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The non‐linear behaviour of inflatable structures, collapse load and windtunnel analysis

Alexis Bloch (PhD)

Thesis Supervisor: Marc FRANCOISCo‐supervisor : Jean‐Christophe THOMASCo‐supervisor: Olivier FLAMAND (CSTB)

GUIMARÃESSeptember 9th, 2015

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• Context

• Models development and improvement

• New measurement methods

• Experimental works

• Conclusions

Outlines

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• Membrane structures are increasly used in C.Eng :

Campus Luigi Einaudi, Turin.

© Michele D'Ottavio

© AIA Lyon

Great Mosquee of Paris. 

© Abaca ‐ N. Pauli

Wealthness center, Montpellier. Solar Impulse Sheltering building.

Inflatable dome for football ground.

Pressurized MembranesMechanicallytensioned membranes

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Context

• How to define limit‐states for inflable beams ?

Serviceability Limit State (SLS) Ultimate Limit State (ULS)Associated to the structural state, or some parts ofthe structure, creating limited damage or makingthe structure unuseable in respect with designrecommendations defined at the begining of theproject. (functionability, aspect,…).

Related to a partial or total collapse of the structureand call into questions the safety of shelteredpeople or equipment.

©J. Llorens

SLS Examples. ULS Examples.

©AP

Thesis context :• SLS : Wrinkle and displacement• ULS : Collapse 

Context

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• Theoretical developments :

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Wrinkle apparition :Loss of linear behaviour

Collapse

v(m)

F(N)

Load‐displacement curve for an inflatable beam under 3 points bending.

Aims :1. Identify the collapse load for an inflatable beam.2. Describe the post‐wrinkling behaviour.

Wrinkle propagates CollapseLinearpart

Comer et Levy (1963)Fichter (1966)

Main et al. (1995)Le Van et al. (2005)Apedo et al. (2009)Nguyen et al. (2015)

Stein et al. (1964)Ligaro et Barsotti (2012)

Comer et Levy (1963)Stein et al. (1964))

Wielgosz et al. (2002)Thomas (2002)

Ligaro et Barsotti (2012)

Models

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• Collapse load :

Hypothesis : 1. Circular cross‐section

Hypothesis :1. Linear stress distribution2. Negligible ovalization in cross‐section

Before wrinkling After wrinkling

Development on initial configuration (pressurized beam) :

Models

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• Collapse load :Before Wrinkling

After Wrinkling

ANALOGY

…equal 0 for π/2 !

Bending moment in cross‐section (initial configuration) :

Definition of the cross‐section ficticious second moment of  area:

Models

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• Experimental validation:

d = 0.206m

L = 4mF

Steel roll (grease)Target positioned at

L/2

Inflationdevice

p=0.25bar

Equipment : Pressure Sensor, Force Sensor, Elphel camera

Experimental set‐up overview.

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F702

F302

F1202

pli (théorie)

ruine (théorie) v(m)

F(N)

load‐displacement curves. Experimental set‐up.

Models

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• Describing displacements:

The relation between the bending moment and the wrinkle angle of aperture shows that several sections are partially wrinkled, it is a non‐local phenomenon

Example – beam under 3 points bending:

Deflection and section rotation conservation

Equilibrium equations:

mf> mwrinkle mf < mwrinkle

ϕ0> 0 ϕ0= 0

Models

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• Numerical – analytical comparison

Comparison between numerical and experimental deflection curves

Models

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Gap 3,4%

Gap 3,9%

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• Numerical validation of hypothesis

Cross‐section shape evolution.

Slack region overview.

Assumptions:

p = 0,3 barl = 4mr = 0,135 m

Fc = 188 N

Fw = 116 N = 61% Fw

Models

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• Modification of beam finite element

Models

Comparison between numerical (3D and FE models) and experimental deflection curves

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Stiffness matrix (Thomas, Jiang, Wielgosz, 2004)

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• Adressed issue :Large displacements : need for specific toolsFull‐field measurement, contactless method.

• Virtual Image Correlation (VIC) :From DIC [Semin, François]: Initial state is a virtual image.The virtual image is created from a reference solution (theoretical or numerical).The virtual image ranges from black (0) to white (1) to ensure the contour detection.

Virtual Image Construction.

Before VIC After VIC

VIC Principle.

Measurement

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• Virtual Image Correlation (VIC) :Inflatable beam under 3 points flexure (test) :

Kf 3xKfKc

Identification (VIC) : Kf = 0,0247 (0,0250 applied);  Kc = 0,0127 (0,0125 applied);   

VIC Principle.

Measurement

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• 2 campaigns completed :

Inflatable beam under bendingHalf‐cylindrical inflatable building

Presentation of experimental works.

Experimental works

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• Bending in windtunnel :

Experiemental Set‐Up:

Objectives : quantify the beam displacement using VIC, Collapse and displacementmodel  validation, estimate the model quality.

Experimental Set‐up.

Experimental works

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• Bending in windtunnel, results:

20 m/s0.3 bar

Experimental works

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• Bending in windtunnel, results:

20 m/s0.3 bar

Experimental works

VIC is usable in windtunnel but limited…18

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• More complex structure – cylindrical building:

Experimental works

Gustave Eiffel’s aerodynamic laboratory (1909),  this wind tunnel is still operating today

Since the first wind tunnels exist, downscaling has been an essential task inaerodynamics

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• Building reduced‐scale models : Vashy‐Buckingham theorem

Experimental works

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• More complex structure – cylindrical building:

SG1 SG2 SG3

Panorama of manufactured structures.

Experimental works

Objectives : 

• Identify wrinkle and collapse load.

• Study the external pressure field.

• Measure displacement and confirm the ability to develop a similitude law.

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• Real beam‐based building : Looking for the wrinkle and collapse loads.

p = 0,03 bar

Experimental works

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Expected : wrinkle 26 m/s and collapse 35 m/s  

Expected : wrinkle 45 m/s and collapse 60 m/s  

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• Real beam‐based building : external pressure‐field

p = 0,03 bar

Experimental works

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Sensors geometry

Sensors quality test

wind

• Real beam‐based building : external pressure‐field

p = 0,03 bar

Experimental works

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ConicalEllipticalReferenceMean values

pressure

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• Real beam‐based building : external pressure‐field

p = 0,03 bar

Experimental works

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• Real beam‐based building : external pressure‐field

p = 0,03 bar

Experimental works

Plauta0 = ‐0.258a1=0.488a2=0.476a3=0.328a1=0.1

Exp.a0 = ‐0.186a1=0.301a2=0.504a3=0.205a1=‐0.026 26

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• Real beam‐based building : global behaviour

Experimental works

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• Real beam‐based building : displacements

p = 0,03 bar

Experimental works

VIC reference :  Finite‐element inflatable beam

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SG3

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• Real beam‐based building : displacements

Experimental works

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• Real beam‐based building : displacements

Experimental works

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SG1

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Experimental works

• Real beam‐based building : similitudes

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• Definition of limit‐states in terms of displacements and collapse load.• Post‐wrinkling displacements model• Efficient measurement method• Tools to build reduced‐scale model for inflatable structures

• Use the VIC to identify the model stiffness and adapt the similitude ratios.

Conclusions :

To be continued :

Conclusions 

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