Table Of ContentINELASTIC BEHAVIOUR OF STRUCTURES UNDER VARIABLE LOADS
SOLID MECHANICS AND ITS APPLICATIONS
Volume 36
Series Editor: G.M.L. GLADWELL
Solid Mechanics Division, Faculty of Engineering
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
Aims and Scope of the Series
The fundamental questions arising in mechanics are: Why?, How?, and How much?
The aim of this series is to provide lucid accounts written by authoritative research
ers giving vision and insight in answering these questions on the subject of
mechanics as it relates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it
includes the foundation of mechanics; variational formulations; computational
mechanics; statics, kinematics and dynamics of rigid and elastic bodies; vibrations
of solids and structures; dynamical systems and chaos; the theories of elasticity,
plasticity and viscoelasticity; composite materials; rods, beams, shells and
membranes; structural control and stability; soils, rocks and geomechanics;
fracture; tribology; experimental mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are
monographs defining the current state of the field; others are accessible to final
year undergraduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, see final pages.
Inelastic Behaviour
of Structures
under Variable Loads
Edited by
ZENON MRÖZ
Institute of Fundamental Technological Research,
Polish Academy of Sciences, Warsaw,
Poland
DIETER WEICHERT
Universite des Sciences et Technologies de Lille,
Villeneuve dAscq,
France
and
STANISLAW DOROSZ
Institute of Fundamental Technological Research,
Polish Academy of Sciences, Warsaw,
Poland
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A CLP. Catalogue record for this book is available from the Library of Congress
ISBN 978-94-010-4120-1 ISBN 978-94-011-0271-1 (eBook)
DOI 10.1007/978-94-011-0271-1
Printed on acid-free paper
All Rights Reserved
© 1995 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1995
Softcover reprint of the hardcover 1st edition 1995
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
CONTENTS
1. MATERIAL MODELLINGFORCYCLIC PLASTICITY
AND DAMAGE 1
Z. MROZ, P RODZIK The modified multisurface hardening model and
itsapplicationto cyclicloading problems. 3
T SIEGMUND, E. WERNER, F.D. FISCHER Structures consisting of
two-phase materialsunderthermomechanical loads. 19
E STEIN, VI HUANG Shakedown for systems of kinematic
hardening materials. 33
DA GOKHFELD, OS SADAKOV, O.F CHERNIAVSKY Related
mathematical models for solids and structures deformation and failure
processesunderrepeated loading 51
A CHERNIAVSKY Nonlinearbehaviouroflow-plastic structures. 83
2. GENERAL THEORY OFACCOMODATED INELASTIC 93
STRUCTURES UNDER VARIABLE LOADS
G. POLIZZOTTO Elastic-viscoplastic solids subjected to thermal and
loading cycles. 95
B NAYROLES Somebasicelementsoftheshakedowntheory 129
G DE SAXCE: A variational deduction of upper and lower bound
shakedowntheorems byMarkov'sand Hill's principlesoveracycle. 153
S. DOROSZ: Influence of cyclic creep on the upper bound to
shakedown inelasticdeflections 169
11 TELEGA On shakedown theorems in the presence of Signorini
conditionsand friction 183
1 SACZUK Ontheoremsofadaptationofelastic-plasticstructures. 203
I KAMENJARZH Extremum problems in shakedowntheory. 219
vi
3. INFLUENCE OF GEOMETRICAL CHANGES ON CYCLIC
RESPONSE OF STRUCTURES 237
G. MAIER, LG. PAN, U PEREGO Geometric effects on shakedown
and ratchetting ofaxisymetric cylindrical shells subjected to variable
thermal loading. 239
J. GROSS-WEEGE, D. WEICHERT: Shakedown ofshells undergoing
moderaterotations 263
A SIEMASZKO: Limit, shakedown, post-yield and inadaptation
analysesofdiscrete plasticstructures. 279
H. STUMPF Constitutive model and incremental shakedown analysis in
finite elastoplasticity. 293
J8. TRITSCH, D. WEICHERT Case studies on the influence of
geometriceffectsonthe shakedownofstructures. 309
F. BONTEMPI, F. CASCIATI Discussion ofthe chaotic behaviour of
an elastic-plasticstructure. 321
4. NUMERICAL TECHNIQUES APPLIED TO INDUSTRIAL 339
PROBLEMS,DAMAGED STRUCTURES
8. SKOCZEN, J SKRZYPEK Inadaptation mechanisms in bellows
subject to sustained pressure and cyclic axial loadings in terms offinite
deformations. 341
J ZWOLINSKI Min-max approach to shakedown and limit load
analysisfor elasticperfectly plasticand kinematic hardening materials. 363
S PYCKO: An indirect incremental method for a shakedown analysis
based onthe min-maxapproach 381
A GAWECKI, P. KRUGER: Slackened systems under variable loads. 399
H.M BONDOK, M. JANAS Plastic analysis and design of skeletal
structuresaccountingfortheir sensitivityto ratchetting 419
W GAMBIN Shakedownofrail corrugations. 433
vii
DA GOKHFELD, OS SADAKOV Steady cyclic state ofa structure
methodsofitsdirectdetermination. 449
o
MAHRENHOLTZ, PINLV An improved boundary element analysis
forthebendingofathin platewith acrack. 463
L. RAAD, D WEICHERT: Stability of pavement structures under long
term repeated loading. 473
PREFACE
This collection of papers is a state ofthe art presentation of theories and methods
related to the problem ofthe behaviour ofmechanical structures under variable loads
beyond their elastic limit In particular, the problems of shakedown, ratchetting,
transient and asymptoticcyclicstatesareaddressed.
The volume is composed of four chapters devoted to material modelling for cyclic
loading conditions; general theory of accommodated states of structures; effects of
changes ofthe geometry on the inelastic structural response; and numerical techniques
with applications to particularengineering problems. It was aimed to provide aunified
approach in order to understand both inelastic material and structural response under
variable loading conditions. The attempt to extend the classical shakedown theory of
Melan and Koiter to geometrically non-linear problems is presented in several papers.
The industrial application ofcyclic plasticity to the analysis and the design ofpressure
bellows, compensators, turbine disks, or flange connections under thermal and
pressurecyclesillustratesthegreat potential ofthe numerical techniques developed for
this purpose usingmostly min-max approaches. Thetreatment ofrailway problems and
the analysis and optimisation ofpavements are further examples ofimportant areas of
applications. Emphasis was laid on approaches that take into account the fact that
loading histories are often not precisely known Therefore, the centerofinterest lies in
otherthan step by step calculationmethods.
The volume evolved from the EUROMECH COLLOQUIUM 298 "Inelastic
Behaviour ofStructures under VariableLoads", held near Warsaw, September 14-18,
1992 However, the content does not coincide with the conference program which
contained 52 presentations covering more broadly inelastic response of structures.
Some volume contributors did not participate in this colloquium which was devoted,
just as this book, to the memory ofProfessor Jan Andrzej Konig, prominent Polish
scientist in the area of inelastic analysis of structures, and author of fundamental
contributionsto thetheory ofshakedowntheory.
The editors wish to heartily thank both the participants ofthe Euromech Colloquium
298 and the authors ofpapers for theirvaluablecontributionsto this important area of
structural mechanics. They also thank all their colleagues at the Laboratoire de
Mecanique de Lille and the Institute ofFundamental Technological Research for their
general assistancein the preparationofthefinal versionofthevolume.
Zenon MROZ, Dieter WEICHERT, Stanislaw DOROSZ
ix
INMEMORIAMJAN ANDRZEJKONIG
born 16May 1937inWarsaw
died8December 1990in Warsaw
ProfessorofMechanics
InstituteofFundamentalTechnologicalResearch
PolishAcademyofSciences
We are greatly saddened by the loss of our colleague and friend, Jan Andrzej
Konig.
Andrzej graduated in civil engineering in 1960 and in mathematics in 1963. He
startedhisresearch careerattheInstituteofFundamentalTechnologicalResearchin 1960
- all his later achievements, degrees and nominations were related to his work at the
Institute.
Andrzej is well known worldwide for his contributions in the field ofshakedown
analysis ofstructures. In fact, he pioneered a number ofdevelopments in this theory
only five years after its publication, his monograph book is now justly considered a
classic treatise on the subject. Among Andrzej's specific contributions we remember his
original and influential papers on methods of assessment of plastic deformation at
shakedown, shakedown-based optimization, novel numerical techniques for shakedown
analysis, methods for evaluation of residual stresses in inelastic structures subject to
xi
xii
variable repeated loads, fonnulations ofshakedown theory for problems with nonlinear
hardening laws, inadaptation assessment accounting for nonlinear geometrical effects,
experimental methods for shakedown evaluation, thennal effects in shakedown analysis
andmanyothers. Duringhis 30 years atthe Institute, Andrzej was also a constant source
ofnovel ideas for many other important branches ofcontemporary nonlinear mechanics.
This, together with his friendship, are today sorely missed among mechanicians in and
outside Poland; his untimely death is a great loss to the entire applied mechanics
community.
Andrzej's professional accomplishments, impressive as they were, shed little light
on him as aperson. Andrzej wasacolleague and a close friend ofmine for more than 20
years. We cooperated closely on very many different occasions - doing research and
publishingpaperstogether, beinginvolvedin the administration ofahuge, five year long
govennentalresearch projectonmechanics(ofwhich Andrzej was the chainnan and Ihis
deputy), editing a book dedicated to the late Professor Antoni Sawczuk, organizing
conferences, lecturing at symposia and courses, and finally, a fact which is not widely
known and clearly outsteps mechanics, being together on the all-Poland election
committee for a candidate running for presidency in the recent election campaign in
Poland. We also spentliterallyhundredsofhourson talking to each other in private. All
these contactsmade me think ofAndrzej as somebody oftruly exceptional personality
his knowledge ofmechanics was deep and thorough, his judgements always clear and
unbiased, hisloyaltyandfriendshipnaturalandfull ofgenuinegenerosity.
It was impossible not to like him - it came as something natural that recently,
shortly before his death, during the election ofa council to represent the Institute's staff,
Andrzej got by far the greatest number ofvotes and was then consequently elected the
chainnan ofthe body - in fact it would have been simply incomprehensible to entrust
somebodyotherthan him with thetaskofrepresentingallofusattheInstitute.
His influence on us was direct as well as indirect - his gentleness and low-key
approach to every problem, however difficult, meant that it was often only much later
thatwewereableto fully appreciatehisargumentsorsuggestions.
Andrzej never strived for credit or recognition for his accomplishments. He will
always be remembered as an example of modesty, fully devoted to research, never
awaitingspecial attention andrecognition. Ihopethatatleast some ofthe spirit and style
ofAndrzej has rubbed offon us - it is a rare, loyal and selfless spirit that enriched all
thoseclosetohim whenhewasalive, andenrichesusstillaswerememberhimtoday.
MichalKleiber
