Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
1/24
Organization (S): EDF/IMA/MN, SAMTECH
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
Document: V3.03.100
SSLS100 - Subjected embedded circular Plaque
with a uniform pressure
Summary:
This problem allows a comparison between the solutions obtained and various elements of plate in elasticity
linear:
·
models of Coils-Kirchhoff (plate known as thin):
-
triangular surface mesh (TRIA3) DKT,
-
quadrangular surface mesh (QUAD4) DKQ,
-
linear mesh (SEG3) COQUE_AXIS,
·
models of Mindlin-Reissner (plate known as thick):
-
triangular surface mesh (TRIA3) DST,
-
quadrangular surface mesh (QUAD4) DSQ,
-
linear mesh (SEG3) COQUE_AXIS,
·
models of hulls thick: COQUE_3D (QUAD9 and TRIA7).
The same reference solution is treated with three forms of loadings: pressure, gravity and
force-hull. The sizes observed are: displacements (translation/rotation), deformations and efforts
generalized.
Modelings C and D were removed: resorption of modeling COQU_CYL.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
2/24
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:
0 A 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
Embedding on the edge of the plate:
in all the points P such as COp = R: U = v = W = 0, X = y = Z = 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
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
3/24
2
Reference solution
2.1
Method of calculation used for the reference solution
Two reference solutions are usable, for the calculation of the deformation:
·
the theory of LOVE-KIRCHHOFF, usually used for the plates known as “thin”, that
one will retain for modelings A, B, C, D, E and I,
·
the theory of MINDLIN-REISSNER, including the effects of shearing for the plates known as
“thick”, that one will retain for modelings F, G, H and J.
In any distant point of R of the center of the plate (R R), the arrow is expressed:
4
2
2
3
(
P R
R
R
E T
W R) = -
1
1
+ with D =
64D
R2
R2
(
12 1 - 2
)
16 T 2 1
with = 0 (LOVE - KIRCHHOFF) or =
(REISSNER.
)
5 R 1 -
For the calculation of the moments the two theories lead to the same expressions:
P R2
R 2
P R2
R 2
M (R)
(3)
(1) M (R) =
(
1+ 3)
(1)
rr
=
+
16
R - +
16
R
- +
In the center of the plate:
4
4
(
P R
P R
W)
0
= -
(LOVE - KIRCHHOFF) or (
W)
0
=
-
(1+) (REISSNER)
64D
64D
P R2
M ()
0
= M ()
0
= -
(1+
)
rr
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 [U4.24.01]).
The value of moment Mxx (or Myy) in a node pertaining to several finite elements can
to be regarded as being the average of the computed values on the elements which have this node
jointly. 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. Extraction of the average values of the components
M
and M
xx
yy of field “EFGE_ELNO_DEPL”.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
TIMOSHENKO and WOINOWSKY-KRIEGER. Plates and hulls. Béranger edition, (1961).
[2]
BATOZ and DHATT. Modeling of the structures by finite elements. Hulls. Presses
Univ. Laval, 1992.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
4/24
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
Limiting conditions:
DDL_IMPO
in all the nodes of arc ABC
(GROUP_NO: ABC DX: 0., DY: 0., DZ: 0.)
DRX:0., DRY:0., DRZ:0.)
in all the nodes of segment] OA [
(GROUP_NO: OA DY: 0., DRX:0., DRZ:0.)
in all the nodes of segment] OC [
(GROUP_NO: OC DX: 0., DRY:0., DRZ:0.)
with the node O
(GROUP_NO: O DX: 0., DY: 0., DRX:0., DRY:0., DRZ:0.)
Not O
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
Keys
AFFE_CARA_ELEM HULL
EPAIS
[U4.24.01]
ANGL_REP
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
“MECHANICAL” AFFE_MODELE “DKT”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFGE_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
OPERATION
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
5/24
4
Results of modeling A
4.1 Values
tested
Not Reference Aster %
difference
tolerance
Coil-Kirchhoff
O (
W R)
170.6251 169.32
0.76
rel 1.102
D (
W R)
95.9766 95.76
0.23 rel 0.5 102
E (
W R)
95.9766 95.73
0.25 rel 0.5 102
F (
W R)
78.897 78.64
0.32 rel 0.5 102
Reference
Not
Mrr
M
Sm/2
O
0.08125 0.08125 0.08125
With
+0.125 +0.0375 +0.08125
B
+0.125 +0.0375 +0.08125
C
+0.125 +0.0375 +0.08125
D
0.02969 0.05156 0.04062
E
0.02969 0.05156 0.04062
F
0.01525 0.04325 0.02925
Aster
Not
Mxx
M yy
Sm/2
O
0.08031 0.08033 0.08032
With
+0.1260 +0.0378 +0.0819
B
+0.08487 +0.08507 +0.08497
C
+0.03778 +0.1259 +0.08184
D
0.03166 0.05328 0.04227
E
0.05330 0.03164 0.04247
F
0.02958 0.02994 0.02974
% difference (with eps 10-14 and % difference on the absolute values)
Not
Mxx
M yy
Sm/2
Relative tolerance
O
1.15 1.14 1.15
1.5
With
+0.81 +0.81 +0.81
1.
B
+4.46 +4.71 +4.58
5.
C
+0.75 +0.75 +0.75
1.
D
+6.65 +3.34 +4.55
7./3.5
E
+3.38 +6.58 +4.55
3.5/7.
F
+1.14 +2.35 +1.71
1.5
4.2 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 MW
Time CPU To use:
5.7 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
6/24
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
Limiting conditions:
DDL_IMPO
in all the nodes of arc ABC
(GROUP_NO: ABC DX: 0., DY: 0., DZ: 0.)
DRX:0., DRY:0., DRZ:0.)
in all the nodes of segment] OA [
(GROUP_NO: OA DY: 0., DRX:0., DRZ:0.)
in all the nodes of segment] OC [
(GROUP_NO: OC DX: 0., DRY:0., DRZ:0.)
with the node O
(GROUP_NO: 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
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
“MECHANICAL” AFFE_MODELE “DKT”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFGE_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
OPERATION
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
7/24
6
Results of modeling B
6.1 Values
tested
Not Reference Aster %
difference
tolerance
Coil-Kirchhoff
O (
W R)
170.6251 170.8384 0.12 rel 0.5 102
D (
W R)
95.9766 96.1477 0.18
rel 0.5 102
E (
W R)
95.9766 96.2078 0.24
rel 0.5 102
F (
W R)
78.897 79.072 0.22
rel 0.5 102
Reference
Not
Mrr
M
Sm/2
O
0.08125 0.08125 0.08125
With
+0.125 +0.0375 +0.08125
B
+0.125 +0.0375 +0.08125
C
+0.125 +0.0375 +0.08125
D
0.02969 0.05156 0.04062
E
0.02969 0.05156 0.04062
F
0.01525 0.04325 0.02925
Aster
Not
Mxx
M yy
Sm/2
O
0.08151 0.08131 0.08141
With
0.1282 0.04083 0.08451
B
0.08340 0.08340 0.08340
C
0.04085 0.12836 0.08460
D
0.03037 0.05249 0.04143
E
0.05259 0.03043 0.04151
F
0.02981 0.02988 0.02985
% difference (with eps 10-14 and % difference on the absolute values)
Not
Mxx
M yy
Sm/2
Relative tolerance
O
0.33 0.07 0.19
0.5
With
2.62 8.88 4.02
3./9.
B
2.64 2.64 2.64
3.
C
8.95 2.69 4.13
9./3.
D
2.29 1.81 1.99
2.5
E
2.01 2.49 2.19
2.5
F
1.92 2.18 2.05
2.5
6.2 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 megawords
Time CPU To use:
9.5 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
8/24
7 Modeling
E
7.1
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
Limiting conditions:
DDL_IMPO
in all the nodes of arc ABC
(GROUP_NO: ABC DX: 0., DY: 0., DZ: 0.)
DRX:0., DRY:0., DRZ:0.)
in all the nodes of segment] OA [
(GROUP_NO: OA DY: 0., DRX:0., DRZ:0.)
in all the nodes of segment] OC [
(GROUP_NO: OC DX: 0., DRY:0., DRZ:0.)
with the node O
(GROUP_NO: 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
7.2
Characteristics of the grid
A number of nodes: 169
A number of meshs and types: 147 QUAD4
7.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
“MECHANICAL” AFFE_MODELE “DKT”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFGE_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
OPERATION
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
9/24
8
Results of modeling E
8.1 Values
tested
Not Reference Aster %
difference
tolerance
Coil-Kirchhoff
O (
W R)
170.6251 171.00
0.22 rel 0.5 102
D (
W R)
95.9766 96.198 0.23
rel 0.5 102
E (
W R)
95.9766 96.198 0.23
rel 0.5 102
F (
W R)
78.897 79.06 0.20
rel 0.5 102
Reference
Not
Mrr
M
Sm/2
O
0.08125 0.08125
0.08125
With
+0.125 +0.0375
+0.08125
B
+0.125 +0.0375
+0.08125
C
+0.125 +0.0375
+0.08125
D
0.02969 0.05156
0.04062
E
0.02969 0.05156
0.04062
F
0.01525 0.04325
0.02925
Aster
Not
Mxx
M yy
Sm/2
O
0.08162 0.08162 0.08162
With
0.1256 0.03768 0.08164
B
0.08141 0.08140 0.08141
C
0.03767 0.12557 0.08162
D
0.03030 0.05314 0.04172
E
0.05314 0.03030 0.04172
F
0.02903 0.02901 0.02902
% difference (with eps 1014 and % difference on the absolute values)
Not
Mxx
M yy
Sm/2
Relative tolerance
O
0.46 0.46 0.46
0.5
With
0.49 0.49 0.49
0.5
B
0.2.0.2.0.2
0.5
C
0.45 0.45 0.45
0.5
D
2.06 3.07 2.71
2.5/3.5
E
3.07 2.06 2.71
3.5/2.5
F
0.73 0.83 0.79
1
8.2 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 megawords
Time CPU To use:
8.4 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
10/24
9 Modeling
F
9.1
Characteristics of modeling
Element of hull DST (modeling of a quarter of plate)
C
B
E
F
O
With
D
Limiting conditions:
DDL_IMPO
in all the nodes of arc ABC
(GROUP_NO: AB DX: 0., DY: 0., DZ: 0.)
DRX:0., DRY:0., DRZ:0.)
in all the nodes of segment] OA [
(GROUP_NO: OA DY: 0., DRX:0., DRZ:0.)
in all the nodes of segment] OC [
(GROUP_NO: OC DX: 0., DRY:0., DRZ:0.)
with the node O
(GROUP_NO: 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
9.2
Characteristics of the grid
A number of nodes: 170
A number of meshs and types: 296 TRIA3
9.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
“MECHANICAL” AFFE_MODELE “DST”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFGE_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
OPERATION
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
11/24
10 Results of modeling F
10.1 Values
tested
Not Reference Aster %
difference tolerance
Reissner
O (
W R)
178.419 179.743 +0.74 rel 1.0 102
D (
W R)
101.82 102.60 +0.77 rel 1.0 102
E (
W R)
101.82 102.67 +0.84 rel 1.0 102
F (
W R)
84.198 84.83 +0.75 rel 1.0 102
Reference
Not
Mrr
M
Sm/2
O
0.08125 0.08125 0.08125
With
+0.125 +0.0375 +0.08125
B
+0.125 +0.0375 +0.08125
C
+0.125 +0.0375 +0.08125
D
0.02969 0.05156 0.04062
E
0.02969 0.05156 0.04062
F
0.01525 0.04325 0.02925
Aster
Not
Mxx
M yy
Sm/2
O
0.08216 0.08204 0.08210
With
+0.12515 +0.04591 +0.08553
B
+0.08289 +0.08289 +0.08289
C
+0.04594 +0.12524 +0.08559
D
0.03108 0.05184 0.04146
E
0.05195 0.03116 0.04155
F
0.02956 0.02963 0.02960
% difference (with eps 1014 and % difference on the absolute values)
Not
Mxx
M yy
Sm/2
Relative tolerance
O
+1.12 0.97 +1.04
1.5/1.
With
+0.12 +22.44 +5.26
0.5/23.
B
+2.02 +2.02 +2.02
2.5
C
+22.52 +0.19 +5.34
23./0.5
D
+4.67 +0.54 +2.07
5./1.
E
+0.76 +4.94 +2.29
1./5.
F
+1.07 +1.33 +1.19
1.5
10.2 Contents of the file results
Values at the points of observation of displacements and moments realized.
10.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 megawords
Time CPU To use:
9.2 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
12/24
11 Modeling
G
11.1 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
Limiting conditions:
DDL_IMPO
in all the nodes of arc ABC
(GROUP_NO: ABC DX: 0., DY: 0., DZ: 0.)
DRX:0., DRY:0., DRZ:0.)
in all the nodes of segment] OA [
(GROUP_NO: OA DY: 0., DRX:0., DRZ:0.)
in all the nodes of segment] OC [
(GROUP_NO: OC DX: 0., DRY:0., DRZ:0.)
with the node O
(GROUP_NO: 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
11.2 Characteristics of the grid
A number of nodes: 169
A number of meshs and types: 147 QUAD4
11.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
“MECHANICAL” AFFE_MODELE “DST”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFGE_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
OPERATION
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
13/24
12 Results of modeling G
12.1 Values
tested
Not Reference Aster %
difference tolerance
Reissner
O (
W R)
178.419 178.754 +0.19 rel 0.3 102
D (
W R)
101.82 102.015 +0.19 rel 0.3 102
E (
W R)
101.82 102.014 +0.19 rel 0.3 102
F (
W R)
84.198 84.318 +0.14 rel 0.3 102
Reference
Not
Mrr
M
Sm/2
O
0.08125 0.08125 0.08125
With
+0.125 +0.0375 +0.08125
B
+0.125 +0.0375 +0.08125
C
+0.125 +0.0375 +0.08125
D
0.02969 0.05156 0.04062
E
0.02969 0.05156 0.04062
F
0.01525 0.04325 0.02925
Aster
Not
Mxx
M yy
Sm/2
O
0.08098 0.08098 0.08098
With
+0.12730 +0.04136 +0.08433
B
+0.08261 +0.08261 +0.08261
C
+0.04114 +0.12727 +0.08420
D
0.03029 0.05217 0.04078
E
0.05217 0.03029 0.04078
F
0.03449 0.03444 0.03447
% difference (with eps 10-14 and % difference on the absolute values)
Not
Mxx
M yy
Sm/2
Relative tolerance
O
0.33 0.33 +0.33
0.5
With
+1.84 +10.31 +3.79
2./11.
B
+1.68 +1.68 +1.69
2.
C
+9.07 +1.82 +3.64
10./2.
D
+2.05 +1.19 +0.4
2.5/1.5
E
+1.19 +2.05 +0.4
1.5/2.5
F
+17.91 +17.74 +17.80
18
12.2 Contents of the file results
Values at the points of observation of displacements and moments realized.
12.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 megawords
Time CPU To use:
8.6 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
14/24
13 Modeling
H
13.1 Characteristics of modeling
Element of hull Q4G (modeling of a quarter of plate)
C
1.0
B
0.5
E
0.0
O
D
With
0.0
0.5
1.0
Limiting conditions:
DDL_IMPO
in all the nodes of arc ABC
(GROUP_NO: ABC DX: 0., DY: 0., DZ: 0.)
D DRX:0., DRY:0., DRZ:0.)
in all the nodes of segment] OA [
(GROUP_NO: OA DY: 0., DRX:0., DRZ:0.)
in all the nodes of segment] OC [
(GROUP_NO: OC DX: 0., DRY:0., DRZ:0.)
with the node O
(GROUP_NO: 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
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
“MECHANICAL” AFFE_MODELE “DKT”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFGE_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
OPERATION
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
15/24
14 Results of modeling H
14.1 Values
tested
Not Reference Aster %
difference tolerance
Reissner
O (
W R)
178.419 178.282 0.08
rel 0.4 102
D (
W R)
101.82 101.532 0.28
rel 0.4 102
E (
W R)
101.82 101.531 0.28
rel 0.4 102
F (
W R)
84.198 83.91 0.34
rel 0.4 102
Reference
Not
Mrr
M
Sm/2
O
0.08125 0.08125 0.08125
With
+0.125 +0.0375 +0.08125
B
+0.125 +0.0375 +0.08125
C
+0.125 +0.0375 +0.08125
D
0.02969 0.05156 0.04062
E
0.02969 0.05156 0.04062
F
0.01525 0.04325 0.02925
Aster
Not
Mxx
M yy
Sm/2
O
0.08119 0.08119 0.08119
With
+0.11589 +0.03348 +0.07468
B
+0.07236 +0.07234 +0.07235
C
+0.03349 +0.11164 +0.07256
D
0.02961 0.05223 0.04092
E
0.05222 0.02961 0.04091
F
0.02897 0.02898 0.02897
% difference (with eps 10-14 and % difference on the absolute values)
Not
Mxx
M yy
Sm/2
Relative tolerance
O
0.07 0.07 0.07
0.1
With
10.73 10.73 10.73
11.
B
10.94 10.96 10.95
11.
C
10.69 10.69 10.69
11.
D
0.25 +1.3 +0.74
0.5/1.5
E
+1.29 0.27 +0.74
1.5/0.5
F
0.95 0.92 0.94
1.
14.2 Contents of the file results
Values at the points of observation of displacements and moments realized.
14.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 megawords
Time CPU To use:
8.4 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
16/24
15 Modeling
I
15.1 Characteristics of modeling
Element of axisymmetric hull SEG3, in theory of Coils-Kirchhoff: one does not consider
modification of metric, coefficient A_CIS is worth 106.
y
p
O
D
With
X
0
0.5
1.0
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX: 0., DY: 0., DRZ: 0.)
(NOEUD:
O
DRZ:
0.)
15.2 Characteristics of the grid
A number of nodes: 21
A number of meshs and types: 10 SEG3
15.3 Functionalities
tested
Commands
Keys
“MECHANICAL” AFFE_MODELE “COQUE_AXIS”
TOUT
[U4.22.01]
AFFE_CARA_ELEM HULL
A_CIS
[U4.24.01]
MODI_METRIQUE
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
TOUT
CALC_CHAM_ELEM “DEGE_ELNO_DEPL”
[U4.61.01]
“EFGE_ELNO_DEPL”
“SIEF_ELGA_DEPL”
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
NOEUD
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
17/24
16 Results of modeling I
16.1 Values
tested
Not Reference
Aster %
difference
tolerance
Coil-Kirchhoff
O arrow (
W R)
170.6251 169.759 0.51 rel 102
D arrow (
W R)
95.9765 95.0383
0.98 rel 102
D rotation (R)
255.940 257.120
0.46 rel 102
Not
Réfé rence
Aster
%
diff érence
Krr
mall
K
K xx
K yy
K xx
K yy
D
170.625 511.875 IJK
60.0456 514.124
0.44
KLM
265.473
514.361
0.49
moy
162.760
514.242
4.61
0.46
Not
Réfé rence
Aster
%
diff érence
M rr
mall
M
M xx
M yy
M xx
M yy
O 0.08125
0.08125
STU
0.08139
0.08139
0.18
0.18
To +0.125
+0.0375
ABC
+0.10717
+0.03215
14.2
14.2
D 0.02969
0.05156
IJK
0.01962
0.04873
5.8
KLM
0.03844
0.05439
- 5.2
moy
0.02903
0.05156
2.21
0.00
Note:
One notes the good results obtained, except on Krr and M rr, which utilize derivative
of a higher nature less better calculated by the element.
16.2 Contents of the file results
Generalized displacements, deformations and efforts and constraints with the nodes.
16.3 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 MW
Time CPU To use:
5.11 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
18/24
17 Modeling
J
17.1 Characteristics of modeling
Element of axisymmetric hull SEG3, in theory of Mindlin-Reissner: one does not consider
modification of metric, coefficient A_CIS is worth 5/6.
y
p
O
D
With
X
0
0.5
1.0
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX: 0., DY: 0., DRZ: 0.)
(NOEUD:
O
DRZ:
0.)
17.2 Characteristics of the grid
A number of nodes: 21
A number of meshs and types: 10 SEG3
17.3 Functionalities
tested
Commands
Keys
“MECHANICAL” AFFE_MODELE “COQUE_AXIS”
TOUT
[U4.22.01]
AFFE_CARA_ELEM HULL
A_CIS
[U4.24.01]
MODI_METRIQUE
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
TOUT
CALC_CHAM_ELEM “DEGE_ELNO_DEPL”
[U4.61.01]
“EFGE_ELNO_DEPL”
“SIEF_ELGA_DEPL”
“SIGM_ELNO_DEPL”
POST_RELEVE ACTION
NOEUD
“EXTRACTION”
[U4.74.03]
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
19/24
18 Results of modeling J
18.1 Values
tested
Not Reference
Aster %
difference
tolerance
REISSNER
O arrow (
W R)
178.424 178.368
0.03
rel 102
D arrow (
W R)
101.827 101.7769
0.05
rel 102
D rotation (R)
255.940 256.001
0.02
rel 102
Not
Réfé rence
Aster
%
diff érence
Krr
mall
K
K xx
K yy
K xx
K yy
D
170.625 511.875 IJK
167.892 512.050 - 1.62 0.03
KLM
178.920
511.952
4.86
0.01
moy
173.406
512.001
1.60
0.02
Not
Réfé rence
Aster
%
diff érence
M rr
mall
M
M xx
M yy
M xx
M yy
O
0.08125 0.08125 STU
0.08175 0.08175 0.62
0.62
To +0.125
+0.0375
ABC
0.12373
+0.03712
1.02
1.01
D 0.02969
0.05156
IJK
0.02944
0.05150
- 0.85
- 0.11
KLM
0.03045
0.05179
2.49
0.46
moy
0.02994
0.05165
0.85
0.17
Note:
One notes the good results obtained, except on Krr and M rr, which utilize derivative
of a higher nature less better calculated by the element.
18.2 Contents of the file results
Generalized displacements, deformations and efforts and constraints with the nodes.
18.3 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 MW
Time CPU To use:
4.99 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
20/24
19 Modeling
K
19.1 Characteristics of modeling
Modeling: Element of hull COQUE_3D MEC3QU9H
C
B
E
O
D
With
Limiting conditions:
DDL_IMPO:
in all the nodes of the arc (Group_no:ABC DX:0., DY: 0., DZ: 0.)
ABC
DRX:0., DRY:0., DRZ:0.)
segment] OA]
(Group_no:OA DY:0., DRX:0., DRZ:0.)
segment] OC]
(Group_no:OC DX:0., DRY:0., DRZ:0.)
with the node O
(Group_no: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
19.2 Characteristics of the grid
A number of nodes: 96
A number of meshs and types: 25 QUAD9
19.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
AFFE_MATERIAU ALL
[U4.23.02]
“MECHANICAL” AFFE_MODELE “COQUE_3D”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFFO_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS
[U4.23.01]
POST_RELEVE ACTION
OPERATION “EXTRACTION”
[U4.74.03]
VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
21/24
20 Results of modeling K
20.1 Values
tested
Not Reference Aster %
difference
tolerance
REISSNER
O
178.419 178.39
0.016 rel 102
With
0. eps
- ABS 1010
B
0. eps
- ABS 1010
C W
(R)
0. eps
- ABS 1010
D
101.82 101.79
0.029 rel 102
E
101.82 101.79
0.029 rel 102
Not Reference
Aster
Mrr
M
Sm/2
M xx
M yy
Sm/2
O 0.08125
0.08125
0.08125
0.08342
0.08342
0.08342
To +0.125
+0.0375
+0.08125
0.03675
0.1234
0.08007
C +0.125
+0.0375
+0.08125
0.1243
0.03582
0.08006
D 0.02969
0.05156
0.04062
0.05241
0.02971
0.04106
E 0.02969
0.05156
0.04062
0.02958
0.05254
0.04106
Not
% difference
Relative tolerance
M xx
M yy
Sm/2
O 2.67
2.67
2.67 3.
To 2.
1.28
1.45 3.
C 0.56
4.48
1.46 5.
D 1.65
0.067
1.08 2.
E 0.37
1.9
0.95 2.
·
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
the 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.
Contents of the file results
Values at the points of observation of displacements and moments realized.
20.2 Parameters
of execution
Version: 4.00.14
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 MW
Time CPU To use:
8.77 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
22/24
21 Modeling
L
21.1 Characteristics of modeling
Modeling: Element of COQUE_3D MEC3TR7H
C
B
E
O
D
With
Limiting conditions:
DDL_IMPO:
in all the nodes of the arc (Group_no:ABC DX:0., DY: 0., DZ: 0.)
ABC
DRX:0., DRY:0., DRZ:0.)
segment] OA]
(Group_no:OA DY:0., DRX:0., DRZ:0.)
segment] OC]
(Group_no:OC DX:0., DRY:0., DRZ:0.)
with the node O
(Group_no: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
21.2 Characteristics of the grid
A number of nodes: 121
A number of meshs and types: 50 TRIA7
21.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM HULL
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_COQUE
PRES
F3
PESANTEUR
AFFE_MATERIAU ALL
[U4.23.02]
“MECHANICAL” AFFE_MODELE “COQUE_3D”
TOUT
[U4.22.01]
CALC_CHAM_ELEM “EFFO_ELNO_DEPL”
[U4.61.01]
“SIGM_ELNO_DEPL”
DEFI_MATERIAU ELAS
[U4.23.01]
POST_RELEVE ACTION
OPERATION “EXTRACTION”
[U4.74.03]
VALE_TEST
EPSI_TEST
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
23/24
22 Results of modeling L
22.1 Values
tested
Not Reference Aster %
difference
tolerance
REISSNER
O
178.419 178.18
0.13
rel 102
With
0. eps
- ABS 1010
B
0. eps
- ABS 1010
C W
(R)
0. eps
- ABS 1010
D
101.82 101.46
0.35 rel 102
E
101.82 101.46
0.35 rel 102
Not Reference
Aster
Mrr
M
Sm/2
M xx
M yy
Sm/2
O 0.08125
0.08125
0.08125
0.08360
0.08360
0.08360
To +0.125
+0.0375
+0.08125
0.03741
0.12294
0.08017
C +0.125
+0.0375
+0.08125
0.12325
0.03711
0.08018
D 0.02969
0.05156
0.04062
0.05117
0.02907
0.04012
E 0.02969
0.05156
0.04062
0.02905
0.05119
0.04012
Not
% difference
Relative tolerance
M xx
M yy
Sm/2
O 2.89
2.89
2.89 3.
With 0.24
1.65
1.33 3.
C 1.4
1.04
1.32 3.
D 0.76
2.09
1.23 3.
E 2.16
0.72
1.23 3.
·
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
the 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.
Contents of the file results
Values at the points of observation of displacements and moments realized.
22.2 Parameters
of execution
Version: 4.00.14
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
16 MW
Time CPU To use:
9.29 seconds
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Code_Aster ®
Version
4.0
Titrate:
Circular SSLS100 Plaque embedded subjected to a pressure
Date:
22/12/98
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V3.03.100-C Page:
24/24
23 Summary of the results
% of the differences compared to the reference solutions
DKT DKQ
DST
DSQ
Q4G
Mode. With
B
E
F
G
H
Coil Kirchhoff
Coil-Kirchhoff
Reissner
Reissner
Reissner
Point 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)
0.76 +0.12 +0.22
+0.74 +0.19 0.08
D (
W R)
0.23 +0.18 +0.23
+0.77 +0.19 0.28
E (
W R)
0.25 +0.24 +0.23
+0.84 +0.19 0.28
F (
W R)
0.32 +0.22 +0.20
+0.75 +0.14 0.34
COQU_AXIS MEC3QU9H
MEC3TR7H
Mode. I
J
K
L
Coil-Kirchhoff
Reissner
Point 21
nodes
96
nodes
121 nodes
10 SEG3
25 QUAD9
50 TRIA7
O (
W R)
+0.51 0.03
0.16 0.13
D (
W R)
+0.28 0.05
0.029
0.35
E (
W R)
- -
0.029
0.35
F (
W R)
- +0.22
- -
DKT DKQ
DST
DSQ
Q4G
Mode. With
B
E
F
G
H
Coil Kirchhoff
Coil-Kirchhoff
Reissner
Reissner
Reissner
Point 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 1.15
+0.19
+0.46
+1.04
0.33
0.07
To Sm/2 +0.81
+4.02
+0.49
+5.26
+3.79
10.73
B Sm/2 +4.58
+2.64
+0.20
+2.02
+1.69
10.95
C Sm/2 +0.75
+4.13
+0.45
+5.34
+3.64
10.69
D Sm/2 +4.55
+1.99
+2.71
+2.07
+0.40
+0.74
E Sm/2 +4.55
+2.19
+2.71
+2.29
+0.40
+0.74
F Sm/2 +1.71
+2.05
0.79
+1.19
+17.80
0.94
COQU_AXIS MEC3QU9H
MEC3TR7H
Mode. I
J
K
L
Coil-Kirchhoff
Reissner
Point 21
nodes
96
nodes
121 nodes
10 SEG3
25 QUAD9
50 TRIA7
O Sm/2
+0.18 +0.62
2.67 2.89
To Sm/2
+14.2 1.01
1.45 1.33
B Sm/2
- -
- -
C Sm/2
- -
1.46
1.32
D Sm/2
+0.84 0.85
1.08 1.23
E Sm/2
- -
0.95
1.23
F Sm/2
- -
- -
Note:
Concerning the efforts, direct calculation with the nodes leads to variations in several nodes,
in particular at the point F in DSQ and on edge ABC in Q4.
Handbook of Validation
V3.03 booklet: Linear statics of the hulls and the plates
HI-75/01/010/A
Outline document