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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
1/34
Organization (S): EDF-R & D/AMA
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
V7.01.100 document
HPLA100 - Heavy thermoelastic hollow Cylindre
in uniform rotation
Summary
The purpose of this test is to test the second members corresponding to the effects of gravity, of a dilation
thermics and of acceleration due to a uniform rotation. For modelings C and D (hull 3D), a calculation
thermo chained rubber band and a thermoelastoplastic calculation without plastic evolution was carried out.
The analytical solution of reference is described in the document [V7.90.03]. One has the results for
modelings:
·
axisymmetric 2D: axisymmetric isoparametric finite elements on meshs QUAD8,
·
axisymmetric hulls: axisymmetric isoparametric finite elements on meshs SEG3
(linear grid of the meridian section),
·
hulls 3D: finite elements MEC3QU9H, MEC3TR7H on meshs QUAD9 and TRIA7,
respectively,
·
plates DKT: finite elements plans DKQ, DKT on meshs QUAD4 and TRIA3, respectively. One
test also the orthotropic hulls of DEFI_COQU_MULT for two layers of the same material
isotropic and key word ELAS_COQU of DEFI_MATERIAU for the assignment of characteristics of
homogenized plates.
Handbook of Validation
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HT-66/03/008/A
Code_Aster ®
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
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:
V7.01.100-C Page:
2/34
1
Problem of reference
1.1 Geometry
Z
IH
Re
Interior radius IH = 19.5 mm
External radius Re = 20.5 mm
Not F
R = 20.0 mm
Thickness
H = 1.0 mm
Height
L = 10.0 mm
R
Z
J
D
C
H
+
R
With
B
F
1.2
Properties of material
The material is homogeneous isotropic, thermoelastic linear, the initial state is virgin. Coefficients
are: E =
5 NR mm2 =
=
- 6 kg mm3 = - 5 °C-
2 10
0 3
810
10
1
.
/
.
.
/
(coefficient of
dilation).
1.3
Boundary conditions and loadings
- 2
·
gravity:
G = 10. ms, according to axis OZ
force traction on the higher face: - 16010 4
. - NR, is one
traction distributed on [CD]: - 810 4
. - NR/mm
·
rotation:
=
-
1
1
. S according to axis OZ
·
thermal dilation:
T () - T
=
+
/2 +
-
-
/with:
ref. (
) (T T
S
I)
(T T
S
I) (R
R) H
case 1:
T = 0 5
. °C, T = - 0 5
. °C, T
= 0. °C
S
I
ref.
case 2:
T = 01
. °C, T = 01
. °C, T
= 0. °C
S
I
ref.
These fields of temperature are calculated with THER_LINEAIRE, using a stationary calculation on
the same grid, but with a plane model in order to have a solution refines in the thickness.
Boundary conditions in displacement (and rotation) being different according to modeling
considered, they will be described later on (in the paragraphs relating to modelings).
Handbook of Validation
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
3/34
2
Reference solution
2.1
Method of calculation used for the reference solution
To refer to the document [V7.90.03] to have the complete analytical solutions.
The analytical results of reference are:
·
displacements and rotations,
·
axial stress, generalized efforts (in theory of hulls),
in skins internal and external on the sections AB and CD.
In axisymmetric 2D, the complete solutions given in [V7.90.03] are such as rz = 0 where R and Z
are the directions radial and axial cylinder, respectively. For the loadings of rotation
uniform and of thermal dilation, the boundary conditions are selected so that them
solutions do not depend on Z (there is in particular zz = 0).
For the hulls, with boundary conditions equivalent, rotation around the axis
orthoradial is null for the loadings of uniform rotation and thermal dilation, which is not
not the case of the loading of gravity where rotation is constant (the cylinder formats then
conical). On the other hand in all the cases, the transverse distortion is null; thus theories of
Coil-Kirchhoff and those of Hencky-Mindlin provide the same reference solution.
Handbook of Validation
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
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3 Modeling
With
3.1
Characteristics of modeling
Finite elements 2D axisymmetric
y
D J C
10
0
WITH F B
X
19.5
20.5
The discretized geometry is represented above:
Edge
group_no
BC BC
DA DA
LOW AB
CD HIGH
3.2
Characteristics of the grid
The grid is regular: 4 elements in the height, 8 in the thickness.
A number of nodes: 121
A number of meshs and type: 32 QUAD8
3.3
Boundary conditions in displacement
3.3.1 Gravity
Displacement DY is blocked at the point F alone.
3.3.2 Rotation
Displacement DY is blocked on sides [AB] (GROUP_NO: BAS) and on [CD] (GROUP_NO:
HAUT).
Handbook of Validation
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Code_Aster ®
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
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3.3.3 Thermal case of dilation n°1
Displacement DY is blocked on all the structure.
3.3.4 Thermal case of dilation n°2
Displacement DY is blocked on sides [AB] (GROUP_NO: BAS) and [CD] (GROUP_NO: HAUT).
3.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“AXIS”
AFFE_CHAR_MECA GRAVITY
ROTATION
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
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V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
6/34
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the N78 node
2.34000 108
2.339999 108 -
Displacement DY of the N120 node
1.185 109
1.184999 109 -
Displacement DY of the N13 node
1.2150 109
1.214999 109 -
Axial stress Siyy with the node N78 (M13)
8.0000 104
7.9999 104 -
Uniform rotation - centrifugal force
Displacement DX of the N120 node
2.94240 107
2.942374 107 0.001
Displacement DX of the N13 node
2.88010 107
2.880065 107 0.001
Axial stress Siyy with the node N120 (M1)
9.94880 104
9.948902 104 0.001
Axial stress Siyy with the node N13 (M32)
9.26310 104
9.263187 104 0.001
Dilation case 1
Displacement DX of the N120 node
1.056145 106
1.05625 106
0.01
Displacement DX of the N13 node
1.110317 106
1.1104166 106
0.009
Axial stress Siyy with the node N120 (M1)
1.4321427
1.4321429
-
Dilation case 2
Displacement DX of the N120 node
2.53500 105
2.5349999 105
-
Axial stress Siyy with the node N120 (M1)
2.00000 101
1.99999 101 -
Handbook of Validation
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
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5 Modeling
B
5.1
Characteristics of modeling
Elements of axisymmetric hull
y
10
J
5
H
F
0
X
20
The discretized geometry is represented above. One chooses the theory of hulls of Coils-Kirchhoff
(for that one takes a transverse coefficient of shearing of 106). One neglects the correction of
metric in the thickness. The thickness is: 1 Misters.
node
group_no
J GRNO13
H GRNO14
F GRNO6
5.2
Characteristics of the grid
A number of nodes: 21
A number of meshs and type: 10 SEG3
5.3
Boundary conditions in displacement and rotation
5.3.1 Gravity
Displacement DY is blocked at the point F alone (GRNO6).
5.3.2 Rotation
Displacement DY is blocked at the point F (GRNO6) at the point J (GRNO13).
Rotation around axis Z is null in these two points.
5.3.3 Thermal case of dilation n°1
Displacement DY as well as rotation around axis Z. are blocked on all the structure
(GROUP_NO: GRNO15)
Handbook of Validation
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HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
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5.3.4 Thermal case of dilation n°2
Displacement DY is blocked at the point F (GROUP_NO: GRNO6) and at the point J (GROUP_NO:
GRNO13). Rotation around axis Z is null on the same groups of nodes.
5.4 Functionalities
tested
Commands
AFFE_MODELE AFFE MODELING
“COQUE_AXIS”
AFFE_CARA_ELEM HULL
EPAIS
A_CIS
MODI_METRIQUE
“NON”
AFFE_CHAR_MECA GRAVITY
ROTATION
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
6
Results of modeling B
6.1 Values
tested
Note:
Index X corresponds here to the first direction of the local reference mark of the element.
Identification Reference
Aster %
difference
Gravity
Displacement DX of the node J
2.40000 108 2.400016
108 -
Displacement DY of the node H
5.00000 109
5.00000 109 -
Rotation DRZ of the node H
2.40000 109 2.400015
109 -
Normal effort Nxx, M10 mesh, node J
8.00000 104
8.00000 104
-
Axial stress Sixx, internal skin,
8.00000 104
8.00000 104 -
net M10, node J
Rotation - centrifugal force
Displacement DX of the node F
2.91200 107
2.91201 107
-
Normal effort Nxx, M1 mesh, node F
9.60000 104
9.60005 104
-
Axial stress Sixx, internal skin,
9.60000 104 9.600013
104 -
net M1, node F
Dilation case 1
Moment Mxx, M1 mesh, node F
2.38095 101
2.38095 101
-
Axial stress Sixx, internal skin,
1.428571
1.428571
-
net M1, node F
Dilation case 2
Displacement DX of the node F
26.0000 106
26.0001 106
-
Normal effort Nxx, M1 mesh, node F
2.00000 101
1.99999 101
-
Axial stress Sixx, internal skin,
2.00000 101 1.99999
101 -
net M1, node F
Handbook of Validation
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HT-66/03/008/A
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
9/34
7 Modeling
C
7.1
Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of hull 3D: QUAD9
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
not node
K NO72
L NO1
MR. NO33
NR NO39
P NO186
Q NO190
The factor of correction of shearing A_CIS is worth 5/6 (theory of hulls of Reissner).
7.2
Characteristics of the grid
A number of external nodes: 121
A number of meshs and types: 32 QUAD9 + 8 SEG3
7.3
Boundary conditions in displacement and rotation
7.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
7.3.2 Rotation
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
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HT-66/03/008/A
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
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:
V7.01.100-C Page:
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7.3.3 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
7.3.4 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
7.4 Functionalities
tested
Commands
AFFE_MODELE AFFE MODELING
“COQUE_3D”
AFFE_CARA_ELEM HULL
EPAIS
A_CIS
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
ROTATION
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
STAT_NON_LINE COMP_INCR
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
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P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
11/34
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.32821
108 2.991
Displacement DY of the point NR
2.40000 108 2.32709
108 3.038
Displacement DZ of the point P
5.00000 109 4.99919
109 0.016
Displacement DZ of the point Q
5.00000 109 4.99911
109
0.018
Rotation DRY of the point P
2.40000 109 2.44618
109
1.924
Rotation DRX of the point Q
2.40000 109 2.44574
109
1.906
Normal effort Nyy, M4 mesh, not K
8.00000 104 8.00157
104
0.020
Normal effort Nyy, M32 mesh, not NR
8.00000 104 8.00184
104 0.023
Axial stress Siyy, internal skin,
net M4, not K
8.00000 104 8.20512
104 2.564
Axial stress Siyy, internal skin,
net M32, not NR
8.00000 104 8.20459
104 2.557
Rotation centrifugal force
Displacement DX of the point L
2.91200 107
2.91181 107
0.006
Displacement DY of the point M
2.91200 107
2.91073 107
0.044
Normal effort Nyy, M1 mesh, not L
9.60000 104
9.60002 104
0.000
Normal effort Nyy, M29 mesh, not M
9.60000 104
9.60004 104
0.000
Axial stress Siyy, internal skin,
net M1, not L
9.84600 104
9.83997 104
0.061
Axial stress Siyy, internal skin,
net M29, not M
9.84600 104 9.83961
104 0.065
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38096 101
0.000
Myy moment, M29 mesh, not M
2.38095 101 2.38096
101
0.000
Axial stress Siyy, internal skin,
net M1, not L
1.428571
1.42858
0.000
Axial stress Siyy, internal skin,
net M29, not M
1.428571
1.42858
0.000
Dilation case 2
Displacement DX of the point L
25.9946 106
25.9907 106
0.015
Displacement DY of the point M
25.9946 106 25.9989
106
0.016
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M29 mesh, not M
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M1, not L
1.97800 101
1.97862 101
0.031
Axial stress Siyy, internal skin,
net M29, not M
2.97800 101 1.97864
101 0.032
8.2 Remarks
Satisfactory and identical results for calculations with MECA_STATIQUE and STAT_NON_LINE.
Handbook of Validation
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
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:
V7.01.100-C Page:
12/34
9 Modeling
D
9.1
Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of hull 3D: TRIA7
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
not node
K NO72
L NO1
MR. NO33
NR NO39
P NO186
Q NO190
The factor of correction of shearing A_CIS is worth 5/6 (theory of Reissner hulls).
9.2
Characteristics of the grid
A number of external nodes: 153
A number of meshs and types: 64 TRIA7 + 8 SEG3
9.3
Boundary conditions in displacement and rotation
9.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
9.3.2 Rotation
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
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HT-66/03/008/A
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
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:
V7.01.100-C Page:
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9.3.3 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
9.3.4 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
9.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“COQUE_3D”
AFFE_CARA_ELEM HULL
EPAIS
A_CIS
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
ROTATION
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
STAT_NON_LINE COMP_INCR
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
14/34
10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.32610
108 3.079
Displacement DY of the point NR
2.40000 108
2.33110 108 2.871
Displacement DZ of the point P
5.00000 109
4.99874 109 0.025
Displacement DZ of the point Q
5.00000 109 4.99940
109
0.012
Rotation DRY of the point P
2.40000 109 2.43797
109
1.582
Rotation DRX of the point Q
2.40000 109
2.43962 109
1.651
Normal effort Nyy, M60 mesh, not K
8.00000 104 7.99979
104
0.003
Normal effort Nyy, M56 mesh, not NR
8.00000 104
8.00431 104 0.054
Axial stress Siyy, internal skin,
net M60, not K
8.00000 104
8.20178 104 2.522
Axial stress Siyy, internal skin,
net M56, not NR
8.00000 104 8.19909
104 2.489
Rotation centrifugal force
Displacement DX of the point L
2.91200 107
2.91170 107
0.010
Displacement DY of the point M
2.91200 107
2.91091 107
0.037
Normal effort Nyy, M25 mesh, not L
9.60000 104
9.60207 104
0.022
Normal effort Nyy, M53 mesh, not M
9.60000 104
9.59935 104
0.007
Axial stress Siyy, internal skin,
net M25, not L
9.84600 104
9.84011 104
0.060
Axial stress Siyy, internal skin,
net M53, not M
9.84600 104 9.84124
104 0.048
Dilation case 1
Myy moment, M25 mesh, not L
2.38095 101
2.38097 101
0.001
Myy moment, M53 mesh, not M
2.38095 101 2.38096
101
0.000
Axial stress Siyy, internal skin,
net M25, not L
1.428571
1.42858
0.000
Axial stress Siyy, internal skin,
net M53 not M
1.428571
1.42858
0.000
Dilation case 2
Displacement DX of the point L
26.0000 106
25.9928 106
0.028
Displacement DY of the point M
26.0000 106 25.9969
106
0.012
Normal effort Nyy, M25 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M53 mesh, not M
2.00000 101
1.99999 101
0.000
Axial stress Siyy, internal skin,
net M25, not L
1.97800 101
1.97821 101
0.011
Axial stress Siyy, internal skin,
net M53, not M
1.97800 101 1.97898
101 0.050
10.2 Remarks
Satisfactory and identical results for calculations with MECA_STATIQUE and STAT_NON_LINE.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
15/34
11 Modeling
E
11.1 Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of plate DKQ: QUAD4
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
not
node
K NO160
L NO203
MR. NO11
NR NO1
P NO226
Q NO6
11.2 Characteristics of the grid
A number of nodes: 231
A number of meshs and types: 200 QUAD4 + 80 SEG2
11.3 Boundary conditions in displacement and rotation
11.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
11.3.2 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
16/34
11.3.3 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
11.4 Functionalities
tested
Commands
AFFE_MODELE AFFE MODELING
“DKT”
AFFE_CARA_ELEM HULL
EPAIS
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
STAT_NON_LINE COMP_INCR
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
17/34
12 Results of modeling E
12.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.37341
108 1.108
Displacement DY of the point NR
2.40000 108
2.37341 108 1.108
Displacement DZ of the point P
5.00000 109
5.00883 109 0.177
Displacement DZ of the point Q
5.00000 109 5.00883
109
0.177
Rotation DRY of the point P
2.40000 109 2.36136
109
1.610
Rotation DRX of the point Q
2.40000 109
2.36136 109
1.610
Normal effort Nyy, M181 mesh, not K
8.00000 104 7.56157
104
5.480
Normal effort Nyy, M200 mesh, not NR
8.00000 104
7.56157 104 5.480
Axial stress Siyy, internal skin,
net M181, not K
8.00000 104
7.56157 104 5.480
Axial stress Siyy, internal skin,
net M200, not NR
8.00000 104 7.56157
104 5.480
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38095 101
0.000
Myy moment, M20 mesh, not M
2.38095 101 2.38095
101
0.000
Axial stress Siyy, internal skin,
net M1, not L
1.428571
1.428571
0.000
Axial stress Siyy, internal skin,
net M20, not M
1.428571
1.428571
0.000
Dilation case 2
Displacement DX of the point L
26.0000 106
26.0000 106
0.000
Displacement DY of the point M
26.0000 106 26.0000
106
0.000
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M20 mesh, not M
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M1, not L
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M20, not M
2.00000 101 2.00000
101 0.000
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
18/34
13 Modeling
F
13.1 Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of plate DKT: TRIA3
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
not
node
K NO1
L NO11
MR. NO161
NR NO227
P NO6
Q NO215
13.2 Characteristics of the grid
A number of nodes: 231
A number of meshs and type: 400 TRIA3 + 80 SEG2
13.3 Boundary conditions in displacement and rotation
13.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
13.3.2 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
19/34
13.3.3 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
13.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“DKT”
AFFE_CARA_ELEM HULL
EPAIS
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
STAT_NON_LINE COMP_INCR
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
20/34
14 Results of modeling F
14.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.32796
108 3.002
Displacement DY of the point NR
2.40000 108
2.32796 108 3.002
Displacement DZ of the point P
5.00000 109
5.02845 109 0.517
Displacement DZ of the point Q
5.00000 109
5.02845 109
0.517
Rotation DRY of the point P
2.40000 109 2.28975
109
4.594
Rotation DRX of the point Q
2.40000 109
2.28975 109
4.594
Normal effort Nyy, M362 mesh, not K
8.00000 104 7.61457
104
4.818
Normal effort Nyy, M400 mesh, not NR
8.00000 104
7.61457 104 4.818
Axial stress Siyy, internal skin,
net M362, not K
8.00000 104
7.61007 104 4.874
Axial stress Siyy, internal skin,
net M400, not NR
8.00000 104 7.61007
104 4.874
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38095 101
0.000
Myy moment, M39 mesh, not M
2.38095 101 2.38095
101
0.000
Axial stress Sixx, internal skin,
net M1, not L
1.428571
1.428571
0.000
Axial stress Sixx, internal skin,
net M39 not M
1.428571
1.428571
0.000
Dilation case 2
Displacement DX of the point L
26.0000 106
25.9999 106
0.000
Displacement DY of the point M
26.0000 106 25.9999
106
0.000
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M39 mesh, not M
2.00000 101
1.99999 101
0.000
Axial stress Siyy, internal skin,
net M1, not L
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M39, not M
2.00000 101 2.00000
101 0.000
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
21/34
15 Modeling
G
15.1 Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of plate DKT: TRIA3. Modeling uses a double-layered plate of which them
characteristics of orthotropism are those of material defined in the §1.2.
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
not
node
K NO1
L NO11
MR. NO161
NR NO227
P NO6
Q NO215
15.2 Characteristics of the grid
A number of nodes: 231
A number of meshs and types: 400 TRIA3 + 80 SEG2
15.3 Boundary conditions in displacement and rotation
15.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
15.3.2 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
22/34
15.3.3 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
15.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“DKT”
AFFE_CARA_ELEM HULL
EPAIS
DEFI_MATERIAU ELAS_ORTH
DEFI_COQU_MULT
EPAIS
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
23/34
16 Results of modeling G
16.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.32796
108 3.002
Displacement DY of the point NR
2.40000 108 2.32796
108 3.002
Displacement DZ of the point P
5.0 109 5.02845
109 0.517
Displacement DZ of the point Q
5.0 109 5.02845
109
0.517
Rotation DRY of the point P
2.40000 109 2.28975
109
4.594
Rotation DRX of the point Q
2.40000 109
2.28975 109
4.594
Normal effort Nyy, M362 mesh, not K
8.00000 104 7.61457
104
4.818
Normal effort Nyy, M400 mesh, not NR
8.00000 104
7.61457 104 4.818
Axial stress Siyy, internal skin,
net M362, not K
8.00000 104
7.61007 104 4.874
Axial stress Siyy, internal skin,
net M400, not NR
8.00000 104 7.61007
104 4.874
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38095 101
0.000
Myy moment, M39 mesh, not M
2.38095 101 2.38095
101
0.000
Axial stress Sixx, internal skin,
net M1, not L
1.428571
1.428571
0.000
Axial stress Sixx, external skin,
net M1, not L
1.428571
1.428571
0.000
Axial stress Sixx, internal skin,
net M39 not M
1.428571
1.428571
0.000
Axial stress Sixx, external skin,
net M39 not M
1.428571
1.428571
0.000
Dilation case 2
Displacement DX of the point L
26.0 106
25.9999 106
0.000
Displacement DY of the point M
26.0 106 25.9999
106
0.000
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M39 mesh, not M
2.00000 101
1.99999 101
0.000
Axial stress Siyy, internal skin,
net M1, not L
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M39, not M
2.00000 101 2.00000
101 0.000
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
24/34
17 Modeling
H
17.1 Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of plate DKQ: QUAD4. Modeling uses a double-layered plate of which them
characteristics of orthotropism are those of material defined in the §1.2.
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
Not
node
K NO160
L NO203
MR. NO11
NR NO1
P NO226
Q NO6
17.2 Characteristics of the grid
A number of external nodes: 231
A number of meshs and types: 200 QUAD4 + 80 SEG2
17.3 Boundary conditions in displacement and rotation
17.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
17.3.2 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
25/34
17.3.3 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
17.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“DKT”
AFFE_CARA_ELEM HULL
EPAIS
DEFI_MATERIAU ELAS_ORTH
DEFI_COQU_MULT
EPAIS
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
26/34
18 Results of modeling H
18.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.37341
108 1.108
Displacement DY of the point NR
2.40000 108
2.37341 108 1.108
Displacement DZ of the point P
5.00000 109
5.00883 109 0.177
Displacement DZ of the point Q
5.00000 109 5.00883
109
0.177
Rotation DRY of the point P
2.40000 109 2.36136
109
1.610
Rotation DRX of the point Q
2.40000 109
2.36136 109
1.610
Normal effort Nyy, M181 mesh, not K
8.00000 104 7.56157
104
5.480
Normal effort Nyy, M200 mesh, not NR
8.00000 104
7.56157 104 5.480
Axial stress Siyy, internal skin,
net M181, not K
8.00000 104
7.56157 104 5.480
Axial stress Siyy, internal skin,
net M200, not NR
8.00000 104 7.56157
104 5.480
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38095 101
0.000
Myy moment, M20 mesh, not M
2.38095 101 2.38095
101
0.000
Axial stress Siyy, internal skin,
net M1, not L
1.428571
1.428571
0.000
Axial stress Siyy, external skin,
net M1, not L
1.428571
1.428571
0.000
Axial stress Siyy, internal skin,
net M20, not M
1.428571
1.428571
0.000
Axial stress Siyy, external skin,
net M20, not M
1.428571
1.428571
0.000
Dilation case 2
Displacement DX of the point L
26.0000 106
26.0000 106
0.000
Displacement DY of the point M
26.0000 106 26.0000
106
0.000
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M20 mesh, not M
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M1, not L
2.00000 101
2.00000 101
0.000
Axial stress Siyy, internal skin,
net M20, not M
2.00000 101 2.00000
101 0.000
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
27/34
19 Modeling
I
19.1 Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of plate DKQ: QUAD4. Assignment of characteristics of homogenized plates
corresponding to material of the §1.2.
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
Not
node
K NO160
L NO203
MR. NO11
NR NO1
P NO226
Q NO6
19.2 Characteristics of the grid
A number of external nodes: 231
A number of meshs and types: 200 QUAD4 + 80 SEG2
19.3 Boundary conditions in displacement and rotation
19.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
19.3.2 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
28/34
19.3.3 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
19.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“DKT”
AFFE_CARA_ELEM HULL
EPAIS
DEFI_MATERIAU ELAS_COQU
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
29/34
20 Results of modeling I
20.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.37341
108 1.108
Displacement DY of the point NR
2.40000 108
2.37341 108 1.108
Displacement DZ of the point P
5.00000 109
5.00883 109 0.177
Displacement DZ of the point Q
5.00000 109 5.00883
109
0.177
Rotation DRY of the point P
2.40000 109 2.36136
109
1.610
Rotation DRX of the point Q
2.40000 109
2.36136 109
1.610
Normal effort Nyy, M181 mesh, not K
8.00000 104 7.56157
104
5.480
Normal effort Nyy, M200 mesh, not NR
8.00000 104
7.56157 104 5.480
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38095 101
0.000
Myy moment, M20 mesh, not M
2.38095 101 2.38095
101
0.000
Dilation case 2
Displacement DX of the point L
26.0000 106
26.0000 106
0.000
Displacement DY of the point M
26.0000 106 26.0000
106
0.000
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M20 mesh, not M
2.00000 101
2.00000 101
0.000
20.2 Remarks
The local constraints are not calculated since the characteristics material of
plate are supposed to come from a calculation of homogenization.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
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21 Modeling
J
21.1 Characteristics of modeling
Modeling of a quarter of cylinder.
Elements of plate DKT: TRIA3. Assignment of characteristics of homogenized plates
corresponding to material of the §1.2.
Z
NR
K
Q
P
y
M
L
X
The discretized geometry is represented above.
not
node
K NO1
L NO11
MR. NO161
NR NO227
P NO6
Q NO215
21.2 Characteristics of the grid
A number of nodes: 231
A number of meshs and types: 400 TRIA3 + 80 SEG2
21.3 Boundary conditions in displacement and rotation
21.3.1 Gravity
Displacement DZ is blocked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
21.3.2 Thermal case of dilation n°1
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
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21.3.3 Thermal case of dilation n°2
Displacement DZ as well as rotations around axes X and Y are blocked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are blocked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are blocked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are blocked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are blocked on the group of nodes
METN.
21.4 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
“DKT”
AFFE_CARA_ELEM HULL
EPAIS
DEFI_MATERIAU ELAS_COQU
AFFE_CHAR_MECA GRAVITY
FORCE_ARETE
TEMP_CALCULEE
MODEL MECA_STATIQUE
CHAM_MATER
CARA_ELEM
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
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22 Results of modeling J
22.1 Values
tested
Identification Reference
Aster %
difference
Gravity
Displacement DX of the point K
2.40000 108 2.32796
108 3.002
Displacement DY of the point NR
2.40000 108 2.32796
108 3.002
Displacement DZ of the point P
5.0 109 5.02845
109 0.517
Displacement DZ of the point Q
5.0 109 5.02845
109
0.517
Rotation DRY of the point P
2.40000 109 2.28975
109
4.594
Rotation DRX of the point Q
2.40000 109
2.28975 109
4.594
Normal effort Nyy, M362 mesh, not K
8.00000 104 7.61457
104
4.818
Normal effort Nyy, M400 mesh, not NR
8.00000 104
7.61457 104 4.818
Dilation case 1
Myy moment, M1 mesh, not L
2.38095 101
2.38095 101
0.000
Myy moment, M39 mesh, not M
2.38095 101 2.38095
101
0.000
Dilation case 2
Displacement DX of the point L
26.0 106
25.9999 106
0.000
Displacement DY of the point M
26.0 106 25.9999
106
0.000
Normal effort Nyy, M1 mesh, not L
2.00000 101
2.00000 101
0.000
Normal effort Nyy, M39 mesh, not M
2.00000 101
1.99999 101
0.000
22.2 Remarks
The local constraints are not calculated since the characteristics material of
plate are supposed to come from a calculation of homogenization.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
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23 Summary of the results
The very good results obtained for modelings A and B are explained by the fact why the solutions
of reference belong to the space generated by the selected finite elements. Only remain them
numerical round-off errors.
Satisfactory results were obtained for modelings of plates and hulls in
space C, D, E, F, G, H, I and J. Pour these last, a chained elastic thermo calculation was carried out.
The results with modeling DKT (E, F, G, H, I and J) show that the elements quadrangle have
a better behavior than the elements triangle. It is necessary to have a discretization
sufficient fine with these plane elements in order to be able to model the geometry correctly
circular of the cylindrical hull. Indeed, to discretize the geometry of the cylinder by plane facets or
parabolic is not in conformity and induces a parasitic inflection which decreases with the smoothness of grid.
Thus a multiplication of the number of elements by two on the height of the structure makes fall
the maximum error relating of 5,48% (case presented here) to 2,8%. Results with modeling
COQUE_3D (C and D) is very good except for gravity with the element triangle.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Code_Aster ®
Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre
Date:
01/12/03
Author (S):
P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
34/34
Intentionally white left page.
Handbook of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A
Outline document