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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
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A

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Titrate:
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Date:
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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
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
HT-66/03/008/A

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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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HT-66/03/008/A

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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).
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:
V7.01.100-C Page:
5/34

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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:
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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 -

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:
V7.01.100-C Page:
7/34

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)
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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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:
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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.
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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
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:
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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.

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:
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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.
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:
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13/34

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


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:
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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

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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:
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
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HT-66/03/008/A

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:
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

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Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre


Date:
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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:
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:
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
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HT-66/03/008/A

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HPLA100 - Thermoelastic hollow Cylindre


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:
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

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Version
6.5
Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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:
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

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Version
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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:
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

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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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:
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 ®
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Titrate:
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:
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

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Version
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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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
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HT-66/03/008/A

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HPLA100 - Thermoelastic hollow Cylindre


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:
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

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Version
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:
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

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Version
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
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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
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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:
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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

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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


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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
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


Date:
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P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
31/34

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:
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P. MASSIN, F. VOLDOIRE Key
:
V7.01.100-C Page:
32/34

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
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Titrate:
HPLA100 - Thermoelastic hollow Cylindre


Date:
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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:
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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

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