Wrinkling of thin sheets under tension Aerospace Engineering

103 Pages·2015·4.26 MB·English

by  Rita Carvalho

Wrinkling of thin sheets under tension

Rita Valente de Carvalho

Thesis to obtain the Master of Science Degree in
Aerospace Engineering

Supervisor: Prof. Nuno Miguel Rosa Pereira Silvestre

Examination Committee

Chairperson: Prof. Filipe Szolnoky Ramos Pinto Cunha
Supervisor: Prof. Nuno Miguel Rosa Pereira Silvestre
Member of the Committee: Prof. Miguel António Lopes de Matos Neves

November 2015

Abstract

Wrinkling of thin membranes has become a huge concern in aerospace engineering due to the
widespread of membrane structures in aerospace applications. The wrinkling of these lightweight
structures is often observed and deteriorates their surface accuracy. Being thought that surface
accuracy is a fundamental requirement in the manipulation and design of the membranes, it is necessary
to evaluate the wrinkling of these materials in order to control and mitigate the wrinkling phenomenon.
In this work, a study of the wrinkling phenomenon in thin rectangular sheets subjected to uniaxial
tension is presented, including the wrinkle profile, the stress field and several parameters that influence
this phenomenon.
First, experimental tests on specimens with different thicknesses and plane dimensions are
performed. Using a tri-dimensional digital image correlation technique (VIC-3D), the images of a
rectangular 𝐾𝑎𝑝𝑡𝑜𝑛 𝐻𝑁® sheet in tension are captured to investigate the evolution of the wrinkles, in
terms of amplitude and wavelength.
Then, a numerical study using the commercial finite element package ABAQUS is made based on
the physical model of the membrane, with the aim to assess the growth, the evolution and the
characteristics of the wrinkles. For that, a buckling and geometrically nonlinear analyses of the
membranes are performed, using thin-shell elements.
After that, the numerical validation of the results is made through the comparison with the numerical
solutions available in published literature as well as the comparison with the experimental data obtained
in this dissertation. Finally, some concluding remarks and future developments are described.

Key words: wrinkling, membrane, buckling, finite element method, non-linear analysis.

i
ii
Resumo

O enrugamento de membranas finas tem-se tornado uma preocupação em engenharia
aeroespacial dada a vasta utilização destas estruturas em aplicações aeroespaciais. O enrugamento
da membrana é frequentemente observado, degradando a precisão da superfície do material, a qual
constitui um requisito fundamental na utilização e dimensionamento destas estruturas. Neste contexto
é necessário avaliar o enrugamento nestes materiais para controlo e mitigação desse fenómeno.
Neste trabalho, o estudo do fenómeno de enrugamento em folhas finas retangulares sujeitas a
forças de tensão uniaxial é apresentado, incluindo o perfil das rugas presentes na membrana, bem
como, o campo de tensões envolvido e diversos parâmetros que afetam este fenómeno.
Primeiramente, são feitos testes experimentais a provetes de diferentes espessuras e dimensões.
Usando uma técnica tridimensional digital de correlação de imagem (VIC-3D), são captadas as imagens
da membrana de 𝐾𝑎𝑝𝑡𝑜𝑛 𝐻𝑁® em tensão de forma a averiguar a evolução das rugas, no que concerne
à amplitude e comprimento de onda das mesmas.
Posteriormente, um estudo numérico usando o programa comercial de elementos finitos ABAQUS
é feito baseado no modelo físico da membrana de forma a obter o crescimento, a evolução e as
características das rugas. Para tal, uma análise de instabilidade linearizada (ou Euler) e outra estática
geometricamente não-linear são simuladas, usando elementos de casca fina.
Em seguida, a verificação numérica dos resultados é feita através de resultados disponíveis em
literatura referentes ao mesmo modelo e, ainda, pela comparação com os resultados experimentais
obtidos na presente dissertação. Finalmente, algumas conclusões e desenvolvimentos futuros são
descritos.

Palavras-chave: Enrugamento, membrana, análise de instabilidade linearizada (ou Euler), método de
elementos finitos, análise não linear.
iii
iv
Acknowledgments

This dissertation represents the end of a unique and unforgettable journey and the support given
by several people was essential for the conclusion of my Master’s degree.
Firstly, I would like to express my gratitude to Professor Nuno Silvestre for the opportunity of
working with him. Since the first day, constant invaluable help and advice were fundamental for the
development of this dissertation.
I also have to manifest my acknowledgment to Claudia Schmidt from DuPont and Maite Fernández,
Coraline Perron and Silvia Silva from Isovolta for efficiently dealing with the process of transporting the
material.
A key help in this journey was given by my colleague Joel Pinheiro and Professor Pedro Amaral,
who continuously provide me the tools, the time, the knowledge and the dedication much above needed
for this thesis.
I would also like to thank the courage and love given by my family, especially by my parents, Lúcia
and Rui, to whom I owe everything I am. They continuously dare me to expand my horizons and show
me their unconditional support.
Additionally, I would like to remember and to thank the people who were present since the first day
of my course in this university, my long-time friends João Ferro, José Bruno Pinto, André Sousa, João
Frazão, Sara Monte, Rita Vieira and Joana Matos, to whom I give responsibility for my success and
accomplishments. I could never forget the friendship and the irreplaceable support and motivation given
along this period of my life.
This appreciation would not be complete if I didn’t mention my boyfriend Tomás Viana who has
always given me his love, respect and admiration. I could have never walked through this journey without
you and words cannot express my gratitude for your friendship and for the support in every single day
of this adventure.

“Serendipity is the way to make discoveries, by accident but also by sagacity, of things one is not in
quest of. Based on experience, knowledge, it is the creative exploitation of the unforeseen.”
Adrian Bejan, Mechanical Engineer at MIT
v
vi
Contents

Abstract......................................................................................................................................................i
Resumo ................................................................................................................................................... iii
Acknowledgments ....................................................................................................................................v
List of figures ........................................................................................................................................... ix
List of tables ............................................................................................................................................ xi
List of acronyms and symbols ............................................................................................................... xiii
1. Introduction ...................................................................................................................................... 1
1.1 Scope ....................................................................................................................................... 1
1.2 Wrinkling phenomena .............................................................................................................. 1
1.3 Membrane structures in Aerospace and other Applications .................................................... 4
1.3.1 Solar Sails ........................................................................................................................ 4
1.3.2 Membrane Mirrors in Space Telescopes ......................................................................... 5
1.3.3 Sunshields ....................................................................................................................... 5
1.3.4 Inflatable Reflector Antennas .......................................................................................... 6
1.3.5 Other applications ............................................................................................................ 7
1.4 Objectives ................................................................................................................................ 9
1.5 Organization of contents ........................................................................................................ 10
2 Literature review ............................................................................................................................ 11
2.1 Wrinkling Criterion ................................................................................................................. 11
2.2 Analytical studies ................................................................................................................... 13
2.2.1 Tension field theory ....................................................................................................... 13
2.2.2 Variable Poisson’s Ratio theory ..................................................................................... 16
2.2.3 Theories with finite bending stiffness ............................................................................ 16
2.3 Numerical studies .................................................................................................................. 23
2.4 Scope of Present Study ......................................................................................................... 25
3 Experimental Studies ..................................................................................................................... 27
3.1 Material characterization ....................................................................................................... 27
3.2 Set-up .................................................................................................................................... 30
3.2.1 Specimen Preparation ................................................................................................... 30
3.2.2 Test Procedure .............................................................................................................. 31
3.3 Results ................................................................................................................................... 33
3.3.1 Wrinkle Profile ................................................................................................................ 33
3.3.2 Discussion ..................................................................................................................... 38
4 Numerical Studies ......................................................................................................................... 41
4.1 Finite Element Method for Wrinkling Analysis ....................................................................... 41
4.2 Analysis Procedure ................................................................................................................ 42
4.2.1 Initial Conditions ............................................................................................................ 43
4.2.2 Buckling analysis ........................................................................................................... 43
vii
4.2.3 Nonlinear Analysis ......................................................................................................... 44
4.3 Finite Element Model – Reference Case ............................................................................... 45
4.4 Sensitivity of FE Model .......................................................................................................... 48
4.4.1 Type of FE ..................................................................................................................... 48
4.4.2 Refinement of FE Mesh ................................................................................................. 49
4.4.3 Sensitivity to the perturbation ........................................................................................ 50
4.4.4 Stabilizing Factor ........................................................................................................... 52
4.5 Results ................................................................................................................................... 52
4.5.1 Buckling Modes and critical strains ............................................................................... 52
4.5.2 Wrinkling Profile ............................................................................................................. 55
4.5.3 Stress Distribution.......................................................................................................... 59
5 Model Validation ............................................................................................................................ 65
5.1 Numerical Model from the literature ...................................................................................... 65
5.2 Experimental Validation ......................................................................................................... 69
6 Conclusions and future work ......................................................................................................... 75
6.1 Conclusions ........................................................................................................................... 75
6.2 Future Developments ............................................................................................................ 77
7 References .................................................................................................................................... 79
A. Eigenvalue buckling analysis ..................................................................................................... 83
B. Experimental results .................................................................................................................. 85

viii