background image
Code_Aster
®
Version
6.0
Titrate:
SSNL118 - Bar subjected to a field speed of wind
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.118-A
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
Organization (S):
EDF/TESE















Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.118



SSNL118 - Bar 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 representing 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:
SSNL118 - Bar subjected to a field speed of wind
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.118-A
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
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 bar: 1.5m
Stiffnesses of the discrete ones: Kax, kay, kbx, kby
1.2
Properties of materials
Material for the linear element: E = 2.0E+08 AP,
= 1000.0 kg/m
3
Mechanical characteristics of the bar: section = “CIRCLE”, radius = 0.5 m, ep = 0.5 m
Stiffness of the springs:
Kxa Kya Kxb Kyb
10 NR/m
20 NR/m
25 NR/m
30 NR/m
1.3
Boundary conditions and loadings
At points A and b: blocking of
DDL
:
DX
,
DY
,
DZ
At the points A1 and B1: blocking of
DDL
:
DZ
Characteristics of the field speed of wind, along the axis y:
Vy wind (m/s)
time (dry)
1.0 1.1
12 12.1
10
20
1.4 Conditions
initial
The bar forms an angle of 30° (
0
= 30°) compared to the axis “X”.
background image
Code_Aster
®
Version
6.0
Titrate:
SSNL118 - Bar subjected to a field speed of wind
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.118-A
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
2
Reference solution
2.1 Equations
of balance
Effort at the A1 point
F =
()
(
)
()
(
)
-
-
+
-
+






=
-
+
+
=
-
+
+
kxa teststemxà
kya teststemyà
L
teststemyà kya
teststemxà kxa
With
teststemxà
L
L
X
teststemyà
L
L
y
O
O
O
O
O
O
.
.
.(
.
.cos (
)
.
.sin (
)) /
.cos
/
.cos
/
.sin
/
.sin
/

2
1
2
2
2
2
with displacements of the point
Effort at the B1 point
Bfr =
()
(
)
()
(
)
-
-
-
+
+
+






= -
+
+
+
= -
+
+
+
kxb xb
kyb yb
L
yb kyb
xb kxb
B
xb
L
L
X
yb
L
L
y
O
O
O
O
O
O
.
.
.(
.
.cos (
)
.
.sin (
)) /
.cos
/
.cos
/
.sin
/
.sin
/

2
1
2
2
2
2
with displacements of the point
Effort due to the wind
·
Speed of the wind in a point M
bar
V
R
=
Vvx
Vvy
0






with 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
p
=
Sin qo Q
Vvy Cos qo Q
Vvx Sin qo Q
Cos qo Q Vvy Cos qo Q
Vvx Sin qo Q
(
).(
.
(
)
.
(
))
(
).(
.
(
)
.
(
))
+
-
+
+
+
+
+
-
+






0
·
Force due to the wind in a point M
Fvent
(M)
= Fcx
(M)
.
V
||V ||
p
p
in our case one chooses Fcx
(M)
= ||V
p
||
one thus obtains Fvent
(M)
= V
p
·
Resultant of the force due to the wind on the bar
Fvent =
L Sin qo Q
Vvy Cos qo Q
Vvx Sin qo Q
L Cos qo Q Vvy Cos qo Q
Vvx Sin qo Q
.
(
).(
.
(
)
.
(
))
.
(
).(
.
(
)
.
(
))
+
-
+
+
+
+
+
-
+






0
Equilibrium equation: F + Bfr + Fvent = 0
background image
Code_Aster
®
Version
6.0
Titrate:
SSNL118 - Bar subjected to a field speed of wind
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.118-A
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
2.2
Sizes and results of reference
Displacements of the points A1 and B1 at the moments: 1. S, 1.05 S and 2. S. These moments correspond
respectively at speeds of wind of 10, 15 and 20m/s
The resolution of the 3 equilibrium equations, projection of “F + Bfr + Fvent = 0”, is done by iterations.
3 unknown factors of the problem are the position of the center of gravity of the bar G: (X, y) and variation of
the angle:
.
In Code_Aster, the effect of the wind is taken into account by a force distributed along the element
linear. The expression of the module of this force distributed is as follows:
Fcx
(v)
=
1
2
.
.V
2
.Cx (v) .D
H
where Fcx
(v)
: is the module of the force distributed along the cable in NR/m, depend on speed.
: is the density of the air in kg/m
3
.
V: is the relative speed of the cable in m/s.
Cx (v): is the coefficient of drag of the cable, depend on relative speed.
D
H
: is the hydraulic diameter of the cable in Mr.
To obtain a simple analytical reference solution, the Fcx function
(Vp)
is taken equalizes with ||V
p
||.
In the command file of Code_Aster the function of Fcxv is thus in the following way defined
:
FCXV=DEFI_FONCTION (
NOM_PARA=' VITE',
VALE= (
0.0,
0.0,
10.0,
10.0),
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
)

2.3
Uncertainties on the solution
None. The resolution of the equilibrium equation is done by iterations with a <1.0E-09 error.

2.4 Reference
bibliographical
[1]
HM77/01/046/A. “M7-01-70 Project. The evolution of Code_Aster for best taken in
count loadings of dynamic wind on the linear elements ".
background image
Code_Aster
®
Version
6.0
Titrate:
SSNL118 - Bar subjected to a field speed of wind
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.118-A
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
3 Modeling
With
3.1
Characteristics of modeling and the mesh
The linear element: '
BAR
'
The discrete ones: '
DIS_T
'
3.2 Functionalities
tested
Controls
LIRE_RESU
EVOL_CHAR
VITE_VENT
AFFE_CARA_ELEM
BAR
FCX
AFFE_CHAR_MECA
EVOL_CHAR
DEFI_FONCTION
NOM_PARA
QUICKLY
STAT_NON_LINE
TYPE_CHARGE
DEFORMATION
SUIV
PETIT_REAC

4
Results of modeling A
4.1
Sizes tested and results
Balance is calculated at the moments: 1. S, 1.05 S and 2. S.
Balance to 1. S
Analytical
Code_Aster
Relative error
teststemxà (m)
­ 0.2092 ­ 0.2036
0.026
teststemyà (m)
0.3276 0.3270
0.002
xb (m)
­ 0.1418 ­ 0.1434
0.011
yb (m)
0.1965 0.1945
0.010
Balance to 1.05 S
Analytical
Code_Aster
Relative error
teststemxà (m)
­ 0.2885 ­ 0.2816
0.024
teststemyà (m)
0.5050 0.5029
0.004
xb (m)
­ 0.1942 ­ 0.1962
0.010
yb (m)
0.3105 0.3074
0.010
Balance to 2. S
Analytical
Code_Aster
Relative error
teststemxà (m)
­ 0.3502 ­ 0.3423
0.023
teststemyà (m)
0.6890 0.6850
0.006
xb (m)
­ 0.2327 ­ 0.2352
0.011
yb (m)
0.4324 0.4279
0.010
4.2 Parameters
of execution
Version:
6.02.07
Machine:
IRIX64
Overall dimension memory:
20 Megawords
Time CPU To use
:
15.0 seconds
background image
Code_Aster
®
Version
6.0
Titrate:
SSNL118 - Bar subjected to a field speed of wind
Date:
19/08/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.118-A
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
5 Synthesis
The test shows the good taking into account of the loadings of the speed type of wind on the elements
linear.