Code_Aster ®
Version
7.4
Titrate:
HSLA303 - Cylindre under pressure and thermal dilation

Date:
25/11/05
Author (S):
X. DESROCHES Key
:
V7.12.303-A Page:
1/6

Organization (S): EDF-R & D/AMA
Handbook of Validation
V7.12 booklet: -
Document: V7.12.303
HSLA303 - Cylindre under pressure and dilation
thermics

Summary:

Calculation is carried out into axisymmetric. The goal of the test is to validate the initial deformations (key word
EPSI_INIT).

The cylinder is subjected to a homogeneous thermal dilation (T constant).

The followed procedure is as follows:

·
that is to say 1 the field of deformations resulting from one the 1st calculation, the cylinder being subjected to a dilation
homogeneous thermics T (U1 the field of resulting displacements),
·
in the second calculation, the cylinder is subjected to an internal pressure, with like deformations
initial the field of deformations 1 (either U2 the resulting field of displacements),
·
one then compares the results with the field U, obtained with cylinder under pressure, but without
initial deformations. One must have the relation: U2 = U + U1.

Handbook of Validation
V7.12 booklet: - HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
HSLA303 - Cylindre under pressure and thermal dilation

Date:
25/11/05
Author (S):
X. DESROCHES Key
:
V7.12.303-A Page:
2/6

1
Problem of reference

1.1 Geometry
O
Z

H

With
D

B
C

L

R

Length:
L
= 1 m
Thickness:
H
= 0.0025 m
External radius:
Re = 0.05 m

1.2
Material properties

E = 2.1 X 1011 Pa

v = 0.3

= 0.12 X 10-4/°C

1.3
Boundary conditions and loadings

·
Section AB in support (direction Z),
·
Thermal dilation in the thickness (calculation 1): T = 100°C
·
Internal pressure (calculation 2): p = 2 X 108 NR/m2
·
Taking into account of the basic effect.

1.4 Conditions
initial

Without object for the static analysis.
Handbook of Validation
V7.12 booklet: - HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
HSLA303 - Cylindre under pressure and thermal dilation

Date:
25/11/05
Author (S):
X. DESROCHES Key
:
V7.12.303-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

·
The deformation due to direct compression is given by:

(1 - 2v) (2R - H)

E
=
p = 3.714 X 10-3, Re = external radius
zz
4Eh

·
Axial displacement due to the pressure is given by:

Uz = Z zz

·
The deformations due to the thermal loading are worth:

= = = T
= 1.2 X 10-3
rr

Z Z

·
Radial displacement due to the thermal loading is worth:

U = R = 1.2 X 10-3 R
R
rr

2.2
Results of reference

·
Deformation and radial and axial displacement at the points A, B, C, D due to the thermal loading.
·
Deformation and axial displacement at the points A, B, C, D due to the pressure.

2.3
Uncertainty on the solution

Analytical solution.

Handbook of Validation
V7.12 booklet: - HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
HSLA303 - Cylindre under pressure and thermal dilation

Date:
25/11/05
Author (S):
X. DESROCHES Key
:
V7.12.303-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

AXIS, mesh Q 8

Cutting:
10 elements according to the length

1 element in the thickness

Limiting conditions:

in A, B
DDL_IMPO = (GROUP_NO = “A”, DY = 0. )

DDL_IMPO = (GROUP_NO = “B”, DY = 0. )

Pressure + basic effect: field U

PRES_REP:
(GROUP_MA = cont_pr, PRES = 2.E8)
FORCE_CONTOUR: (GROUP_MA = effond, FY = 1.95E9)

Thermal dilation: U1 field

char_no:

CREA_CHAMP
(AFFE = (ALL = “YES”, NOM_CMP = “TEMP”, VALE = 100.) )

char_th:

AFFE_CHAR_MECA
(TEMP_CALCULEE = char_no)

Initial deformations: U2 field

EPSI_INIT:
(ALL = “YES”, EPXX = 1.2E-3, EPYY = 1.2E-3,

EPZZ = 1.2E-3, EPXY = 0.)

Names of the nodes:

With = N1
B = N2
C = N3
D = N4

3.2
Characteristics of the grid

A number of nodes: 53

A number of meshs and types: 10 QUAD8, 22 SEG3

3.3 Functionalities
tested

Commands


“MECHANICAL” AFFE_MODELE
“AXIS”
TOUT

AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


TEMP_CALCULEE

PRES_REP
GROUP_MA
CREA_CHAMP AFFE


CALC_CHAM_ELEM OPTION
“EPSI_ELNO_DEPL”


AFFE_CHAR_MECA EPSI_INIT



Handbook of Validation
V7.12 booklet: - HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
HSLA303 - Cylindre under pressure and thermal dilation

Date:
25/11/05
Author (S):
X. DESROCHES Key
:
V7.12.303-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Results concerning the fields U1, U2, U

Field Localization Variables Reference Aster
% Reference
Field
In Ur (DX)
5.7 X 10-5
5.7 X 10-5
- 6.42 X 10-11
U1 thermics
B
Ur
(DX)
6 X 10-5
6 X 10-5
- 7.14 X 10-11
C
Ur (DX)
6 X 10-5
6 X 10-5
8.29 X 10-12
DY
1.2 X 10-3
1.2 X 10-3
3.9 X 10-10
D
Ur (DX)
5.7 X 10-5
5.7 X 10-5
1.19 X 10-11
U (DY)
1.2 X 10-3
1.2 X 10-3
3.9 X 10-10

With, M1 mesh
rr
1.2 X 10-3
1.2 X 10-3
- 1.91 X 10-10



1.2 X 10-3
1.2 X 10-3
5.54 X 10-10


zz
1.2 X 10-3
1.2 X 10-3
- 1.12 X 10-10

B, M1 mesh
rr
1.2 X 10-3
1.2 X 10-3
- 1.89 X 10-10



1.2 X 10-3
1.2 X 10-3
5.57 X 10-10


zz
1.2 X 10-3
1.2 X 10-3
- 1.16 X 10-10

C, M10 mesh
rr
1.2 X 10-3
1.2 X 10-3
- 3.74 X 10-11



1.2 X 10-3
1.2 X 10-3
1.08 X 10-10


zz
1.2 X 10-3
1.2 X 10-3
- 4.74 X 10-12

D, M10 mesh
rr
1.2 X 10-3
1.2 X 10-3
- 3.98 X 10-11



1.2 X 10-3
1.2 X 10-3
1.12 X 10-10


zz
1.2 X 10-3
1.2 X 10-3 - 2.93
x10-12
Field of
C
U (DY)
3.714 X 10-3
3.997 X 10-3
7.614
pressure U
D
U (DY)
3.714 X 10-3
3.997 X 10-3
7.614

C, M10 mesh

3.714 X 10-3
3.996 X 10-3
7.602

D, M10 mesh

3.714 X 10-3
3.996 X 10-3
7.602
U2 field
C
U
4.914 X 10-3
5.197 X 10-3
5.754
D
U
4.914 X 10-3
5.197 X 10-3
5.754
C,
net

4.914 X 10-3
5.196 X 10-3
5.746
D,
net

4.914 X 10-3
5.196 X 10-3
5.746

4.2 Remarks

·
The goal of the test is not to obtain a high degree of accuracy on the level of the results, but simply
to check the relation: U2 = U + U1; so calculation was carried out only with one grid
coarse.

·
It is noted that the required relation is well checked at the loose lead of the cylinder.

·
It is checked in addition that the field of deformation resulting from thermal dilation is
uniformly equal to 1.2 X 10-3.
Handbook of Validation
V7.12 booklet: - HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
HSLA303 - Cylindre under pressure and thermal dilation

Date:
25/11/05
Author (S):
X. DESROCHES Key
:
V7.12.303-A Page:
6/6

5
Summary of the results

Option EPSI_INIT (initial deformations into constant) provides completely satisfactory results.

Handbook of Validation
V7.12 booklet: - HT-66/05/005/A

Outline document