Inelastic Behaviour of Structures under Variable Loads PDF
Preview Inelastic Behaviour of Structures under Variable Loads
INELASTIC 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
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