Code_Aster
®
Version
8.2
Titrate:
DEMO005 - Thin cylinder under hydrostatic pressure
Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key
:
V3.06.104-A
Page:
1/6
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA, DeltaCAD
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
Document: V3.06.104
DEMO005 - Thin cylinder under pressure
hydrostatic
Summary:
Case-test DEMO005 is a very simple example of use of Code_Aster. It makes it possible to illustrate them
controls “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 modelize the problem, the mesh representing a vertical section of the cylinder.
One calculates displacements and the stresses in the vertical section of the cylinder.
Code_Aster
®
Version
8.2
Titrate:
DEMO005 - Thin cylinder under hydrostatic pressure
Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key
:
V3.06.104-A
Page:
2/6
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
P
R = 1 m
L = 4 m
Appear 1.1-a: geometrical Characteristics 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 10
11
AP
·
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 ² 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.
Z
y
X
Code_Aster
®
Version
8.2
Titrate:
DEMO005 - Thin cylinder under hydrostatic pressure
Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key
:
V3.06.104-A
Page:
3/6
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A
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 10
6
DX out of B
1
4.6528 10
6
DX out of C
1
1.2022 10
6
DY out of C
1
- 2.6396 10
6
DX in D
1
3.3102 10
9
DY in D
1
- 2.8170 10
6
Displacements are expressed in meters.
2.3
Uncertainty on the solution
Reference solution: not regression
Code_Aster
®
Version
8.2
Titrate:
DEMO005 - Thin cylinder under hydrostatic pressure
Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key
:
V3.06.104-A
Page:
4/6
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
The cylinder is modelized in elements axisymmetric 2D.
ldf
lfa
support
charg
With
B
C
D
y
X
Discretization:
- 5 meshs according to X
- 20 meshs following y
Appear 3.1-a: longitudinal Section of the cylinder
3.2
Characteristics of the mesh
The longitudinal section of the cylinder is represented by a regular mesh 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 lock 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.
Code_Aster
®
Version
8.2
Titrate:
DEMO005 - Thin cylinder under hydrostatic pressure
Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key
:
V3.06.104-A
Page:
5/6
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A
3.3
Command file Aster
·
BEGINNING: obligatory control to start
·
Reading of mesh (PRE_GMSH) and generation of mesh (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 mesh 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 locked at the base of the cylinder on the level of the group of
meshs SUPPORT.
·
Resolution of the linear elastic problem (MECA_STATIQUE).
Calculation of displacements and the stresses at the points of Gauss of each element to be left
displacements.
·
Calculation of the stresses 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 stresses of all the mesh.
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.
·
END: obligatory control to close an execution.
3.4 Notice
For modeling “AXIS”, the axis of revolution is always axis Y.
Code_Aster
®
Version
8.2
Titrate:
DEMO005 - Thin cylinder under hydrostatic pressure
Date:
01/09/05
Author (S):
J. LAVERNE, F. LEBOUVIER
Key
:
V3.06.104-A
Page:
6/6
Manual of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A
4
Results of modeling A
4.1 Values
tested
Identification unit Reference Aster %
difference
DX in A
m
4.6814 10
6
4.6814
10
6
0.
DX out of B
m
4.6528 10
6
4.6528
10
6
0.
DX out of C
m
1.2022 10
6
1.2022
10
6
0.
DY out of C
m
- 2.6396 10
6
- 2.6396
10
6
0.
DX in D
m
3.3102 10
9
3.3102
10
9
0.
DY in D
m
- 2.8170 10
6
- 2.8170
10
6
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.