Buckling and Postbuckling Structures: Experimental, Analytical and Numerical Studies

526 Pages·2008·41.94 MB·English

by  B. G. Falzon

Computational and Experimental Methods in Structures – Vol. 1
BUCKLING AND POSTBUCKLING
STRUCTURES
Experimental, Analytical and Numerical Studies
Computational and Experimental Methods in Structures
Series Editor: Ferri M. H. Aliabadi (Imperial College London, UK)
Vol. 1 Buckling and Postbuckling Structures: Experimental, Analytical and
Numerical Studies
edited by B. G. Falzon and M. H. Aliabadi
(Imperial College London, UK)
Vol. 2 Advances in Multiphysics Simulation and Experimental Testing
of MEMS
edited by A. Frangi, C. Cercignani (Politecnico di Milano, Italy),
S. Mukherjee (Cornell University, USA) and N. Aluru (University of
Illinois at Urbana Champaign, USA)
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Computational and Experimental Methods in Structures
Editorial Board
Ramon Abascal Peter Gudmundson Eugenio Onate
Escuela Superior de Ingenieros Department of Solid CIMNE, UPC, Barcelona
Camino de los descubrimientos Mechanics Spain
Spain KTH Engineering Sciences
Spiros Pantelakis
Sweden
B. Abersek Department of Mechanical
University of Maribor Mario Gugalinao Engineering and Aeronautics
Slovenia University of Milan, Italy University of Patras, Greece
K. J. Bathe David Hills Carmine Pappalettere
Massachusetts Institute of Lincoln College Department of Engineering
Technology, USA Oxford University, UK Bari University, Italy
A. Chan R. Huiskes (Rik) K. Ravi-Chandar
Department of Engineering Department of Biomedical Department of Aerospace
University of Birmingham Engineering Engineering and
UK Eindhoven University of Engineering Mechanics
Technology University of Texas at Austin
P. Dabnichki
The Netherlands USA
Department of Engineering
Queen Mary, Ian Hutchings A. Sellier
University of London Institute for Manufacturing LadHyX. Ecole Polytechnique
UK University of Cambridge Palaiseau cedex, France
UK
M. Denda Jan Sladek
Department of Mechanical and Alojz Ivankovic Slovak Academy of Sciences
Aerospace Engineering Department of Mechanical Slovakia
Rutgers University Engineering
Paulo Sollero
USA University College Dublin
University of Campinas
Ireland
Manuel Doblare Brasil
Department of Mechanical Pierre Jacquot
J. C. F. Telles
Engineering Nanophotonics and Metrology
COPPE, Brasil
Aragón Institute of Laboratory
Engineering Research Swiss Federal Institute of Ole Thybo Thomsen
Spain Technology Lausanne Department of Mechanical
Switzerland Engineering
M. Edirisinghe
Aalborg University
Department of Engineering Wing Kam Liu
Denmark
University College London Department of Mechanical
UK Engineering Kon-Well Wang
Northwestern University The Pennsylvania State
H. Espinosa
USA University
Mechanical Engineering
USA
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USA Technische Universität Wien J. Woody
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Brian Falzon
Technology Environmental Engineering
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Austria UCLA, USA
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Ugo Galvanetto
Department of Mechanical University of Siegen
Department Engineering
Engineering Germany
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Imperial College London
Italy
UK
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Computational and Experimental Methods in Structures – Vol. 1
BUCKLING AND POSTBUCKLING
STRUCTURES
Experimental, Analytical and Numerical Studies
edited by
B G Falzon & M H Aliabadi
Imperial College London, UK
Imperial College Press
ICP
Published by
Imperial College Press
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Computational and Experimental Methods in Structures — Vol. 1
BUCKLING AND POSTBUCKLING STRUCTURES
Experimental, Analytical and Numerical Studies
Copyright © 2008 by Imperial College Press
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ISBN-13978-1-86094-794-0
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PREFACE

The use of slender or thin-walled construction in aeronautical, space,
civil, maritime and offshore structures, necessitates the need to consider
their stability under compressive loads. A number of case histories exist
which attribute structural failure to buckling. These include the collapse
of silos, bridges still under construction, oil platforms and structural
failure of aircraft operating beyond their design ultimate loads. In most
cases, the desire to utilise this form of construction arises from the need
to minimise weight. This is the primary objective in the development of
aircraft structures where a light airframe leads to reduced payload costs
which, in turn, minimises environmental impact. The emergence of
carbon-fibre composites, with their superior specific weight and stiffness,
has greatly contributed to the development of even lighter structures.
New generations of aircraft are utilising an increased level of this
material in their primary structure and the possibility of developing
postbuckling primary composite aerostructures paves the way for the
development of very lightweight airframes. Composites also have the
added advantage that they do not corrode and have excellent fatigue
properties compared to metals.

This book brings together a number of established researchers in the
field of structural stability and presents the state-of-the-art. An emphasis
is placed on the structural stability of composite structures. Despite their
obvious advantages, their anisotropic nature, coupled with a relatively
weak through-thickness strength, present numerous challenges to the
structural analyst. It will be shown that more sophisticated tools are
required to characterise their structural response. The results of a
number of experimental programmes are also presented which enhance
our understanding of stability phenomena and serve as a valuable
database for validating numerical and analytical models.

In the design of plate structures, it has been known for decades that a
metallic plate, suitably supported along its edges, may be designed to
carry load beyond initial buckling. Further demonstrations followed
v
vi B. G. Falzon & M. H. Aliabadi
whereby thin-skinned panels, with stiffeners attached, were shown to be
capable of sustaining load beyond initial skin-buckling. In the 1980s a
number of papers were published highlighting the same postbuckling
load-carrying capability in thin-skinned composite structures with
stiffeners co-cured, co-bonded or secondary bonded onto the skin. Most
of these experimental studies were conducted under uniaxial loading and
a number of numerical studies, using the finite element method (FEM),
were undertaken to predict their structural response.

Chapter 1 builds on this experimental database by presenting the
results of a new experimental programme where curved stiffened
composite panels, which are arguably more representative of wing or
fuselage sections, are loaded in compression until failure. Torsion boxes,
constructed from two of these stiffened panels, mounted on aluminium
side panels, are also tested in compression, torsion and combined
loading. This work formed part of a large European Union funded
programme. In Chapter 2, experimental results on stiffened cylindrical
shells under loading conditions similar to those used on the boxes in
Chapter 1 are presented. Indeed, this work also formed a part of the same
research programme and together these two chapters present a wealth of
experimental results which yield valuable insight into the postbuckling
response of thin-skinned composite structures and may be used reliably
in the validation of analytical or computational models.

In Chapter 3, the observed phenomenon of ‘mode-jumping’, where
highly postbuckled structures undergo secondary instabilities beyond
initial buckling, is discussed and the difficulties that this poses to
standard nonlinear finite element solution schemes are highlighted. A
numerical methodology is proposed which combines aspects of quasi-
static implicit and pseudo-transient schemes. This is shown to be robust
and capable of predicting mode-jumping with good accuracy.

The central aim of Chapter 4 is to provide less conservative
guidelines for the design of imperfection-sensitive composite shell
structures. A similar experimental procedure to Chapter 2 is followed
whereby geometric imperfections are measured on a set of composite
Preface vii
shells which are subsequently tested in compression and combined
compression-torsion loading. These measured imperfections are used to
determine a manufacturing-process-specific imperfection signature for
the shells.

Chapter 5 also deals with stiffened composite structures. A number
of curved stiffened panels, with different lay-up, dimensions and material
system to the ones presented in Chapter 1, are tested in uniaxial
compression. The challenges presented to numerical analysis support the
concerns raised in Chapter 3 and a nonlinear finite element solution
strategy, using commercially-available finite element software, is
presented. Collectively, the first five chapters attest to the interest in
characterising the structural behaviour of thin-walled stiffened structures
which predominate most advanced composite airframe construction.

The anisotropy associated with composite materials is hardly ever
exploited and is often seen as a hindrance in the design of composite
structures. This is partly due to the added analytical complexity which
must be dealt with even at a preliminary design stage. In Chapter 6,
buckling and postbuckling formulae are derived for anisotropic plates
and shells which demonstrate the structural efficiency that may be gained
by utilising this anisotropy. These expressions are particularly useful at a
preliminary design stage prior to the use of numerical methods for
detailed analysis and design. The use of genetic algorithms and a finite-
strip buckling analysis program to optimise the buckling load of stiffened
composite panels is presented in Chapter 7.

Tubes and pipelines find widespread use in engineering applications
across scales ranging from millimetres to kilometres. Their susceptibility
to local buckling, when subjected to bending or external pressure
loads, is demonstrated through the non-linear finite element method in
Chapter 8. Both metallic and composite tubes and pipelines are
considered and the problem of delamination in composite tubes under
external pressure is discussed at some length.
viii B. G. Falzon & M. H. Aliabadi
Chapter 9 presents a mixed variational finite element formulation for
the modelling of imperfection-sensitive spherical caps subjected to an
external pressure load. The results obtained from the numerical
modelling are validated using a comprehensive experimental programme
where initial geometric imperfections on thin membrane polymer caps
were measured prior to loading.

The use of sandwich construction, where metallic (or, indeed,
composite) face sheets are bonded onto a softer core, are being
increasingly utilised in the design of advanced lightweight structures.
Chapter 10 deals with the complex global and local instabilities which
may arise in such structures. Instabilities in these types of structures are
also investigated in Chapter 13.

In Chapter 11, boundary element method (BEM) formulations for the
analysis of the buckling and postbuckling of plates and shells are
explained. This provides an alternative numerical approach to the more
established traditional one of using the finite element method. A special
feature of the BEM presented, is its ability to model nonlinear problems
and still retain its boundary only modelling philosophy.

Chapter 12 presents a progressive failure analysis of compression-
loaded composite structures where a novel approach for accounting for
fibre microbuckling, a highly localised instability which leads to
structural failure, is presented. Highly localised instabilities in cellular
materials, at the micro and meso levels, are modelled in Chapter 13 using
detailed finite element analysis. This chapter shows how instabilities at
the micro level propagate to create instabilities at higher levels leading to
structural failure at much larger length scales.

In developing this book, we have endeavoured to ensure that enough
introductory material was included in each chapter to make it accessible
to a wider readership. Engineering graduates new to this field can gain an
overview of our current understanding of structural stability and the
strategies being adopted to model this behaviour. Researchers, academics
and practicing engineers who are familiar with these issues will find it