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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
1/16
Organization (S): EDF/AMA
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.109
SSLV109 - Full Cylindre in nonuniform pressure
mode 1
Summary:
This test validates all the elements of Fourier (triangles and quadrangles of degrees 1 and 2) in elasticity.
functionalities are as follows:
· variable pressure in space,
· imposed displacements,
· matrices of rigidity Fourier mode 1,
· constraints with the nodes Fourier mode 1,
· recombination of Fourier on displacements and constraints (modeling A),
· transverse isotropic material (modeling F).
The test has a quadratic analytical solution in displacements.
The interest of the test lies in:
· the comparison between solution calculated and analytical solution on the various finite elements,
· the comparison between the results and Code PERMAS on elements TRIA6 (modeling A).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
2/16
1
Problem of reference
1.1 Geometry
L = 12
With
C
p = R
Z
R = 1
R
B
D
The modelled field is ACDB (plane = 0).
1.2
Material properties
E = 72 NR/M2
= 0.3
1.3
Boundary conditions and loadings
ur ()
With
= uz ()
With
= uq ()
With
= 0
uz (A)
B
= 0
R
p = p
cos
R
with p = 1. and R = 1 applied in Z = 12
1.4 Conditions
initial
Without object for the static analysis.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
3/16
2
Reference solution
2.1
Method of calculation used for the reference solution
M
p
2
U
,
=
,
cos with
,
=
+
2
R (R Z
)
(ur Z)
(ur Z)
Z
R
2EI
2ER
p
U
,
=
,
cos with
,
= -
Z (R Z
)
v (R Z)
v (R Z)
rz
2EI
M
p
2
U
2
(R, Z,)
=
(wr, Z) (- sin) with (wr, Z) =
Z -
R
2EI
2ER
p
All the constraints are null except zz (R, Z) = - R.
R
The data were selected in such way that (
u.a.) = (
U 0, L) = 1.
Displacements are thus written here:
(
z2
R 2
R Z
z2
R 2
U R, Z) =
+
v (R, Z) = -
(
W R, Z) =
-
144
480
72
144
480
and:
zz (R, Z) = - R
2.2
Results of reference
U, v, W, zz
in
R = 0., 0.5, 1.
Z = 0., 6., 12.
U, U, U
R
Z
in R = 0., Z = 6., 12., = 45°
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
PERMAS-HS. Axisymmetric Continua with arbitrary loads. Stuttgart 1985. INTES publication
n°224 p 42 - 49.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
4/16
3 Modeling
With
3.1
Characteristics of modeling
Number of the nodes:
With = N1
B = N3
C = N13
D = N15
E = N7
F = N8
G = N9
blocked node
With
E
C
face
blocked
F
y (Z)
in Z
B
G
D
X (R)
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX = 0.
DY = 0.
DZ = 0.)
face AB
(GROUP_NO: AB DY = 0.)
Pressure on the face CD: PRES_REP (GROUP_MA: Boils NEAR: p)
p being defined by AFFE_CHAR_MECA_F by p (X) = X
3.2
Characteristics of the grid
A number of nodes: 15
A number of meshs and types: 4 TRIA6, 1SEG3 on segment CD
3.3 Functionalities
tested
Commands
AFFE_MODELE
MECANIQUE
“AXIS_FOURIER”
TOUT
DEFI_FONCTION
NOM_PARA
“X”
AFFE_CHAR_MECA_F
DDL_IMPO
NOEUD
PRES_REP
GROUP_MA
CALC_MATR_ELEM
“RIGI_MECA”
MODE_FOURIER
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
MODE_FOURIER
COMB_CHAM_NO
COMB_FOURIER
COMB_CHAM_ELEM
COMB_FOURIER
3.4 Remarks
The number of the mode of Fourier not affecting the loading, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM (by defect, it is regarded as being worth 0).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
5/16
4
Results of modeling A
4.1 Values
tested
Node Size
Reference
Aster %
difference
B
U
2.0833 103 2.0835
103 9.103
v
0.
DDL_IMPO
W
2.0833 103
2.0834 103 3.103
zz
1. 1.000001
6.104
E
U 0.25
0.250001
5.104
v
0.
4.106
W
0.25
0.250000
2.104
zz
0.
1.104
F
U 0.250521
0.250522
4.104
v
0.04166 0.041668 3.103
W
0.0249479
0.0249479
6.10-3
zz
0.5 0.50005 1.102
G
U 0.252083
0.252084
3.104
v
0.083333
0.083333 7.103
W
0.247917 0.247916
1.104
zz
1. 1.
9.103
C
U 1. 1.0006
6.103
v
0.
5.105
W
1.
1.00006
6.103
zz
0.
1.1 103
D
U 1.00208
1.00215
7.103
v
0.16666 0.166691 1.5 102
W
0.99791 0.997981
1.9 102
zz
1. 0.999 0.1
4.2 Remarks
The analytical solution is found with a precision < 0.02% for displacements and < 0.1%
for the constraints.
With a numerical formula of integration at 6 points of GAUSS (instead of 3) to calculate the stiffness,
one would find the relation except for 1010 (like PERMAS).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
6/16
5 Modeling
B
5.1
Characteristics of modeling
Number of the nodes:
With = N1
B = N3
C = N13
D = N15
E = N7
F = N8
G = N9
blocked node
C
With
E
y (Z)
face
blocked
F
in Z
B
G
D
X (R)
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX = 0.
DY = 0.
DZ = 0.)
face AB
(GROUP_NO: AB DY = 0.)
Pressure on the face CD: PRES_REP (GROUP_MA: Boils NEAR: p)
p being defined by AFFE_CHAR_MECA_F by p (X) = X
5.2
Characteristics of the grid
A number of nodes: 15
A number of meshs and types: 2 QUAD8, 1 SEG3 on segment CD
5.3 Functionalities
tested
Commands
AFFE_MODELE
MECANIQUE
“AXIS_FOURIER”
TOUT
DEFI_FONCTION
NOM_PARA
“X”
AFFE_CHAR_MECA_F
DDL_IMPO
NOEUD
PRES_REP
GROUP_MA
CALC_MATR_ELEM
“RIGI_MECA”
MODE_FOURIER
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
MODE_FOURIER
5.4 Remarks
The number of the mode of Fourier not affecting the loading, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM (by defect, it is regarded as being worth 0).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
7/16
6
Results of modeling B
6.1 Values
tested
Node Size Reference
Aster %
difference
B
U
2.0833 103 2.0833
103 10.1011
v
0.
DDL_IMPO
W
2.0833 103
2.0833 103
10.1011
zz
1. 1 10.1011
E
U 0.25
0.25
10.1011
v
0.
3.9 1014
W
0.25
0.25
10.1011
zz
0.
4.1012
F
U 0.250521
0.250521
10.1011
v
0.04166 0.04166 10.1011
W
0.0249479
0.0249479
10.1011
zz
0.5 0.5 10.1011
G
U 0.252083
0.252083
10.1011
v
0.08333 0.08333 10.1011
W
0.247917 0.247917
10.1011
zz
1. 1. 10.1010
C
U 1. 1. 10.1011
v
0.
4.3.1014
W
1.
1
10.1011
zz
0.
6.1012
D
U 1.00208
1.00208
10.1011
v
0.16666 0.16666 10.1011
W
0.99791 0.99791
10.1011
zz
1. 1. 10.1011
6.2 Remarks
The analytical solution is found with 10 or 11 significant digits.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
8/16
7 Modeling
C
7.1
Characteristics of modeling
Number of the nodes:
With = N1
B = N3
C = N13
D = N15
E = N7
F = N8
G = N9
blocked node
With
E
C
face
y (Z)
blocked
F
in Z
B
G
D
X (R)
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX = 0.
DY = 0.
DZ = 0.)
face AB
(GROUP_NO: AB DY = 0.)
Pressure on the face CD: PRES_REP (GROUP_MA: Boils NEAR: p)
p being defined by AFFE_CHAR_MECA_F by p (X) = X
7.2
Characteristics of the grid
A number of nodes:15
A number of meshs and types: 2 QUAD9, 1 SEG3 on segment CD
7.3 Functionalities
tested
Commands
AFFE_MODELE
MECANIQUE
“AXIS_FOURIER”
TOUT
DEFI_FONCTION
NOM_PARA
“X”
AFFE_CHAR_MECA_F
DDL_IMPO
NOEUD
PRES_REP
GROUP_MA
CALC_MATR_ELEM
“RIGI_MECA”
MODE_FOURIER
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
MODE_FOURIER
7.4 Remarks
The number of the mode of Fourier not affecting the loading, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM (by defect, it is regarded as being worth 0).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
9/16
8
Results of modeling C
8.1 Values
tested
Node Size
Reference
Aster %
difference
B
U
2.0833 103 2.0833
103 10.1011
v
0.
DDL_IMPO
W
2.0833 103
2.0833 103
10.1011
zz
1. 1 10.1010
E
U 0.25 0.25 10.1011
v
0.
3.9 1014
W
0.25
0.25
10.1011
zz
0.
4.1012
F
U 0.250521
0.250521
10.1011
v
0.04166
0.04166
10.1011
W
0.0249479
0.0249479
10.1011
zz
0.5 0.5 10.1011
G
U 0.252083
0.252083
10.1011
v
0.08333
0.08333
10.1011
W
0.247917
0.247917
10.1011
zz
1. 1. 10.1011
C
U 1.
1.
10.1011
v
0.
4.3.1014
W
1.
1.
10.1011
zz
0.
6.1012
D
U 1.00208
1.00208
10.1011
v
0.16666
0.16666
10.1011
W
0.99791
0.99791
10.1011
zz
1. 1. 10.1011
8.2 Remarks
The analytical solution is found with 10 or 11 significant digits.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
10/16
9 Modeling
D
9.1
Characteristics of modeling
Number of the nodes:
With = N1
B = N1129
C = N1369
D = N2169
E = N141
F = N705
G = N1269
blocked node
With
E
C
face
y (Z)
blocked
F
in Z
B
G
D
X (R)
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX = 0.
DY = 0.
DZ = 0.)
face AB
(GROUP_NO: AB DY = 0.)
Pressure on the face CD: PRES_REP (GROUP_MA: Boils NEAR: p)
p being defined by AFFE_CHAR_MECA_F by p (X) = X
9.2
Characteristics of the grid
A number of nodes: 2169
A number of meshs and types: 1920 QUAD4, 8 SEG2 on segment CD
9.3 Functionalities
tested
Commands
AFFE_MODELE
MECANIQUE
“AXIS_FOURIER”
TOUT
DEFI_FONCTION
NOM_PARA
“X”
AFFE_CHAR_MECA_F
DDL_IMPO
NOEUD
PRES_REP
GROUP_MA
CALC_MATR_ELEM
“RIGI_MECA”
MODE_FOURIER
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
MODE_FOURIER
9.4 Remarks
The number of the mode of Fourier not affecting the loading, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM (by defect, it is regarded as being worth 0).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
11/16
10 Results of modeling D
10.1 Values
tested
Node Size
Reference
Aster %
difference
B
U
2.0833 103 2.0919
103
0.41
v
0.
DDL_IMPO
W
2.0833 103
2.0674 103
0.76
zz
1. 1.00974
0.97
E
U 0.25 0.2498 0.07
v
0.
2.7.1010
W
0.25
0.2498 0.07
zz
0. 0.0090
0.90
F
U 0.250521
0.250347
0.07
v
0.04166
0.04164
0.07
W
0.0249479
0.0249317 0.06
zz
0.5 0.51005
2.01
G
U 0.252083
0.251911
0.07
v
0.083333
0.083273
0.07
W
0.247917
0.247752 0.07
zz
1. 1.0103
1.03
C
U 1.
0.99927
0.07
v
0.
2.3.107
W
1.
0.99928 0.07
zz
0. 0.0088
D
U 1.00208
1.001357
0.07
v
0.16666
0.16653
0.08
W
0.99791
0.997208 0.06
zz
1. 1.0027
0.27
10.2 Remarks
To obtain a precision of about 1% on the constraints, it is necessary to model
structure very finely (8 elements radially and 240 axially).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
12/16
11 Modeling
E
11.1 Characteristics of modeling
Number of the nodes:
With = N1
B = N2421
E = N121
F = N1331
G = N2541
blocked node
With
E
y (Z)
face
blocked
F
in Z
B
G
X (R)
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX = 0.
DY = 0.
DZ = 0.)
face AB
(GROUP_NO: AB DY = 0.)
Pressure on face EG: PRES_REP (GROUP_MA: Boils NEAR: p)
p being defined by AFFE_CHAR_MECA_F by p (X) = X
11.2 Characteristics of the grid
A number of nodes: 2541
A number of meshs and types: 4800 TRIA3, 20 SEG2 on segment EG
11.3 Functionalities
tested
Commands
AFFE_MODELE
MECANIQUE
“AXIS_FOURIER”
TOUT
DEFI_FONCTION
NOM_PARA
“X”
AFFE_CHAR_MECA_F
DDL_IMPO
NOEUD
PRES_REP
GROUP_MA
CALC_MATR_ELEM
“RIGI_MECA”
MODE_FOURIER
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
MODE_FOURIER
11.4 Remarks
To decrease the number of nodes, one modelled the structure for y 6.
The precision on the results is nevertheless less than for elements QUAD4.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
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:
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13/16
12 Results of modeling E
12.1 Values
tested
Node Size
Reference
Aster %
difference
B
U
2.0833 103 2.0228
103
2.90
v
0.
DDL_IMPO
W
2.0833 103
2.1143 103
1.49
zz
1. 1.0078
0.78
E
U 0.25 0.24949 0.20
v
0.
2.4 105
W
0.25
0.24950 0.20
zz
0.
5.3 102
F
U 0.250521
0.25003 0.19
v
0.04166 0.04161
0.13
W
0.249479 0.24900 0.19
zz
0.5 0.49738
0.52
G
U 0.252083
0.251605
0.19
v
0.083333 0.083157
0.21
W
0.247917 0.247449 0.19
zz
1. 0.9814
1.86
12.2 Remarks
The precision on displacements is lower than 3%, that on the constraints lower than 2%.
On this example, the TRIA3 converge definitely less quickly than the QUAD4 towards the solution
exact.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
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Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
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13 Modeling
F
13.1 Characteristics of modeling
Number of the nodes:
With = N1
B = N3
C = N13
D = N15
E = N7
G = N9
blocked node
With
N4
E
N12
C
y (Z)
face
blocked N2
N14
in Z
B
G
N12
D
X (R)
Limiting conditions:
DDL_IMPO:
(NOEUD: WITH DX = 0.
DY = 0.
DZ = 0.)
face AB
(GROUP_NO: AB DY = 0.)
Pressure on the face CD: PRES_REP (GROUP_MA: Boils NEAR: p)
p being defined by AFFE_CHAR_MECA_F by p (X) = X
13.2 Characteristics of the grid
A number of nodes: 15
A number of meshs and types: 2 QUAD8, 1SEG3 on segment CD
13.3 Functionalities
tested
Commands
AFFE_MODELE
MECANIQUE
“AXIS_FOURIER”
TOUT
DEFI_MATERIAU
ELAS_ORTH
DEFI_FONCTION
NOM_PARA
“X”
AFFE_CHAR_MECA_F
DDL_IMPO
NOEUD
PRES_REP
GROUP_MA
CALC_MATR_ELEM
“RIGI_MECA”
MODE_FOURIER
CALC_CHAM_ELEM
“SIGM_ELNO_DEPL”
MODE_FOURIER
13.4 Remarks
The number of the mode of Fourier not affecting the loading, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM (by defect, it is regarded as being worth 0).
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
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:
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14 Results of modeling F
14.1 Values
tested
Node Size
Reference
Aster %
difference
N2
U 2.6041666
2.6041666
1.109
W
2.6041666 2.6041666
1.109
With
zz
0.
1.1013
B
zz
1. 1. 3.1010
N4
U 0.0625 0.0625 4.1010
W
0.0625
0.0625
4.1010
E U
0.25
0.25
3.1010
W
0.25
0.25
3.1010
zz
0.
1. 1014
G v
0.083333 0.083333
2.1010
zz
1. 1. 2.1011
N10 U
0.5625 0.5625 2.1010
W
0.5625 0.5625 2.1010
N12 v
0.125 0.125 1.1010
C U
1. 1. 1.1010
W
1. 1. 1.1010
zz
0.
7.1014
N14 v
0.083333 0.083333 9.1011
D v
0.166666 0.166666 9.1011
zz
1. 1. 1.1011
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSLV109 - Full Cylindre in pressure nonuniform mode 1
Date:
23/09/02
Author (S):
X. DESROCHES Key
:
V3.04.109-C Page:
16/16
15 Summary of the results
The elements of command 2 give the analytical solution.
The elements of command 1 converge slowly towards the solution and require very fine grids.
Times calculations remain however reasonable.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal structures
HT-66/02/001/A
Outline document