background image
Code_Aster
®
Version
6.0
Titrate:
SDNL102 - Beam subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. FLEJOU
Key
:
V5.02.102-A
Page:
1/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Organization (S):
EDF/ERMEL/PEL















Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
Document: V5.02.102



SDNL102 - Beam subjected to a field speed
of wind


Summary:

This test relates to the validation of the application of the loadings of wind on the linear elements.
loading is described by fields speeds of wind.

This problem makes it possible to test:
·
linear finite elements [bars, cables, beams (except the curved beams)] with loadings
follower of nature “wind”,
·
loadings using speeds of wind:
- reading of the data of the fields of wind,
- projection of the fields of wind attached to the scatter plot on the mesh deformed of
structure,
- calculation relative speed,
·
the taking into account of the function giving the force distributed according to the relative speed of
structure,
·
the reactualization of the geometry to take account of great displacements and large
rotations.
background image
Code_Aster
®
Version
6.0
Titrate:
SDNL102 - Beam subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. FLEJOU
Key
:
V5.02.102-A
Page:
2/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
1
Problem of reference
1.1 Geometry
G
+
O
Kay
X
y
O
Wind
W
2
Kax
Kby
Kbx
Wp
With
B
A1
B1
Length of the beam: 1.5m
Stiffnesses of the discrete ones: Kax, kay, kbx, kby
1.2
Properties of material
Material for the linear element: E = 2.0E+10,
= 1000.0
Characteristics mechanics of the beam: section = “CIRCLE”, radius = 0.1, ep = 0.1
Stiffness of the springs:
Kxa Kya Kxb Kyb
10 NR/m
20 NR/m
25 NR/m
22 NR/m
1.3
Boundary conditions and loadings
At points A and b: blockings of the DDL: DX, DY, DZ
At the points A1 and B1: blockings of the DDL: DZ, DRX, DRY
The springs are modelized by the discrete ones without dimensions. The nodes A and A1, B and B1 are
geometrically confused.
Characteristics of the field speed of wind, along the axis y:
Vy = 20.Sin (
.t), with = 2. .f and F = 0.2 Hz
1.4 Conditions
initial
The beam forms an angle of 30° (
0
= 30°) compared to the axis “X”.
background image
Code_Aster
®
Version
6.0
Titrate:
SDNL102 - Beam subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. FLEJOU
Key
:
V5.02.102-A
Page:
3/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
2
Reference solution
2.1 Equations
of balance
The study is carried out around the initial position of the structure in the xy plan. The equations are
written in the center of gravity of the beam.
Effort of inertia
M
M X
M y
MR. L
G
.
. “
. “
.
. “
=








2
12
Effort at the A1 point
(
)
(
)
(
)
()
(
)
()
(
)
F
kxa teststemxà
kya teststemyà
L teststemyà kya Cos
teststemxà kxa Sin
teststemxà
L Cos
L Cos
X
teststemyà
L Sin
L Sin
y
O
O
O
O
O
O
=
-
-
+
-
+








=
-
+
+
=
-
+
+
.
.
.
.
.
.
.
/
.
/
.
/
.
/
.
/

2
2
2
2
2
with displacements of the A1 point
Effort at the B1 point
(
)
(
)
(
)
()
(
)
()
(
)
Bfr
kxb xb
kyb yb
L
yb kyb Cos
xb kxb Sin
xb
L Cos
L Cos
X
yb
L Sin
L Sin
y
O
O
O
O
O
O
=
-
-
-
+
+
+








= -
+
+
+
= -
+
+
+
.
.
.
.
.
.
.
/
.
/
.
/
.
/
.
/

2
2
2
2
2
with displacements of the B1 point
Effort due to the wind
·
Relative speed of a point M
(
)
(
)
V
Vvx S Sin
X
Vvy S Cos
y
R
O
O
=
+
+
-
-
+
-








.
. '
'
.
. '
'
0
with
S: the curvilinear X-coordinate of the point M on the beam S
[­ L/2, L/2]
Vvx, Vvy: speed of the wind following the axis “X” and centers it “y”.
·
Speed relating perpendicular to the bar to the point M:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
V
Sin
Vvy Cos
Vvx Sin
S
Sin
X Cos
y
Cos
Vvy Cos
Vvx Sin
S
Sin
X Cos
y
p
O
O
O
O
O
O
O
O
O
O
=
+
-
+
+
+
+
-
+
+
+
+
+
-
+
-
+
+
-
+




.
.
.
. '
. '
. '
.
.
.
. '
. '
. '
0
Force due to the wind in a point M
()
()
Fvent
Fcx
V
V
M
M
p
p
=
.
in our case one chooses
()
Fcx
V
M
p
=
one thus obtains
()
Fvent
V
M
p
=
background image
Code_Aster
®
Version
6.0
Titrate:
SDNL102 - Beam subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. FLEJOU
Key
:
V5.02.102-A
Page:
4/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
·
Resultant of the force due to the wind on the bar
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
Fvent
L Sin
Vvy y Cos
Vvx X Sin
L Cos
Vvy y Cos
Vvx X Sin
L
O
O
O
O
O
O
=
+
-
+
+
+
-
+
+
-
+
+ -
+
+
-




.
.
'.
'.
.
.
'.
'.
. '/12
3
Final equation of dynamics
M
F Bfr Fvent
G
.
=
+
+
2.2
Sizes and results of reference
Displacements and rotation of the point G at the moments: 2.0sec, 3.0sec, 4.0sec, 5.0sec and 6.0sec.
2.3
Uncertainties on the solution
None. The resolution of the equilibrium equation is done by a method of integration of Runge Kutta
of command 4.
background image
Code_Aster
®
Version
6.0
Titrate:
SDNL102 - Beam subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. FLEJOU
Key
:
V5.02.102-A
Page:
5/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
3 Modeling
With
3.1
Characteristics of modeling and the mesh
The linear element: “beam” cut out in 12 meshs.
The discrete ones: “DIS_T'
3.2 Functionalities
tested
Controls
LIRE_RESU EVOL_CHAR VITE_VENT
AFFE_CARA_ELEM BEAM
FCX
AFFE_CHAR_MECA EVOL_CHAR
DEFI_FONCTION NOM_PARA
QUICKLY
DYNA_NON_LINE TYPE_CHARGE
DEFORMATION
SUIV
PETIT_REAC


4
Summary of the results
4.1
Sizes tested and results
Time
2.0sec
Analytical
Code_Aster
Absolute error
Relative error
X (m)
­ 0.27571
­ 0.27500
0.00070
0.00255
y (m)
0.46478
0.46358
0.00120
0.00259
Rz (rd)
­ 0.04851
­ 0.04850
0.00001
0.00027
Time
3.0sec
Analytical
Code_Aster
Absolute error
Relative error
X (m)
­ 0.43640
­ 0.43522
0.00118
0.00271
y (m)
0.68149
0.67959
0.00190
0.00279
Rz (rd)
­ 0.16767
­ 0.16688
0.00079
0.00472
Time
4.0sec
Analytical
Code_Aster
Absolute error
Relative error
X (m)
­ 0.21266
­ 0.21223
0.00043
0.00201
y (m)
0.07494
0.07605
0.00111
0.01476
Rz (rd)
­ 0.15769
­ 0.15743
0.00026
0.00163
Time
5.0sec
Analytical
Code_Aster
Absolute error
Relative error
X (m)
0.30290
0.30182
0.00108
0.00357
y (m)
­ 0.98487
­ 0.97951
0.00536
0.00544
Rz (rd)
0.11188
0.11162
0.00027
0.00241
Time
6.0sec
Analytical
Code_Aster
Absolute error
Relative error
X (m)
0.59847
0.59815
0.00032
0.00054
y (m)
­ 1.24735
­ 1.24413
0.00322
0.00258
Rz (rd)
0.44284
0.44534
0.00251
0.00566
background image
Code_Aster
®
Version
6.0
Titrate:
SDNL102 - Beam subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. FLEJOU
Key
:
V5.02.102-A
Page:
6/6
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
- 1.400
- 1.200
- 1.000
- 0.800
- 0.600
- 0.400
- 0.200
0.000
0.200
0.400
0.600
0.800
0.0
1.0
2.0
3.0
4.0
5.0
6.0
X Theoretical
Y Theoretical
Rz Théorique
X Aster
Y Aster
Rz Aster
Time
(dryness)
Displacement (m)
Rotation (Rd)
Comparison enters the theoretical results and those of Code_Aster.

4.2 Parameters
of execution
Version:
6.0
Machine:
IRIX64
Overall dimension memory: 30 Megawords
Time CPU To use: 75.0 seconds