tensinet symposium 2010, 16.-17. september 2010, sofia, bulgaria straight and curved: recent...
TRANSCRIPT
Tensinet Symposium 2010, 16.-17. September 2010, Sofia, Bulgaria
Straight and curved: Recent developments with Tensairity®
Rolf H. LuchsingerCenter for Synergetic Structures
EMPA, Swiss Federal Laboratories for Materials Testing and Research
Überlandstrasse 129, CH-8600 Dübendorf, Switzerland
Introduction
Introduction
Tensairity telescope enclosure, 12m, Tenerife, Spain, 2008, Airlight Ltd
Introduction
Tensairity roof 38 m, National Tennis Center, London, 2010, Airlight Ltd
Straight I: Tensairity column
0 1 2 3 4 5 6 7 80
2
4
6
8
10
12
buckling phase
pre-buckling phase
main compressive phase
initial phase
Measured
Co
mp
ress
ive
Lo
ad
(kN
)
Axial Displacement (mm)0 50 100 150 200 250
0
1
2
3
4
5
6
7
Measured FE FE imperfect Analytical
Slo
pe
(kN
/mm
)
Internal Air-Pressure (mbar)
p = 150 mbar
Plagianakos TS, Teutsch U, Crettol R & Luchsinger RH. Static response of a spindle-shaped Tensairity column to axial compression. Engineering Structures 31, 1822-1831 (2009)
5 m span, 16 kg mass, 11 kN max load
Wever TE, Plagianakos TS, Luchsinger RH, Marti P. Effect of fabric webs on the static response of spindle-shaped Tensairity columns. Journal of Structural Engineering ASCE 136(4), 410-418, (2010).
Straight I: Tensairity column
0 1 2 3 4 5 6 7 80
2
4
6
8
10
12
14
16
18
Plain-Spindle
p=20 mbar p=50 mbar p=150 mbar p=250 mbar
Co
mp
ress
ive
Lo
ad
(kN
)
Axial Displacement (mm)
0 1 2 3 4 5 60
2
4
6
8
10
12
14
16
18
20
22
Web-Spindle
p=20 mbar p=50 mbar p=150 mbar p=250 mbar
Com
pres
sive
Loa
d (k
N)
Axial Displacement (mm)
plain spindle web spindle
Stiffness: +100 % , Buckling load: +40%
IEpπ2H
8
γLqH
0Rpn
Tension/compressionelements:
Fabric: (~10 kN/m)
qp Air pressure: (~ 50-300 mbar)
Deflection:
H
? (Experiments, FEM)
Straight II: Tensairity beam - Basic principles
Compact transport, fast set up, light weight
Straight II: Tensairity beam
High load bearing capacity
Straight II: Tensairity beam
Beam on elastic foundation with compressive forces
qwkwdx
dHw
dx
dEI 112
2
14
4
k = ?
Tensairity beam: Analytical model
2
pk
qwwkwdx
dHw
dx
dEI )( 2112
2
14
4
0)()( 21222
2
wwkzwdx
dH
22 )(1 lxfz
Two coupled ODE´s
Tensairity beam: Analytical model
EIH
HEIk
2
2
.14
42
16
6
constwdx
dw
dx
d
32
24
1041 )cosh(1
CxCxCxCw
14
4
12
2
12 wdx
d
k
EIw
dx
d
k
Hw
k
qw
,0)(1 lw ,0)(2 lw 02
12
lx
dx
wd
220
2
)cosh( l
f
kEI
Hq
lEI
kC
221
2
24 l
f
H
q
EI
kC
212
02 6)cosh(
2lCl
CC
22
414
03 )cosh( lClCl
CC
BC:
Determination of H
dxHxwl
f
AE
sH l
),(2
0
2222
2
Tensairity beam: Analytical model
0 1 2 3 4-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
x [m]
w [m
]
p = 150 mbar
w1w2
0 1 2 3 4-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
x [m]
w [m
]
p = 300 mbar
w1w2
q=1 kN/m, q=1 kN/m,
f
lqHH
2
2
0 2202 )/(1 lxww
lL 2
fL (slenderness)
k
qww 2010
k
qLw 210 16
32
pk
Approximation
Tensairity beam: Analytical model
222
210
11
1283
1
LkAEL
w
Lqm
Tensairity beam: Analytical model
Straight III: Tensairity “madraz”
Straight III: Tensairity “madraz”
Dimension: 3 x 0.5 x 0.25 mWeight: 6.1 kg (3.7 kg metal + 2.4 kg hull) = 4 kg/m2
Load: 3.6 kN, 2.4 kN/m2, L/D = 60 Deflection: 23 mm, L/128
Straight III: Tensairity “madraz”
web - Tensairity
-1.5 -1 -0.5 0 0.5 1 1.5-25
-20
-15
-10
-5
0
span [m]
disp
lace
men
t [m
m]
distributed load 1 kN/m
analyticalexperimental
0 5 10 15 20 250
200
400
600
800
1000
1200
deflection [mm]
load
[N/m
]
analyticalexperimental
)(
)(2
2
xEI
xM
dx
wd
222
1ln2
1arctan)2ln(
32)(
l
x
l
x
l
x
EA
Lqxw
ct
Beam theory:
p = 150 mbar
LLw ctct 173.04
)2ln()0( fL
ttcc
ttccct AEAE
AEAEE
k
qLw 210 16
3
Straight III: Tensairity “madraz”
Straight IV: Foldable Tensairity
De Laet L, Luchsinger RH, Crettol R, Mollaert M, De Temmermann N. Deployable Tensairity Structures. Journal of the International Association for Shell and Spatial Structures 50 (2), 121-128 (2009)
Curved I: Tensairity arch
ABAQUS/Explicit
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
Curved I: Tensairity arch
10 m span, 90 kg mass, 3.5 ton max load
HP Gasser AG
Curved II: Tensairity kite
8 m span, 11m2 area, 3 kg mass, 1 kN max load
Breuer JMC, Luchsinger RH, “Inflatable kites using the concept of Tensairity”. Aerospace Science and Technology. doi:10.1016/j.ast.2010.04.009 (2010)
Curved and Straight: Tensairity actuator
Luchsinger RH, Bräker M. A novel pneumatic actuator with Tensairity. In: Brebbia CA (ed.) , Design & Nature V, 365-374, WIT Press, Southampton (2010)
- Recently major steps in the R&D of Tensairity have been done
- Close interaction between models, experiments, FEM and analysis
- Dedicated team
Conclusion
Conclusion