Code_Aster
®
Version
5.7
Titrate:
SSLL112 - Arch circular under uniform pressure
Date:
20/08/02
Author (S):
J.M. PROIX
Key
:
V3.01.112-A
Page:
1/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.112
SSLL112 - Arch circular under uniform pressure
Summary:
This test makes it possible to check the internal efforts on the curved model of beam POU_C_T.
Code_Aster
®
Version
5.7
Titrate:
SSLL112 - Arch circular under uniform pressure
Date:
20/08/02
Author (S):
J.M. PROIX
Key
:
V3.01.112-A
Page:
2/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
1.1.1 Arch circular
R
p
B
With
X
y
Appear 1.1.1-a
Radius: R = 1 m
1.2
Properties of materials
Young modulus:
E = 2. 10
11
AP
Poisson's ratio:
= 0.3
1.3
Boundary conditions and loading
Boundary condition:
DX = DY = DZ = DRX = 0 on point A
DY = DZ = 0 on the point B
Loading: Force distributed
p = 100N/m on AB
Code_Aster
®
Version
5.7
Titrate:
SSLL112 - Arch circular under uniform pressure
Date:
20/08/02
Author (S):
J.M. PROIX
Key
:
V3.01.112-A
Page:
3/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
2
Reference solutions
2.1
Method of calculation used for the reference solutions
The beam of the figure [Fgure 1.1.1-a] checks the equilibrium equations (plane problem).
0
=
R
+
,
D
D
+
NR
,
y
y
y
V
D
DM
R
p
V
D
dN
V
-
=
=
(p: normal constant loading divided into any point of the beam).
NR (
)
, V
y
(
), M
Z
(
) indicate the efforts (normal, edge and moment bending) in a point of the vault
expressed in the local reference mark.
Their integration with the limiting conditions:
0
)
0
(
0
)
0
(
=
M
,
V
Z
y
=
give:
()
()
()
.
0
0
R
p
=
NR
,
=
M
,
V
y
-
=
2.2
Results of reference
Interior efforts for
= 0°, 6°, 42° and 60°.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Report/ratio n° 2314/A of the Institute Aerotechnics “Proposal and realization for new cases
tests missing with the validation beams ASTER “
Code_Aster
®
Version
5.7
Titrate:
SSLL112 - Arch circular under uniform pressure
Date:
20/08/02
Author (S):
J.M. PROIX
Key
:
V3.01.112-A
Page:
4/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
The model is composed of 30 elements curved beam of Timoshenko.
3.2
Characteristics of the mesh
It consists of 30 elements POU_C_T.
3.3 Functionalities
tested
Controls
AFFE_CARA_ELEM
BEAM
SECTION
RING
CALC_ELEM
OPTION
EFGE_ELNO_DEPL
SIGM_ELNO_DEPL
AFFE_CHAR_MECA
FORCE_POUTRE
VY
4
Results of modeling A
4.1 Values
tested
Type of effort
Reference
Aster Variation
(%)
V
y
(0°) 0.0000
5.E-5
5.E-5
V
y
(6°) 0.0000
5.E-5
5.E-5
NR (60°) 1.000E+02
9.99E+01
0.1
MFZ (42°) 0.0000
3.93E05
3.93E05
5
Summary of the results
The normal effort in the vault (only effort not no one) is calculated with a good precision (0,1%) for
adopted modeling.