Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
1/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
Organization (S)
: EDF/IMA/MN, SAMTECH SA
Manual of Validation
V6.01 booklet: Nonlinear statics into axisymmetric
Document: V6.01.302
SSNA302 - Plate circular simply supported
subjected to pressure
Summary:
This test consists in applying a transverse pressure to a circular, simply supported plate and
composed of an elastic material. It is intended to study the taking into account of nonthe geometrical linearities
particularly in the absence of initial curvature when the transverse stiffness is only due to the effect of
plate.
Modeling is made with voluminal elements of type HEXA20 and PENTA15 and elements
surface of type QUAD8 and TRIA6 for the application of the pressure.
The reference is software the SAMCEF software. One has for information the results resulting from the theory of the hulls
thin.
The control
COMP_ELAS
with the option `
GREEN
'is compared with
COMP_INCR
with the option `
PETIT_REAC
'.
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
2/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
pressure p
radius R
thickness H
With
B
center
symmetry
1.2
Material properties
Isotropic elastic material:
E = 200000 Mpa
= 0.3
1.3
Boundary conditions and loadings
Not b:
U
X
=0
U
y
=0.
One applies a transverse pressure p to the plate: p = 222.72 NR/mm
2
. This pressure corresponds
with an arrow W
0
of 1.5 Misters.
Radius R = 10 mm
Thickness H = 1 mm
The problem is axisymmetric.
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
3/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
2
Reference solution
2.1
Reference solution
The reference is software the SAMCEF software. , For information, in the paragraph [§2.2], they are presented
theoretical results related to an assumption of thin the hull type. Then, the results are presented
obtained with the SAMCEF software according to whether one chooses an assumption of thick the hull type or type
volume. It is the latter which is taken into account for the evaluation of Code_Aster.
2.2
Analytical solution and results of reference
The following formula gives the arrow W
0
in the center of the plate:
W
H
With wh
LP
E
R
H
0
0 3
4
+ =
with A = 1.852 and B = 0.696
The stresses with mid thickness are worth:
rr
R
T
E W
R
E W
R
=
=
02
2
02
2
The stresses in lower skin are worth
rr
R
T
E W H
R
E W H
R
,
,
=
=
0
2
0
2
The coefficients are worth:
In the center of the plate:
R
T
=
= 0.905
R
T
=
= 1.778
At the edge of the plate:
R
= 0.610
T
= 0.183
R
= 0
T
= 0.755
For a pressure of 222.72 MPa, the arrow W
0
are worth 1.5 mm and one obtains the following stresses:
Position
rr
(MPa)
(MPa)
rr
`(MPa)
`(MPa)
Center
4072.5 4072.5 5334.0 5334.0
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
4/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
These results correspond to an assumption of thin hull.
The following table shows the results obtained by the SAMCEF software for a modeling of the hull type
thick and of volume type.
Identification Hull
thick
Volume
Arrow w0 (mm)
1.43041 E3
1.441838 E3
SIXX (MPa) center, miepaissor
3899.88
3850.88
SIYY (MPa) center, miepaissor
3899.53
3850.91
SIXX (MPa) center, skin inf
8085.81
8133.60
SIYY (MPa) center, skin inf
8083.32
8133.65
SIXX (MPa) R =R/2, miepaissor
3596.91
3512.79
SIYY (MPa) R =R/2, miepaissor
3056.37
2947.55
SIXX (MPa) R =R/2, skin inf
7798.18
7815.73
SIYY (MPa) R =R/2, skin inf
7264.69
7307.04
The values of the stresses are values by element extrapolated with the nodes.
The results obtained with the SAMCEF software are close one to the other.
Variations of results between the mean theory hull and calculation finite element using the assumption hull
thick are important.
One chooses to take as reference the voluminal calculation obtained by the SAMCEF software.
2.3 References
bibliographical
[1]
Theory off Punts and Shells, Timoshenko S.P., 2
Nd
edition, p 412
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
5/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling A
Face 1:
Fixing on X
Appear 3.1-a: Face 2: Fixing on y
Only one quarter of plate is modelized. One introduces conditions of symmetry on the two faces
shown above.
Moreover one fixes according to X, y, Z all the nodes of the edge located at semi thickness.
In order to most accurately represent the assumptions of thin hull, stresses are introduced
linear on the degrees of freedom of the nodes of the edge. Those Ci are written:
for two nodes I and J located on both sides of the average layer:
U
I
+ U
J
= 0
v
I
+ v
J
= 0
where U and v indicate displacements along axes X and Y.
The syntax used in the data file of Code_Aster is as follows:
LIAISON_DDL (Node: Nor NR
J
), DDL: (“DX”, “DX”), COEF_MULT: (1, 1), COEF_IMPO: 0
One applies the pressure linearly by using 6 increments.
3.2
Characteristics of the mesh
A number of nodes:
2091
A number of meshs and types:
368 HEXA20, 28 PENTA15
92 QUAD8, 7 TRIA6
3.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU ELAS
[U4.23.01]
STAT_NON_LINE COMP_ELAS RELATION ELAS
[U4.32.01]
DEFORMATION
GREEN
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
6/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
EXCIT
TYPE_CHARGE
“SUIV”
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster
% difference
Arrow w0 (mm)
1.441838E3
1.43823E3
0.250
SIXX (MPa) center, miepaissor
3850.9
3901.8
1.322
SIYY (MPa) center, miepaissor
3850.9
3901.8
1.323
SIXX (MPa) center, skin inf
8133.6
8341.0
2.550
SIYY (MPa) center, skin inf
8133.6
8341.1
2.549
SIXX (MPa) R =R/2, miepaissor
3512.8
3513.1
0.010
SIYY (MPa) R =R/2, miepaissor
2947.5
3016.6
2.344
SIXX (MPa) R =R/2, skin inf
7815.7
7885.4
0.892
SIYY (MPa) R =R/2, skin inf
7307.0
7439.5
1.813
4.2 Remarks
One obtains the same precision on the results by using only one increment of loading. Time
CPU is then 736.19 seconds.
4.3 Parameters
of execution
Version: 5.02
Machine: SGI ORIGIN 2000 - R12000
Overall dimension memory: 64 megawords
Time CPU To use:
475 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
7/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling B
Idem modeling A, but by treating nonthe geometrical linearities by control COMP_INCR
option PETIT_REAC.
5.2
Characteristics of the mesh
A number of nodes:
2091
A number of meshs and types: 368 HEXA20, 28 PENTA15
92 QUAD8, 7 TRIA6
5.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU ELAS
[U4.23.01]
STAT_NON_LINE COMP_INCR RELATION ELAS
[U4.32.01]
DEFORMATION
“PETIT_REAC”
EXCIT
TYPE_CHARGE
“SUIV”
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster
% difference
Arrow w0 (mm)
1.441838E3
1.3692E3
5.036
SIXX (MPa) center, miepaissor
3850.9
4219.3
9.568
SIYY (MPa) center, miepaissor
3850.9
4219.4
9.569
SIXX (MPa) center, skin inf
8133.6
7950.5
2.251
SIYY (MPa) center, skin inf
8133.6
7950.5
2.252
SIXX (MPa) R =R/2, miepaissor
3512.8
3838.4
9.268
SIYY (MPa) R =R/2, miepaissor
2947.5
3314.2
12.440
SIXX (MPa) R =R/2, skin inf
7815.7
7593.9
2.839
SIYY (MPa) R =R/2, skin inf
7307.0
7123.7
2.509
6.2 Remarks
One notes an important difference between the reference solution and the solution provided by Code_Aster.
It is checked that this variation tends towards 0 when one increases the number of increments.
6.3 Parameters
of execution
Version: 5.02
Machine: SGI ORIGIN 2000 - R12000
Overall dimension memory: 64 megawords
Time CPU To use: 924 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
8/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling C
Z
With
B
R
·
axisymmetric modeling
·
boundary conditions:
B:
DX = 0
DY = 0
As for modeling A (3D), of the linear stresses are introduced for better representing
a kinematics of hull. They relate to the nodes of the edge external of the disc. If I and J indicate
2 nodes on both sides of the average layer, they are written:
U
U
U
I
J
+
= 0
where indicates radial displacement
7.2
Characteristics of the mesh
A number of nodes:
149
A number of meshs and types: 40 QUAD8, 10 SEG3
7.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU ELAS
[U4.23.01]
STAT_NON_LINE COMP_ELAS RELATION ELAS
[U4.32.01]
DEFORMATION
“GREEN”
EXCIT
TYPE_CHARGE
“SUIV”
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
9/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster
% difference
Arrow w0 (mm)
1.430
1.438
0.5
SIXX (MPa) center, miepaissor
3900
3909
0.2
SIZZ (MPa) center, miepaissor
3900
3896
0.1
8.2 Remarks
In the absence of an axisymmetric calculation of reference the SAMCEF software, one bases oneself on calculation in hull
thick (always the SAMCEF software) and one compares only the arrow and the stresses with the center with mid-
thickness.
8.3 Parameters
of execution
Version: 5.02
Machine: SGI ORIGIN 2000 - R12000
Overall dimension memory: 64 megawords
Time CPU To use: 12 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNA302 - Plate circular subjected to pressure
Date:
03/01/00
Author (S)
:
E. LORENTZ, L. LAMMERANT, J.P. DELSEMME
Key:
V6.01.302-A
Page:
10/10
Manual of Validation
V6.04 booklet: Nonlinear statics into axisymmetric
HT-66/02/001/A
9
Summary of the results
The performances in time calculation and precision of the results are satisfactory while using
order
COMP_ELAS
option “
GREEN
”. On the other hand, processing of nonthe geometrical linearities
by the control
COMP_INCR
option “
PETIT_REAC
” provides results rather far away from
reference solution by adopting a discretization in 6 pitches of time which leads to costs in
already important times calculation.
The following table recapitulates the performances (calculating time and iteration count) between
Code_Aster and the SAMCEF software. The number of imposed increments is identical in both cases
(6 increments).
GREEN
(A)
PETIT_REAC
(B)
Iteration count Code_Aster 27 67
Time CPU Code_Aster (in S)
470
5108
Iteration count the SAMCEF software
26
-
Time CPU the SAMCEF software (in S)
403
-