2
Results of reference

Arrow and moments at the points: O, A, B C, D E, F.

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
TIMOSHENKO and WOINOWSKY-KRIEGER, Plaques and hulls, Édition Béranger - (1961).
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
4/22

3 Modeling
With

3.1
Characteristics of modeling

Element of hull DKT (modeling of a quarter of plate)

C
B
E
F
O
With
D


3.1.1 Conditions
limits

in all the nodes of arc ABC
: DX: 0., DY: 0., DZ: 0.
in all the nodes of segment] OA [
: DY: 0., DRX:0., DRZ:0.
in all the nodes of segment] OC [: DX: 0., DRY:0., DRZ:0.
with the node O
: DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.

Point 0
meshs: M30 M33
Not A
meshs: M76
Not B
meshs: M39 M40 M51
Not C
meshs: M1
Not D
meshs: M55 M56 M65
Not E
meshs: M8 M17 M18
Not F
meshs: M34 M35 M37 M41 M46 M47 M48

3.2
Characteristics of the grid

A number of nodes: 50
A number of meshs and types: 76 TRIA3

3.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL
EPAIS


ANGL_REP
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES
AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “DKT” ALL

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION
“EXTRACTION”

VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
5/22

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
0 (
W R) ­ 695.6256
­ 687.95
­ 1.10
D (
W R) ­ 489.727
­ 484.76
­ 1.01
E (
W R) ­ 489.727
­ 484.69
­ 1.03
F (
W R) ­ 435.8974
­ 431.33
­ 1.05

Reference

Not
M
Sm/
rr
M
2
O ­ 0.20625
­ 0.20625
­ 0.20625
To 0.
­ 0.0875
­ 0.04375
B 0.
­ 0.0875
­ 0.04375
C 0.
­ 0.0875
­ 0.04375
D ­ 0.15469
­ 0.17656
­ 0.1656
E ­ 0.15469
­ 0.17656
­ 0.1656
F ­ 0.14025
­ 0.16825
­ 0.15425

Aster

Not
M
Sm/
xx
M yy
2
O ­ 0.20377
­ 0.20382
­ 0.20379
To 0.00992
­ 0.08265
­ 0.04628
B ­ 0.03827
­ 0.03771
­ 0.03799
C ­ 0.08263
0.00990
­ 0.04626
D ­ 0.15516
­ 0.17680
­ 0.16597
E ­ 0.17677
­ 0.15509
­ 0.16593
F ­ 0.15307
­ 0.15342
­ 0.15324

% difference (% difference on the absolute values)

Not
Mxx
M yy
Sm/2
Relative tolerance
O
­ 1.20 ­ 1.18 ­ 1.19
1.5
With
- ­ 5.54
+5.79
-/6.
B
­ 12.5 ­ 13.8 ­ 13.1
13./14.
C
­ 5.56 - +5.73
6./-
D
0.30 0.14
+0.2
0.5
E
0.12 0.26
+0.19
0.3
F
+9.15 ­ 8.81 ­ 0.66
10.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
6/22

5 Modeling
B

5.1
Characteristics of modeling

Element of hull DKT (modeling of a quarter of plate)

C
B
E
F
O
With
D
-


5.1.1 Conditions
limits

in all the nodes of arc ABC
: DX: 0., DY: 0., DZ: 0.
in all the nodes of segment] OA [
: DY: 0., DRX:0., DRZ:0.
in all the nodes of segment] OC [
: DX: 0., DRY:0., DRZ:0.
with the node O
: DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.

Not O
meshs: M1 m2
Not A
meshs: M248 M255
Not B
meshs: M292 M293 M296
Not C
meshs: M74 M75
Not D
meshs: M76 M108 M109
Not E
meshs: M34 M40 M41
Not F
meshs: M122 M123 M124 M148 M152 M153

5.2
Characteristics of the grid

A number of nodes: 170
A number of meshs and types: 296 TRIA3

5.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES
F3
PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “DKT” ALL

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION
“EXTRACTION”

VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
7/22

6
Results of modeling B

6.1 Values
tested

Identification Reference Aster %
difference
O (
W R) ­ 695.6256
­ 694.97
­ 0.09
D (
W R) ­ 489.727
­ 489.24
­ 0.1
E (
W R) ­ 489.727
­ 489.31
­ 0.09
F (
W R) ­ 435.8974
­ 435.48
­ 0.09

Reference

Not
Mrr
M
Sm/2
O ­ 0.20625
­ 0.20625
­ 0.20625
To 0.
­ 0.0875
­ 0.04375
B 0.
­ 0.0875
­ 0.04375
C 0.
­ 0.0875
­ 0.04375
D ­ 0.15469
­ 0.17656
­ 0.1656
E ­ 0.15469
­ 0.17656
­ 0.1656
F ­ 0.14025
­ 0.16825
­ 0.15425

Aster

Not
Mxx
M yy
Sm/2
O ­ 0.20631
­ 0.20609
­ 0.20620
To 0.00238
­ 0.08459
­ 0.04348
B ­ 0.4132
­ 0.04134
­ 0.04133
C ­ 0.08460
0.00238
­ 0.04349
D ­ 0.15516
­ 0.17727
­ 0.16621
E ­ 0.17739
­ 0.15523
­ 0.16631
F ­ 0.15461
­ 0.15468
­ 0.15464

% difference (% difference on the absolute values)

Not
Mxx
M yy
Sm/2
Relative tolerance
O
0.03 ­ 0.7
0.02
0.1
With
- ­ 3.32
­ 0.06
-/3.5
B
­ 5.56 ­ 5.51 ­ 5.53
6.
C
­ 3.31 - ­ 0.06
3.5/-
D
+0.30 +0.40 +0.35
0.5
E
+0.47 +0.35 +0.42
0.5
F
+0.23 +0.28 +0.25
0.3

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
8/22

7 Modeling
C

7.1
Characteristics of modeling

Element of hull SHB8 (modeling of a quarter of plate)

C
1.0
B
0.5
E
0.0
O
D
With
0.0
0.5
1.0


7.1.1 Conditions
limits

in all the nodes of arc ABC
: DX: 0., DY: 0., DZ: 0.
in all the nodes of face] OA [
: DY: 0.,
in all the nodes of face] OC [
: DX: 0.,
with the node O
: DX: 0., DY: 0.,

The grid is built starting from the surface grid of modeling E, by thickening, with
assistance of CREA_MAILLAGE/COQU_VOLU. One builds 2 layers of meshs HEXA8.

7.2
Characteristics of the grid

A number of nodes: 338
A number of meshs and types: 147 HEXA8

7.3 Functionalities
tested

Commands




AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_FACE
F2
FORCE_INTERN
F2
PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE SHB8
TOUT

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



CREA_MAILLAGE COQU_VOLU



CALC_CHAM_ELEM OPTION
COOR_ELGA

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
9/22

8
Results of modeling C

8.1 Values
tested

Identification Reference
Aster %
difference
O (
W R) ­ 695.6256
­ 698.6
0.4
D (
W R) ­ 489.727
491.4
0.3
E (
W R) ­ 489.727
­ 491.4
0.3
F (
W R) ­ 435.8974
­ 436.6
0.2

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
10/22

9 Modeling
E

9.1
Characteristics of modeling

Element of hull DKQ (modeling of a quarter of plate)

C
1.0
B
0.5
E
0.0
O
D
With
0.0
0.5
1.0


9.1.1 Conditions
limits

in all the nodes of arc ABC
: DX: 0., DY: 0., DZ: 0.
in all the nodes of segment] OA [
: DY: 0., DRX:0., DRZ:0.
in all the nodes of segment] OC [
: DX: 0., DRY:0., DRZ:0.
with the node O
: DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.

Not O
meshs: M1
Not A
meshs: M147
Not B
meshs: M98 M111
Not C
meshs: M14
Not D
meshs: M85 M99
Not E
meshs: M7 M8
Not F
meshs: M91 M92 M105

9.2
Characteristics of the grid

A number of nodes: 169
A number of meshs and types: 147 QUAD4

9.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES
F3
PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “DKT” ALL

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION
“EXTRACTION”

VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
11/22

10 Results of modeling E

10.1 Values
tested

Identification Reference
Aster %
difference
O (
W R) ­ 695.6256
­ 695.01
­ 0.09
D (
W R) ­ 489.727
­ 489.20
­ 0.11
E (
W R) ­ 489.727
­ 489.20
­ 0.12
F (
W R) ­ 435.8974
­ 435.38
­ 0.09

Reference

Not
Mrr
M
Sm/2

O
­ 0.20625 ­ 0.20625 ­ 0.20625

To 0.
­ 0.0875
­ 0.04375

B 0.
­ 0.0875
­ 0.04375

C 0.
­ 0.0875
­ 0.04375

D
­ 0.15469 ­ 0.17656 ­ 0.1656

E
­ 0.15469 ­ 0.17656 ­ 0.1656

F
­ 0.14025 ­ 0.16825 ­ 0.15425


Aster

Not
Mxx
M yy
Sm/2
O
­ 0.20639 ­ 0.20639 ­ 0.20639

To +0.00036
­ 0.087104
­ 0.04353

B
­ 0.04330 ­ 0.04332 ­ 0.04331

C ­ 0.087133
+0.00034
­ 0.04355

D
­ 0.15506 ­ 0.17790 ­ 0.16648

E
­ 0.17790 ­ 0.15507 ­ 0.16648

F
­ 0.15380 ­ 0.15377 ­ 0.15378


% difference (% difference on the absolute values)

Not
Mxx
M yy
Sm/2
Relative tolerance
O
+0.07 +0.07 +0.07
0.1
With
- ­ 0.45
­ 0.49
-/0.5
B
­ 1.02 +0.98 +1.0
1.1
C
­ 0.42 - ­ 0.46
0.5/-
D
+0.24 +0.76 +0.5
1.
E
+0.76 +0.24 +0.5
1.
F
­ 0.29 ­ 0.31 ­ 0.3
0.5

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
12/22

11 Modeling
F

11.1 Characteristics of modeling

Element of hull DST (modeling of a quarter of plate)

C
B
E
F
O
With
D


11.1.1 Limiting conditions

in all the nodes of arc ABC
: DX: 0., DY: 0., DZ: 0.
in all the nodes of segment] OA [
: DY: 0., DRX:0., DRZ:0.
in all the nodes of segment] OC [
: DX: 0., DRY:0., DRZ:0.
with the node O
: DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.

Not O
meshs: M1 m2
Not A
meshs: M248 M255
Not B
meshs: M3292 M293 M296
Not C
meshs: M74 M75
Not D
meshs: M76 M108 M109
Not E
meshs: M34 M40 M41
Not F
meshs: M122 M123 M124 M148 M152 M153

11.2 Characteristics of the grid

A number of nodes: 170
A number of meshs and types: 296 TRIA3

11.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES
F3
PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “DST” ALL

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION
“EXTRACTION”

VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
13/22

12 Results of modeling F

12.1 Values
tested

Identification Reference
Reissner Aster %
difference
0 (
W R) ­ 703.40
­ 704.25
+0.12
D (
W R) ­ 495.56
­ 495.96
+0,08
E (
W R) ­ 495.56
­ 496.04
+0.09
F (
W R) ­ 441.18
­ 441.50
+0.07

Reference

Not
Mrr
M
Sm/2

O ­ 0.20625
­ 0.20625
­ 0.20625

To 0.
­ 0.0875
­ 0.04375

B 0.
­ 0.0875
­ 0.04375

C 0.
­ 0.0875
­ 0.04375

D ­ 0.15469
­ 0.17656
­ 0.1656

E ­ 0.15469
­ 0.17656
­ 0.1656

F ­ 0.14025
­ 0.16825
­ 0.15425


Aster

Not
Mxx
M yy
Sm/2

O
­ 0.20705 ­ 0.20692 ­ 0.20698

With
­ 0.01143 ­ 0.07992 ­ 0.04567

B
­ 0.03976 ­ 0.03977 ­ 0.03977

C
­ 0.07993 ­ 0.01143 ­ 0.4568

D
­ 0.15597 ­ 0.17665 ­ 0.16631

E
­ 0.17678 ­ 0.15606 ­ 0.16642

F
­ 0.15445 ­ 0.15452 ­ 0.15448


% difference (% difference on the absolute values)

Not
Mxx
M yy
Sm/2
Relative tolerance
O
­ 0.39 ­ 0.32 +0.07
0.4
With
- ­ 8.66
­ 4.40
-/9.
B
­ 9.12 ­ 9.09 ­ 9.10
9.5
C
­ 8.64 - ­ 4.41
9./-
D
+0.83 +0.05 +0.43
0.9
E
+0.13 +0.89 +0.49
0.9
F
+0.13 +0.18 +0.15
0.2

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
14/22

13 Modeling
G

13.1 Characteristics of modeling

Element of hull DSQ (modeling of a quarter of plate)

C
1.0
B
0.5
E
0.0
O
D
With
0.0
0.5
1.0


13.1.1 Limiting conditions

in all the nodes of arc ABC
:
DX: 0., DY: 0., DZ: 0.
in all the nodes of segment] OA [
:
DY: 0., DRX:0., DRZ:0.
in all the nodes of segment] OC [
:
DX: 0., DRY:0., DRZ:0.
with the node O
:
DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.

Not O
meshs: M1
Not A
meshs: M147
Not B
meshs: M98 M111
Not C
meshs: M14
Not D
meshs: M85 M99
Not E
meshs: M7 M8
Not F
meshs: M91 M92 M105

13.2 Characteristics of the grid

A number of nodes: 169
A number of meshs and types: 147 QUAD4

13.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES
F3
PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “DST” ALL

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION
“EXTRACTION”

VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
15/22

14 Results of modeling G

14.1 Values
tested

Identification Reference
Reissner Aster %
difference
O (
W R) ­ 703.40
­ 702.61
­ 0.11
D (
W R) ­ 495.56
­ 494.90
­ 0.13
E (
W R) ­ 495.56
­ 494.90
­ 0.13
F (
W R) ­ 441.18
­ 440.51
­ 0.15

Reference

Not
Mrr
M
Sm/2

O ­ 0.20625
­ 0.20625
­ 0.20625

To 0.
­ 0.0875
­ 0.04375

B 0.
­ 0.0875
­ 0.04375

C 0.
­ 0.0875
­ 0.04375

D ­ 0.15469
­ 0.17656
­ 0.1656

E ­ 0.15469
­ 0.17656
­ 0.1656

F ­ 0.14025
­ 0.16825
­ 0.15425


Aster

Not
Mxx
M yy
Sm/2

O ­ 0.20469
­ 0.20469
­ 0.20469

To +0.00654
­ 0.08547
­ 0.39465

B ­ 0.04063
­ 0.04063
­ 0.04063

C ­ 0.08553
+0.00629
­ 0.39620

D ­ 0.15560
­ 0.17723
­ 0.16641

E ­ 0.17723
­ 0.15563
­ 0.16643

F ­ 0.18352
­ 0.18349
­ 0.18350


% difference (% difference on the absolute values)

Not
Mxx
M yy
Sm/2
Relative tolerance
O
­ 0.76 ­ 0.76 ­ 0.76
1.
With
- ­ 2.32
­ 9.80
-/2.5
B
­ 7.11 ­ 7.12 ­ 7.12
7.5
C
­ 2.24 - ­ 9.44
2.5/-
D
+0.59 +0.37 +0.49
0.6
E
+0.38 +0.60 +0.50
0.7
F
+19.0 +18.9 +19.
19.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
16/22

15 Modeling
H

15.1 Characteristics of modeling

Element of hull Q4 (modeling of a quarter of plate)

C
1.0
B
0.5
E
0.0
O
D
With
0.0
0.5
1.0


15.1.1 Limiting conditions

in all the nodes of arc ABC
:
DX: 0., DY: 0., DZ: 0.
in all the nodes of segment] OA [
:
DY: 0., DRX:0., DRZ:0.
in all the nodes of segment] OC [
:
DX: 0., DRY:0., DRZ:0.
with the node O
:
DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.

Not O
meshs: M1
Not A
meshs: M147
Not B
meshs: M98 M111
Not C
meshs: M14
Not D
meshs: M85 M99
Not E
meshs: M7 M8
Not F
meshs: M91 M92 M105

15.2 Characteristics of the grid

A number of nodes: 169
A number of meshs and types: 147 QUAD4

15.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES
F3
PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “DKT” ALL

CALC_CHAM_ELEM “EFGE_ELNO_DEPL”



“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION
“EXTRACTION”

VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
17/22

16 Results of modeling H

16.1 Values
tested

Identification Reference
Reissner Aster %
difference
O (
W R)
­ 703.40 ­ 702.18 ­ 0.15
D (
W R)
­ 495.56 ­ 494.53 ­ 0.20
E (
W R)
­ 495.56 ­ 494.53 ­ 0.20
F (
W R)
­ 441.18 ­ 440.23 ­ 0.21

Reference

Not
Mrr
M
Sm/2

O ­ 0.20625
­ 0.20625
­ 0.20625

To 0.
­ 0.0875
­ 0.04375

B 0.
­ 0.0875
­ 0.04375

C 0.
­ 0.0875
­ 0.04375

D ­ 0.15469
­ 0.17656
­ 0.1656

E ­ 0.15469
­ 0.17656
­ 0.1656

F ­ 0.14025
­ 0.16825
­ 0.15425


Aster

Not
Mxx
M yy
Sm/2

O ­ 0.20595
­ 0.20595
­ 0.20595

With ­ 0.01204
­ 0.09107
­ 0.05155

B ­ 0.05233
­ 0.05236
­ 0.05234

C ­ 0.09107
­ 0.01207
­ 0.05157

D ­ 0.15438
­ 0.17699
­ 0.16568

E ­ 0.17699
­ 0.15437
­ 0.16568

F ­ 0.15374
­ 0.15374
­ 0.15374


% difference (% difference on the absolute values)

Not
Mxx
M yy
Sm/2
Relative tolerance
O
­ 0.14 ­ 0.14 ­ 0.14
0.2
With
- +4.08
+17.8
-/4.5
B
+19.6 +19.7 +19.7
20.
C
+4.08 - +17.9
4.5/-
D
­ 0.2 +0.24 +0.05
0.25
E
+0.24 ­ 0.2 +0.05
0.25
F
­ 0.33 ­ 0.33 ­ 0.33
0.35

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
18/22

17 Modeling
I

17.1 Characteristics of modeling
Modeling: Element of COQUE_3D MEC3QU9H

C
B
E
O
D
With

17.1.1 Limiting conditions

in all the nodes of arc DX:0., DY: 0., DZ: 0.
ABC
DRX:0., DRY:0., DRZ:0.
segment] OA]
DY:0., DRX:0., DRZ:0.
segment] OC]
DX:0., DRY:0., DRZ:0.
with the node O
DX:0., DY:0., DRX:0., DRY:0., DRZ:0.

Names of the nodes:

Point 0
meshs: M1
Not A
meshs: M21
Not B
meshs: M25
Not C
meshs: M5
Not D
meshs: M11
Not E
meshs: M3

17.2 Characteristics of the grid

A number of nodes: 96
A number of meshs and types: 25 QUAD9

17.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES


F3


PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “COQUE_3D”
TOUT

CALC_CHAM_ELEM “EFFO_ELNO_DEPL”



“SIGM_ELNO_DEPL”



DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION “EXTRACTION”

VALE_TEST


EPSI_TEST



Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
19/22

18 Results of modeling I

18.1 Values
tested

Not Reference Aster %
difference
REISSNER
O
­ 703.40 ­ 703.41 1.42 10­3
With
0. eps -
B
0. eps -
C W
(R)
0. eps -
D
­ 495.56 ­ 496.57 2. 10­3
E
­ 495.56 ­ 496.57 2. 10­3

Not Reference
Aster

Mrr
M
Sm/2
M xx
M yy
Sm/2
O ­ 0.20625
­ 0.20625
­ 0.20625
­ 0.20842
­ 0.20842
­ 0.20842
To 0.
­ 0.0875
­ 0.04375
­ 0.08846
­ 0.00159
­ 0.04502
C 0.
­ 0.0875
­ 0.04375
­ 0.00067
­ 0.08938
­ 0.04502
D ­ 0.15469
­ 0.17656
­ 0.1656
­ 0.17743
­ 0.15472
­ 0.16607
E ­ 0.15469
­ 0.17656
­ 0.1656
­ 0.15459
­ 0.17757
­ 0.16608

Not
% difference
Relative tolerance

M xx
M yy
Sm/2
O 1.05
1.05
1.05 3
At 1.09
-
2.9 3
C -
2.1
2.9 5
D 0.49
0.02
0.28 1
E ­ 0.06
0.57
0.28 1

· with eps 10­14 and % difference on the absolute values

Note:

The test of the values is carried out automatically using the functionalities offered by
procedure POST_RELEVE:

· extraction on the nodes corresponding to the points observed of the average values of
components Mxx and Myy; these values are extracted from field “EFGE_ELNO_DEPL”, and
average is calculated for all the liquid assets on the meshs which contain it
node observed,
· calculation of the variation compared to the value of reference provided by observing the rules of
correspondence between Mxx, Myy and Mrr, M given page 3.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
20/22

19 Modeling
J

19.1 Characteristics of modeling

Modeling: Element of COQUE_3D MEC3TR7H

C
B
E
O
D
With

19.1.1 Limiting conditions

in all the nodes of arc DX:0., DY: 0., DZ: 0.
ABC
DRX:0., DRY:0., DRZ:0.
segment] OA]
DY:0., DRX:0., DRZ:0.
segment] OC]
DX:0., DRY:0., DRZ:0.
with the node O
DX:0., DY:0., DRX:0., DRY:0., DRZ:0.

Names of the nodes:

Point 0
meshs: M1 and m2
Not A
meshs: M41
Not B
meshs: M49 and M50
Not C
meshs: M10
Not D
meshs: M21
Not E
meshs: M6

19.2 Characteristics of the grid

A number of nodes: 121
A number of meshs and types: 50 TRIA7

19.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL



AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_COQUE
PRES


F3


PESANTEUR



AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “COQUE_3D”
TOUT

CALC_CHAM_ELEM “EFFO_ELNO_DEPL”



“SIGM_ELNO_DEPL”



DEFI_MATERIAU ELAS



POST_RELEVE ACTION
OPERATION “EXTRACTION”

VALE_TEST


EPSI_TEST


Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
21/22

20 Results of modeling J

20.1 Values
tested

Not Reference Aster %
difference
REISSNER
O
­ 703.40 ­ 703.19 ­ 0.03
With
0. eps -
B
0. eps -
C W
(R)
0. eps -
D
­ 495.56 ­ 495.22 ­ 0.07
E
­ 495.56 ­ 495.22 ­ 0.07

Not Reference
Aster

Mrr
M
Sm/2
M xx
M yy
Sm/2
O ­ 0.20625
­ 0.20625
­ 0.20625
­ 0.20860
­ 0.20860
­ 0.20860
To 0.
­ 0.0875
­ 0.04375
­ 0.08619
­ 0.00154
­ 0.04386
C 0.
­ 0.0875
­ 0.04375
­ 0.00134
­ 0.08639
­ 0.04386
D ­ 0.15469
­ 0.17656
­ 0.1656
­ 0.17617
­ 0.15409
­ 0.16513
E ­ 0.15469
­ 0.17656
­ 0.1656
­ 0.15407
­ 0.17619
­ 0.16513

Not
% difference
Relative tolerance

M xx
M yy
Sm/2
O 1.14
1.14
1.14 2
With ­ 1.49
-
0.25 2
C -
­ 1.27
0.25 2
D ­ 0.22
­ 0.39
­ 0.28 1.
E ­ 0.40
­ 0.21
­ 0.28 1.

· with eps 10­14 and % difference on the absolute values

Note:

The test of the values is carried out automatically using the functionalities offered by
procedure POST_RELEVE:

· extraction on the nodes corresponding to the points observed of the average values of
components Mxx and Myy; these values are extracted from field “EFGE_ELNO_DEPL”, and
average is calculated for all the liquid assets on the meshs which contain it
node observed,
· calculation of the variation compared to the value of reference provided by observing the rules of
correspondence between Mxx, Myy and Mrr, M given page 3.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
Circular SSLS101 Plaque posed subjected to a uniform pressure
Date:
05/01/04
Author (S):
J.M. PROIX, P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.101-D Page:
22/22

21 Summary of the results

% of the differences compared to the reference solutions

DKT
DKQ
DST
DSQ
Q4G
WITH B
E
F
G
H
Coil-Kirchhoff
Coil-Kirchhoff
Coil-Kirchhoff
Reissner
Reissner
Reissner
50
nodes
170 nodes
169 nodes
170 nodes
169 nodes
169 nodes
76 TRIA3
296 TRIA3
147 QUAD4
296 TRIA3
147 QUAD4 147 QUAD4
O (
W R)
­ 1.10 ­ 0.09 ­ 0.09
+0.12
­ 0.11
­ 0.15
D (
W R)
­ 1.01 ­ 0.1 ­ 0.11
+0.08
­ 0.13
­ 0.20
E (
W R)
­ 1.03 ­ 0.09 ­ 0.12
+0.09
­ 0.13
­ 0.20
F (
W R)
­ 1.05 ­ 0.09 ­ 0.09
+0.07
­ 0.15
­ 0.21

MEC3QU9H MEC3TR7H
SHB8



I J C



96
nodes
121 nodes
338 nodes



25 QUAD9
50 TRIA7
147 HEXA8
O (
W R) 1.42
10­3 ­ 0.03 0.4
D (
W R) 2.
10­3 ­ 0.07 0.3
E (
W R) 2.
10­3 ­ 0.07 0.3
F (
W R) -
-
0.2








DKT
DKQ
DST
DSQ
Q4G
WITH B
E
F
G
H
Coil-Kirchhoff
Coil-Kirchhoff
Coil-Kirchhoff
Reissner
Reissner
Reissner
50
nodes
170 nodes
169 nodes
170 nodes
169 nodes
169 nodes
76 TRIA3
296 TRIA3
147 QUAD4
296 TRIA3
147 QUAD4 147 QUAD4
O Sm/2
­ 1.19
+0.02
+0.07
+0.07
­ 0.76
­ 0.14
To Sm/2
+5.79
­ 0.06
­ 0.49
­ 4.40
­ 9.80
+17.80
B Sm/2
­ 13.100
­ 5.53
+1.00
­ 9.10
­ 7.12
+19.70
C Sm/2
+5.73
­ 0.06
­ 0.46
­ 4.41
­ 9.44
+17.90
D Sm/2
+0.20
+0.35
+0.50
+0.43
+0.49
+0.05
E Sm/2
+0.19
+0.42
+0.50
+0.49
+0.50
+0.05
F Sm/2
­ 0.66
+0.25
­ 0.30
+0.15
+19.00
­ 0.33

MEC3QU9H MEC3TR7H




I J




96
nodes
121 nodes




25 QUAD9
50 TRIA7
O Sm/2
1.05
1.14




To Sm/2
2.9
0.25




B Sm/2
-
-




C Sm/2
2.9
0.25




D Sm/2
0.28
­ 0.28




E Sm/2
0.28
­ 0.28




F Sm/2
-
-





Concerning the efforts:

· the value on the supported edge is unacceptable for DSQ and Q4 and to a lesser extent
for DST,
· for DSQ, one notes in more one important error at the point F.

Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HT-66/03/008/A

Outline document