Code_Aster ®
Version
6.0
Titrate:
SSNL118 - Barre subjected to a field speed of wind

Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.118-A Page:
1/6

Organization (S): EDF/TESE

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

SSNL118 - Barre 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 grid 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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL118 - Barre subjected to a field speed of wind

Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.118-A Page:
2/6

1
Problem of reference

1.1 Geometry
y
Kbx
B1
Wp
W
B
2
Kby
+o
G
Kax A1
O
X
Kay
Wind
With


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 Pa, = 1000.0 kg/m3

Mechanical characteristics of the bar: section = “CERCLE”, 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 the DDL: DX, DY, DZ
At the points A1 and B1: blocking of the DDL: DZ

Characteristics of the field speed of wind, along the axis y:

Vy wind (m/s)
20
10
1.0 1.1
12 12.1
time (dry)

1.4 Conditions
initial

The bar forms an angle of 30° (0 = 30°) compared to the axis “X”.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL118 - Barre subjected to a field speed of wind

Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.118-A Page:
3/6

2
Reference solution

2.1 Equations
of balance

Effort at the A1 point


- kxa. X
has

with displacements of the A1 point


F =
- kya. y
has
teststemxà
= L.co (S O
)/2 - L.co (S O
+)/2 + X


L. (y
a. kya.cos (+) - teststemxà
.kxa.sin (+)) /2 teststemyàs
= L.si (
N O
)/2 - L.si (
N O
+)/2 + y
O
O

Effort at the B1 point


- kxb. X
B

with displacements of the point B
1


Bfr =
- kyb. y
B
xb
= - L.co (S O
)/2 + L.co (S O
+)/2 + X


L. (- y
b.kyb.cos (+) + xb
.kxb.sin (+)) /2 yb
= - L.si (
N O
)/2 + L.si (
N O
+)/2 + y
O
O

Effort due to the wind

· Speed of the wind in a point M bars
Vvx




Vr = Vvy

with Vvx, Vvy: speed of the wind following the axis “X” and centers it “y”.
0


· Speed relating perpendicular to the bar to the point M:
Sin (qo + Q).(Vvy
-
.Cos (qo + Q) +Vvx.Sin (qo + Q))


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



0

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


Fvent = L.Cos (qo + Q). V
(vy.Cos (qo + Q) - Vvx.Sin (qo + Q))



0


Equilibrium equation: F + Bfr + Fvent = 0
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL118 - Barre subjected to a field speed of wind

Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.118-A Page:
4/6

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. Ces 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:
1
Fcx (v) =..V2.Cx (v) .D
2
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/m3.
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.
Dh: is the hydraulic diameter of the cable in Mr.

To obtain a simple analytical reference solution, the function Fcx (Vp) is taken equalizes with ||Vp||.
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 ".
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL118 - Barre subjected to a field speed of wind

Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.118-A Page:
5/6

3 Modeling
With

3.1
Characteristics of modeling and the grid

The linear element: “BARRE”
The discrete ones: “DIS_T'

3.2 Functionalities
tested

Commands



LIRE_RESU
EVOL_CHAR
VITE_VENT
AFFE_CARA_ELEM
BARRE
FCX
AFFE_CHAR_MECA
EVOL_CHAR
DEFI_FONCTION
NOM_PARA
VITE
STAT_NON_LINE
TYPE_CHARGE
SUIV
DEFORMATION
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
Obstruction memory:
20 Megawords
Time CPU To use
:
15.0 seconds
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Code_Aster ®
Version
6.0
Titrate:
SSNL118 - Barre subjected to a field speed of wind

Date:
19/08/02
Author (S):
J.L. Key FLEJOU
:
V6.02.118-A Page:
6/6

5 Synthesis

The test shows the good taking into account of the loadings of the speed type of wind on the elements
linear.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A

Outline document