Code_Aster ®
Version
6.0
Titrate:
SDNL102 - Poutre subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. Key FLEJOU
:
V5.02.102-A Page:
1/6
Organization (S): EDF/ERMEL/PEL
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
Document: V5.02.102
SDNL102 - Poutre 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 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
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Code_Aster ®
Version
6.0
Titrate:
SDNL102 - Poutre subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. Key FLEJOU
:
V5.02.102-A Page:
2/6
1
Problem of reference
1.1 Geometry
y
Kbx
B1
Wp
W2
Kby
+o
B
G
Kax A1
O
X
Kay
Wind
With
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 = “CERCLE”, 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 modelled 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”.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Code_Aster ®
Version
6.0
Titrate:
SDNL102 - Poutre subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. Key FLEJOU
:
V5.02.102-A Page:
3/6
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
Mr. X "
Mr. = Mr. y
G
“
Mr. L
2
. “
12
Effort at the A1 point
- kxa. teststemxà
with displacements of the A1 point
F =
- kya. teststemyà
X
= L.Co (S has
O
)/2 - L.Co (S O
+)/2 + X
L
=.
/2 -.
+/2 +
.(y
a. kya.
(
Cos +) - X
a. kxa.
(
Sin +)
teststemyà
L If
/2
(N
O)
L If (
N O
)
y
O
O
Effort at the B1 point
- kxb. xb
with displacements of the B1 point
Bfr =
- kyb. yb
X
B = - L.Co (S
O
)/2 + L.Co (S O
+)/2 + X
L
= -.
/2 +.
+/2 +
.(- y
b.kyb.
(
Cos +) + xb.kxb.
(
Sin +)
yb
L If
/2
(N
O)
L If (
N O
)
y
O
O
Effort due to the wind
·
Relative speed of a point M
Vvx + S. (
Sin
. ' '
O +)
- X
V = Vvy
- S.
(
Cos O
+).'- y
R
'
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:
(
Sin
O
+).(- Vvy.
(
Cos O
+) +Vvx. (
Sin O
+) + S
. '-
(
Sin O
+) .x'+
(
Cos O
+) .y) '
V =
(
Cos
.
.
.
. '
. '
O +) (Vvy
(
Cos O +) - Vvx
(
Sin O +) - S +
(
Sin O +) X - Co (
S O +) .y
p
) '
0
Force due to the wind in a point M
V
Fvent
p
(
=
=
M)
F (
cx M).
in our case one chooses FC (
X M)
Vp
Vp
one thus obtains
(
Fvent) = V
M
p
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Code_Aster ®
Version
6.0
Titrate:
SDNL102 - Poutre subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. Key FLEJOU
:
V5.02.102-A Page:
4/6
·
Resultant of the force due to the wind on the bar
L.S (
in
O
+). (- Vvy + y) '.
(
Cos O
+) + (Vvx - X) '.S (
in O
+)
Fvent = L.Co (
S O
+). (Vvy - y) '.Co (S O
+) + (- Vvx + X) '.Si (
N O
+)
- L3
.'/12
Final equation of dynamics
Mr. = 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.
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Code_Aster ®
Version
6.0
Titrate:
SDNL102 - Poutre subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. Key FLEJOU
:
V5.02.102-A Page:
5/6
3 Modeling
With
3.1
Characteristics of modeling and the grid
The linear element: “beam” cut out in 12 meshs.
The discrete ones: “DIS_T'
3.2 Functionalities
tested
Commands
LIRE_RESU EVOL_CHAR VITE_VENT
AFFE_CARA_ELEM BEAM
FCX
AFFE_CHAR_MECA EVOL_CHAR
DEFI_FONCTION NOM_PARA
VITE
DYNA_NON_LINE TYPE_CHARGE
SUIV
DEFORMATION
PETIT_REAC
4
Summary of the results
4.1
Sizes tested and results
Time
Analytical
Code_Aster
Absolute error
Relative error
2.0sec
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
Analytical
Code_Aster
Absolute error
Relative error
3.0sec
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
Analytical
Code_Aster
Absolute error
Relative error
4.0sec
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
Analytical
Code_Aster
Absolute error
Relative error
5.0sec
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
Analytical
Code_Aster
Absolute error
Relative error
6.0sec
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
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Code_Aster ®
Version
6.0
Titrate:
SDNL102 - Poutre subjected to a field speed of wind
Date:
12/04/02
Author (S):
J.L. Key FLEJOU
:
V5.02.102-A Page:
6/6
0.800
Displacement (m)
Rotation (Rd)
0.600
0.400
0.200
0.000
0.0
1.0
2.0
3.0
4.0
5.0
6.0
- 0.200
Time
(dryness)
- 0.400
- 0.600
- 0.800
- 1.000
X Theoretical
Y Theoretical
Rz Théorique
- 1.200
X Aster
Y Aster
Rz Aster
- 1.400
Comparison enters the theoretical results and those of Code_Aster.
4.2 Parameters
of execution
Version:
6.0
Machine:
IRIX64
Obstruction memory: 30 Megawords
Time CPU To use: 75.0 seconds
Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
HR-17/02/019/A
Outline document