Inelastic Behaviour of Structures under Variable Repeated Loads

CISM COURSES AND LECTURES Series Editors: The Rectors Manuel Garcia Velarde - Madrid Mahir Sayir - Zurich Wilhelm Schneider - Wien The Secretary General Bernhard Schrefier - Padua Former Secretary General Giovanni Bianchi - Milan Executive Editor Carlo Tasso- Udine The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences. INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 432 . f'J"'V1h ~ ~o• B CISM -"'lliJ\J" INELASTIC BEHAVIOUR OF STRUCTURES UNDER VARIABLE REPEATED LOADS DIRECT ANALYSIS METHODS EDITED BY DIETER WEICHERT RHEINISCH-WESTFALISCHE TECHNISCHE HOCHSCHULE AACHEN ~ GIULIO MAIER POLITECNICO DI MILANO Springer-Verlag Wien GmbH This volume contains 166 illustrations This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2002 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 2002 SPIN 10877360 In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader. ISBN 978-3-211-83687-3 DOI 10.1007/978-3-7091-2558-8 ISBN 978-3-7091-2558-8 (eBook) PREFACE The integrity assessment of structural elements susceptible to operate beyond the elastic limits under variable repeated thermo-mechanical loads is an important task in many situations of structural engineering. Examples of such situations can be found in both mechanical and civil engineering (transportation technologies, pressure vessels, general machinery, constructions such as dams, pavements, offshore platforms, pipelines and buildings in seismic zones). The so-called "direct" or "simplified" methods based on the shakedown theorems and their specialisation to limit theorems are receiving increasing attention for the prediction of structural failure in the inelastic range, although they basically originated decades ago within classical plasticity. Reasons for such revival are, first, that these methods provide the information which are essential in practice (e.g. safety factor and collapse mechanisms) by means ofprocedures potentially more economical than step-by-step inelastic analysis; second, they only need a minimum of information on the evolution of loads as functions of time (many technical problems do not permit to assume the precise knowledge of the loading history for time-marching simulations). These methods are the subject of the present book. It reflects the lectures held in the framework of the CISM-Course "Inelastic Behaviour of Structures under Variable Repeated Loads" which took place at Udine in October 2000. The volume includes the presentation of the foundations and recent developments of shakedown theory and of limit analysis as particular case. Both the so-called static and the kinematic approach and related bounding methods are discussed, as well as new developments based on advanced material models. The addressed audience are engineers and scientists active in research and development in the following fields: structural engineering (mechanical and civil engineering), inelastic behaviour of structures, safety and reliability of structures and structural elements, computational and materials mechanics. The book is composed of seven main chapters, according to the number of lecturers. Each lecturer is the responsible author of his individual part, eventually thematically subdivided and co-authored. Basically, the structure of the book follows that of the course: The first chapter is mainly devoted to the mathematical foundations and the variational formulation of shakedown theory, followed by a second chapter on limit- and shakedown analysis by using the kinematic approach and on new extensions to poroplasticity. The third chapter deals with shakedown analysis for dynamic systems and materials with temperature-dependent yield limits, including damage. Also upper bound techniques on history dependent quantities are presented in this part. Material modelling, the influence of geometrical effects as well as finite-element formulations for shakedown and limit analysis are subject of the fourth chapter. The fifth chapter focuses on the numerically particularly efficient linear matching method for shakedown analysis with examples of application to technical problems. The combination of 'shakedown- and reliability analysis as well as structural optimisation under constraints are the subject of the sixth chapter. In the seventh chapter, the relation between high cycle fatigue modelling and shakedown theory is discussed, including the problem of multiaxial polycyclic fatigue criteria. The editors express their gratitude to all the authors who made possible by their efforts this state-of-the-art presentation of the theory of direct methods and their applications to engineering problems. Although this volume is not intended to be comprehensive, we believe that it gives to the reader a fruitful introduction into the fast moving field of research in direct methods. Special thanks go to Dr. A. Hachemi for his valuable help in putting the book into final shape. Dieter Weichert Giulio Maier CONTENTS Chapter 1 Basic Definitions and Results by G. de Saxce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Variational Formulation by G. de Saxce ........................................ ........................................ ............. 27 Nature of the Solutions by G. de Saxce ........................................ ........................................ ............. 41 Implicit Standard Materials by G. de Saxce and L. Bousshine ........................................ ............................... 59 Shakedown with Non Associated Flow Rule by G. de Saxce and J.-B. Tritsch ........................................ ............................... 77 Chapter 2 Fundamentals of Direct Methods in Poroplasticity by G. Maier and G. Cocchetti ........................................ .................................. 91 A Kinematical Method for Shakedown and Limit Analysis of Periodic Heterogeneous Media by G. Maier and V. Carvelli ........................................ .................................... 115 Chapter 3 Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques by C. Polizzotto, G. Borino and P. Fuschi ........................................ .................. 133 Shakedown of Structures Accounting for Damage Effects by C. Polizzotto, G. Borino and P. Fuschi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Chapter4 Advanced Material Modelling in Shakedown Theory by D. Weichert and A. Hachemi ........................................ .............................. 203 Shakedown ofThin-Walled Structures with Geometrical Non-Linear Effects by D. Weichert and A. Hachemi ........................................ .............................. 229 Application of Shakedown Theory and Numerical Methods by D. Weichert and A. Hachemi ........................................ ............................... 239 Chapter 5 A Linear Matching Method for Shakedown Analysis by A. R. S. Ponter ........................................................................................ 267 Chapter6 Shakedown, Limit, lnadaptation and Post-Yield Analysis by A. Siemaszko .......................................................................................... 319 Limit and Shakedown Reliability Analysis by A. Siemaszko .......................................................................................... 333 Computational Methods for Shakedown and Limit Reliability Analysis by A. Siemaszko .......................................................................................... 345 Limit and Shakedown reliability Optimization Accounting for Nonlinear Geometric Effects by A. Siemaszko .......................................................................................... 361 Chapter 7 Application of Shakedown Theory to Fatigue Analysis of Structures by K. D. Van .............................................................................................. 377