Thạc Sĩ Numerical modeling and buckling analysis of inflatable structures

Acknowledgments
During my time in Lyon, there are a number of people who have supported me both inside
and outside the lab. From my early days at IUT Lyon 1, I had many difficulties to adapt
a new life in French, which is different deeply from Vietnam. At that time, I received
a tremendous amount of help and support from the personnels of IUT Lyon 1 - Gratte
Ciel, specially Professor Christian Jardin, Mrs. Bettina Fenet and Mr. Benoit Thomas.
I would like to thank them for all their kindness during my time here.
Although being a Ph.D. student at UCBL has not always been easy and straightforward
to me, there has been so much help and support around.
First, I would like to thank my supervisors, Sylvie Ronel and Michel Massenzio for
providing me the opportunity to work with them. It is a superb experience to have them
as supervisors and learn how to face, think, approach and evaluate problems directly
from them. Sylvie Ronel with her keen insight into science of structures has always
amazed me. She has a wonderful ability to see and find beautiful things from what looks
somewhat boring and unimportant. I would like to thank her for her consistent support
and encouragement in the middle of failures and sometimes slow progresses. Also, Michel
Massenzio, who just makes everything in our group much simpler, is also thanked for
careful reading and helpful advices throughout this thesis.
In particular, I would like to thank Professor Eric Jacquelin for giving me lots of
valuable suggestions in research. He has always inspired me to see how to research in
each paper with challenging questions that I had never thought of. Those questions
always have guided and helped me gain a solid understanding of my research projects
with new insights.
Special thanks are due to Professor Le Van Anh and Professor Frédéric Lebon for their
input, for reviewing this thesis, and for being members of the graduate committee.
I would also like to thank Professor Phan Dinh Huan for being an examiner of this
thesis and a member of the graduate committee. I owe him many thanks for teaching me
i
to be a scientist. Professor Pham Huy Hoang and Mr. Nguyen Tuan Kiet are gratefully
acknowledged in the same way for their advices and encouragement.
Komla Lolonyo Apedo has been much more than a colleague and a friend to me over
the first two years. Komla and I were on the same research theme at LBMC and worked
beside together in a same office. My work is a development based on his work. Komla’s
infectious friendliness, his passion for science and his obsession with understanding have
been instrumental in making my life at LBMC joyful and productive. We spent many
memorable time wrestling the formulations, explained me to understand how an inflatable
beam is. In addition, Komla’s deep understanding of inflatable structures provided a
fantastic resource to bounce ideas back and forth several times a day.
I want to single out and thank the people I have worked most closely at Laboratory
DDS of GMP, IUT Lyon 1, especially Abdelkrim Bennani and Lagarde Gérard for their
availability.
I am also grateful for the financial support from the Vietnamese government for this
thesis and from LBMC-IFSTTAR/UCBL for my first European Conference in Austria.
Losberger Company and specially Mr. Robert Dartois are acknowledged for having
provided the material samples and inflatable beams which were very useful for the experiments
in this thesis.
Parents, to whom I have dedicated this work, have supported and encouraged me as
I worked toward this degree. Finally, I would like to thank my girlfriend for all her love
and support over the years and for her encouragement and faith in my ability to finish
the degree program. Let anyone who has contributed directly or indirectly to the success
of this project, finds here my acknowledgments.

Contents
List of Figures ix
List of Tables xv
Notations and conventions xvii
GENERAL INTRODUCTION 1
1 Textile fabric composites 2
2 Inflatable structures . 3
3 Stability of inflatable structures 3
4 Objectives 4
5 Thesis Outline 4
Chapter 1 BACKGROUND 7
1.1 Textile structures and textile preforms 9
1.1.1 Context . 9
1.1.2 Classification of textile preforms 9
1.2 Microscopic observation 16
1.2.1 Unit cell and geometric parameter . 16
1.2.2 Stress transfer and characteristics lengths . 20
1.2.3 Damage due to tensile loading . 21
1.3 Prediction of engineering properties using micro-mechanics . 24
1.4 Prediction of engineering properties using numerical approach . 26
1.5 Experimental measurement of engineering properties 29
1.6 The role of experiments in structural stability 39
v
Contents
Chapter 2 EXPERIMENTAL STUDIES 41
2.1 Introduction . 43
2.2 Mechanical behavior of the fabric . 44
2.2.1 Engineering constants . 44
2.2.2 Strain measurement . 47
2.3 Fabric tensile testing at our laboratory: Biaxial beam inflation test on
fabric beam . 48
2.3.1 Analysis of elastic moduli . 48
2.3.2 Determination of shear modulus of HOWF composite 51
2.4 Experimental buckling of an inflatable beam . 53
2.4.1 Introduction . 53
2.4.2 Experimental buckling test on a simply supported HOWF beam 54
2.4.2.1 Test set-up and instrumentation . 54
2.4.2.2 Boundary conditions . 56
2.4.2.3 Measurement of displacements . 59
2.5 Conclusion 65
Chapter 3 ANALYTICAL BUCKLING ANALYSIS OF AN HOWF INFLATABLE
BEAM 67
3.1 Introduction . 69
3.2 Theoretical background . 71
3.2.1 Kinematics . 73
3.2.2 Constitutive equations . 75
3.2.3 Virtual work principle . 77
3.2.4 Theoretical buckling loads . 85
3.2.5 Previous works on the critical load 89
3.3 Examples: in-plane buckling for linearized problems . 90
3.3.1 Simply supported inflatable beam under compressive concentrated
load . 92
3.3.2 Cantilever inflatable beam under compressive axial load at the free
end 99
3.3.3 Clamped-clamped inflatable beam under compressive axial load 101
3.4 Influence of the slenderness ratio on the critical load of an inflatable beam 106
3.5 Wrinkling load for an inflatable beam under a compressive concentrated load109
3.6 Conclusion 111
vi
Chapter 4 FINITE ELEMENT BUCKLING ANALYSIS OF AN HOWF
INFLATABLE BEAM 113
4.1 Literature review 115
4.2 Finite element formulations 118
4.2.1 Linear eigen buckling 118
4.2.2 Nonlinear buckling . 121
4.2.3 Implementation of an iterative algorithm for solving the NLIBFE
model 122
4.3 Applications and results 124
4.3.1 Linear eigen buckling 128
4.3.2 Nonlinear buckling of a simply supported NLIBFE model 132
4.3.2.1 Wrinkling loads and maximum deflections: Limit of validity
for numerical solutions 135
4.3.2.2 Validation of the NLIBFE model: the reference model 137
4.3.2.3 Comparison with the experimental results . 140
4.3.2.4 Parametric studies of NLIBFE model 142
4.4 Conclusion 145
GENERAL CONCLUSION AND FUTURE WORK 149
Appendices 155
Appendix A Reminders in mechanics and material science 155
A.1 Mechanical properties of composite materials . 155
A.2 Hyperelasticity: theoretical basis . 157
A.3 Hyperelasticity and orthotropic materials . 160
A.3.1 Orthotropic materials 160
A.3.2 St. Venant-Kirchhoff orthotropic material 162
A.4 Thin-walled structures : thin-shells and membranes . 164
Appendix B Theoretical model 171
Appendix C Nonlinear finite element model 175
Bibliography 181