Code_Aster ®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow Cylindre


Date:
19/10/01
Author (S):
I. DEBOST Key
:
V7.01.101-A Page:
1/6

Organization (S): EDF/MTI/MN

Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of the structures
axisymmetric
V7.01.101 document

HPLA101 - Elastic thermo hollow Cylindre.
Derived compared to a variation from field

Summary

The purpose of this test is to test calculations of derived from the temperature, displacements and the constraints by
report/ratio with a variation of field (variation of the radius interns tube), under thermal dilation.

The analytical solution of reference for the mechanical thermo fields is described in the document
[V7.90.03]. The derivative are calculated by Mathematica. One has the results for modeling
following:

·
axisymmetric 2D: isoparametric finite elements axisymmetric QUAD8.
Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow Cylindre


Date:
19/10/01
Author (S):
I. DEBOST Key
:
V7.01.101-A Page:
2/6

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
thermo elasticity are: E =
5 NR mm2 =
=
=
= - 5 °C-
2 10
0 3
1
0
10
1
.
/
.

(dilation coefficient).

1.3
Boundary conditions and loadings

Thermal dilation: T (R) - T
= 0 5
. (T + T) + 2.(T + T) (R - R)/H
ref.
E
I
E
I


with:

T = 0 5
. °C, T = - 0 5
. °C, T
= 0. °C
E
I
ref.


where

1
R - R
T (R) = (T + T) +
(T - T
I
E
E
I)
2
H


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.

Vertical displacements are blocked on all the structure.
Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow Cylindre


Date:
19/10/01
Author (S):
I. DEBOST Key
:
V7.01.101-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

To refer to the document [V7.90.03].

The analytical results of reference are:

·
temperatures,
·
displacements,
·
axial stress.

One deduces the derivative from it from the temperature, displacements and axial stresses by report/ratio
with a variation of IH (with Mathematica) in the thickness of the cylinder.
Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow Cylindre


Date:
19/10/01
Author (S):
I. DEBOST Key
:
V7.01.101-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

Finite elements 2D axisymmetric

D J
10
C
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 Functionalities
tested

Commands
AFFE_MODELE AFFE
MODELISATION
“AXIS”
AFFE_CHAR_MECA TEMP_CALCULEE


MODEL MECA_STATIQUE


CHAM_MATER
SENSIBILITE
CALC_THETA
THETA_BANDE
OPTION: “BANDE”

THER_LINEAIRE SENSITIVITY

CALC_ELEM SENSITIVITY


CALC_NO OPTION
:
“DETE_NOEU_DLTE”


“DEDE_NOEU_DLDE”


“DESI_NOEU_DLSI”

Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow Cylindre


Date:
19/10/01
Author (S):
I. DEBOST Key
:
V7.01.101-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification

Reference
Precision
Aster
% difference
Derived from T compared to IH in A (N120): ­ 1
10­3 ­ 1
1.07
10­12

F (N69):
­ 0.5
10­3 ­ 0.5 1.78
10­13
Derived from DX compared to IH in a:
8.2804 10­6 10­3 8.2792
10­6 4.05
10­5

F:
1.1902 10­6 10­3 1.1903
10­6 ­ 2.46
10­4
Derived from Siyy compared to IH out of F:
1.42491
10­3 1.42493
­ 2.70
10­4

4.2 Remarks

Good results.
The derivative of the constraints compared to a variation of field in the zone close to the radius
intern are very sensitive to the refinement of the grid.

4.3 Parameters
of execution

Version: 5.04.20

Machine: SGI 02000 claster

Obstruction memory: 64 Mo
Time CPU To use: 6.94 seconds
Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
HPLA101 - Elastic thermo hollow Cylindre


Date:
19/10/01
Author (S):
I. DEBOST Key
:
V7.01.101-A Page:
6/6

5
Summary of the results

One obtains good results for the derivative eulériennes of the temperature and displacements
compared to a variation of field. For the derivative of the constraints, one needs a very fine grid
radially.
Handbook of Validation
V7.01 booklet: Thermomechanical stationary linear of axisymmetric structures HI-75/01/010/A

Outline document