Code_Aster
®
Version
6.4
Titrate:
SSLV301 - Cylindrical beam comforts under load linearly distributed
Date
:
17/06/03
Author (S):
X. DESROCHES
Key
:
V3.04.301-A
Page:
1/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
Document: V3.04.301
SSLV301 - Cylindrical beam comforts under load
linearly distributed
Summary:
The goal of the test is to validate a load linearly distributed, starting from an analysis 2D with decomposition in
Fourier series of the load.
2 calculations here are carried out:
·
a calculation with the first 2 modes (0 and 1),
·
a calculation with the first 10 modes.
Code_Aster
®
Version
6.4
Titrate:
SSLV301 - Cylindrical beam comforts under load linearly distributed
Date
:
17/06/03
Author (S):
X. DESROCHES
Key
:
V3.04.301-A
Page:
2/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
Length
: L
= 0.240 m
Radius
: R
= 0.006 m
1.2
Material properties
E = 2.1 X 10
11
NR/m
2
= 0.3
1.3
Boundary conditions and loadings
·
Embedded edge AB
·
Load varying linearly according to Z on generator BC, being worth:
Q = 0 out of C and Q = 3000 NR/m out of B
1.4 Conditions
initial
Without object for the static analysis.
C
Code_Aster
®
Version
6.4
Titrate:
SSLV301 - Cylindrical beam comforts under load linearly distributed
Date
:
17/06/03
Author (S):
X. DESROCHES
Key
:
V3.04.301-A
Page:
3/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is obtained analytically [bib1].
2.2
Results of reference
·
Radial displacement of the point C: U
rc
= 1.552 X 10
3
m
·
Stresses of embedding at point b:
zz
(B) = 169.8 X 10
6
AP
2.3
Uncertainty on the solution
Analytical solution.
2.4 Reference
bibliographical
[1]
S. TIMOSHENKO: Resistance of materials, 1ère left. Polytechnic bookstore
CH. Béranger, Paris, 1947
Code_Aster
®
Version
6.4
Titrate:
SSLV301 - Cylindrical beam comforts under load linearly distributed
Date
:
17/06/03
Author (S):
X. DESROCHES
Key
:
V3.04.301-A
Page:
4/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS_FOURIER, T6 mesh
Cutting: 80 elements according to the length
2 elements in the thickness
3.2
Characteristics of the mesh
A number of nodes: 805
A number of meshs and types: 320 TRIA6
3.3 Functionalities
tested
Controls
“MECHANICAL” AFFE_MODELE “AXIS_FOURIER”
ALL
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO
AFFE_CHAR_MECA_F FORCE_CONTOUR
GROUP_MA
COMB_FOURIER NOM_CHAM
“DEPL”
“SIGM_ELNO_DEPL”
CREA_CHAMP “EXTR”
R
B
With
D
Z
C
Code_Aster
®
Version
6.4
Titrate:
SSLV301 - Cylindrical beam comforts under load linearly distributed
Date
:
17/06/03
Author (S):
X. DESROCHES
Key
:
V3.04.301-A
Page:
5/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
Values provided for
= 0.
Standard localization
of
value
Reference
Aster
% difference
Calculation 1 (2 modes)
Not C
U
R
(m)
1.552 X 10
3
1.54839 X 10
3
0.232
Not B
zz
(AP)
169.8 X 10
6
168.73 X 10
6
0.63
Calculation 2 (10 modes)
Not C
U
R
(m)
1.552 X 10
3
1.54839 X 10
3
0.232
Not B
zz
(AP)
169.8 X 10
6
168.59 X 10
6
0.71
4.2 Notice
The values of the arrow of the beam and the stress of embedding are obtained with precision
with the first two modes only.
Code_Aster
®
Version
6.4
Titrate:
SSLV301 - Cylindrical beam comforts under load linearly distributed
Date
:
17/06/03
Author (S):
X. DESROCHES
Key
:
V3.04.301-A
Page:
6/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/03/008/A
5
Summary of the results
The results resulting from calculation are in concord with the analytical solution.