Code_Aster
Version
8.2
Titrate:
DEMO005 - Thin Cylindre under hydrostatic pressure

Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER Key
:
V3.06.104-A Page:
1/6

Organization (S): EDF-R & D/AMA, DeltaCAD

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
Document: V3.06.104

DEMO005 - Thin Cylindre under pressure
hydrostatic

Summary:

Case-test DEMO005 is a very simple example of use of Code_Aster. It makes it possible to illustrate them
commands “impossible to circumvent” on the calculation of a tank.

The thin cylindrical tank is subjected to a variable pressure with the height corresponding to one
hydrostatic pressure.

Since the geometry and the loading are axisymmetric, an axisymmetric modeling 2D is
chosen to model the problem, the grid representing a vertical section of the cylinder.

One calculates displacements and the constraints in the vertical section of the cylinder.
Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster
Version
8.2
Titrate:
DEMO005 - Thin Cylindre under hydrostatic pressure

Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER Key
:
V3.06.104-A Page:
2/6

1
Problem of reference

1.1 Geometry

R = 1 m
y
X
P
Z
L = 4 m

Appear 1.1-a: Caractristiques geometrical and loadings

Selected geometrical dimensions are as follows:


height
L = 4 m

average radius
R = 1 m

thickness
E = 0.02 m

1.2
Properties of material

The cylinder consists of a homogeneous material (steel) which follows an elastic law of behavior
linear:


Young modulus:

E = 2.1 1011 Pa

Poisson's ratio:
= 0.3

1.3
Boundary conditions and loadings

The pressure P is applied to the internal wall of the cylinder. This pressure varies linearly: it
is worth 20.000 NR/m at the base of the cylinder and 0 in the high part.

Following displacements at the base of the cylinder are null there, the cylinder can move radially.

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster
Version
8.2
Titrate:
DEMO005 - Thin Cylindre under hydrostatic pressure

Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER Key
:
V3.06.104-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solution is obtained numerically. It is thus only about one test of not
regression.

2.2
Results of modeling

Urgent displacements Reference
DX in A
1
4.6814 106
DX out of B
1
4.6528 106
DX out of C
1
1.2022 106
DY out of C
1
- 2.6396 106
DX in D
1
3.3102 109
DY in D
1
- 2.8170 106

Displacements are expressed in meters.

2.3
Uncertainty on the solution

Reference solution: not regression
Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster
Version
8.2
Titrate:
DEMO005 - Thin Cylindre under hydrostatic pressure

Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER Key
:
V3.06.104-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

The cylinder is modelled in elements axisymmetric 2D.


y
D
C
ldf
Discretization:

- 5 meshs according to X
- 20 meshs following y
charg
lfa
B
In support
X

Appear longitudinal 3.1-a: Coupe of the cylinder

3.2
Characteristics of the grid

The longitudinal section of the cylinder is represented by a regular grid containing:


136 elements (6 POI1, 30 SEG2, 100 QUAD4).

126 nodes.

Creations of groups of meshs for the application of the loading and the limiting conditions:

support: to block vertical displacement
ldf, lfa: to apply a variable pressure to the part cylinder interns.

Creations of groups of nodes:

WITH, B, C, D: used to note displacements in these characteristic nodes.
Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster
Version
8.2
Titrate:
DEMO005 - Thin Cylindre under hydrostatic pressure

Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER Key
:
V3.06.104-A Page:
5/6

3.3
Command file Aster


DEBUT: obligatory command to start


Reading of grid (PRE_GMSH) and generation of grid (LIRE_MAILLAGE).


Definition of groups of nodes and meshs for the assignment of the loading and of
limiting conditions (DEFI_GROUP).


Definition of the finite elements used (AFFE_MODELE).
One assigns to all the meshs grid modeling AXIS.


Definition and assignment of material (DEFI_MATERIAU and AFFE_MATERIAU).
The mechanical characteristics are identical on all the structure.

Assignment of the loading: Definition of a function representing the pressure P on the face
intern of cylinder (DEFI_FONCTION), then assignment of the pressure on the internal edges
cylinder represented by the groups of meshs LDF and LFA (AFFE_CHAR_MECA_F).

Assignment of the boundary conditions (AFFE_CHAR_MECA).
Displacements following there are blocked at the base of the cylinder on the level of the group of
meshs APPUI.


Resolution of the linear elastic problem (MECA_STATIQUE).
Calculation of displacements and the constraints at the points of Gauss of each element to be left
displacements.


Calculation of the constraints to the nodes.
One calculates the stress field to the nodes of each element from
displacements (CALC_ELEM).


Impression of results (IMPR_RESU).
One prints in form listing the displacement and the constraints of all the grid.
One also prints the field of displacement to format GMSH, for a visualization
results with GMSH.


Tests relating to the values of displacements to nodes A, B, C, D. (TEST_RESU)
These tests make it possible to check nonthe regression of the code.


FIN: obligatory command to close an execution.

3.4 Notice

For modeling “AXIS”, the axis of revolution is always axis Y.
Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster
Version
8.2
Titrate:
DEMO005 - Thin Cylindre under hydrostatic pressure

Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER Key
:
V3.06.104-A Page:
6/6

4
Results of modeling A

4.1 Values
tested

Identification unit Rfrence Aster %
difference
DX in A
m
4.6814 106 4.6814
106 0.
DX out of B
m
4.6528 106 4.6528
106 0.
DX out of C
m
1.2022 106 1.2022
106 0.
DY out of C
m
- 2.6396 106 - 2.6396
106 0.
DX in D
m
3.3102 109 3.3102
109 0.
DY in D
m
- 2.8170 106 - 2.8170
106 0.

5
Summary of the results

Following displacements X are relatively important at the base of the cylinder, where the loading
is highest. One can note that following displacements there of the high part of the cylinder
are negative, which was foreseeable with the sight of the problem.

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Outline document