This collection of papers is a state of the art presentation of theories and methods related to the problem of the behaviour of mechanical structures under variable loads beyond their elastic limit In particular, the problems of shakedown, ratchetting, transient and asymptotic cyclic states are addressed. 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 of the geometry on the inelastic structural response; and numerical techniques with applications to particular engineering problems. It was aimed to provide a unified 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 of cyclic plasticity to the analysis and the design of pressure bellows, compensators, turbine disks, or flange connections under thermal and pressure cycles illustrates the great potential of the numerical techniques developed for this purpose using mostly min-max approaches. The treatment of railway problems and the analysis and optimisation of pavements are further examples of important areas of applications. Emphasis was laid on approaches that take into account the fact that loading histories are often not precisely known Therefore, the center of interest lies in other than step by step calculation methods.

This collection of papers is a state of the art presentation of theories and methods related to the problem of the behaviour of mechanical structures under variable loads beyond their elastic limit In particular, the problems of shakedown, ratchetting, transient and asymptotic cyclic states are addressed. 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 of the geometry on the inelastic structural response; and numerical techniques with applications to particular engineering problems. It was aimed to provide a unified 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 of cyclic plasticity to the analysis and the design of pressure bellows, compensators, turbine disks, or flange connections under thermal and pressure cycles illustrates the great potential of the numerical techniques developed for this purpose using mostly min-max approaches. The treatment of railway problems and the analysis and optimisation of pavements are further examples of important areas of applications. Emphasis was laid on approaches that take into account the fact that loading histories are often not precisely known Therefore, the center of interest lies in other than step by step calculation methods.

The nature and the human creations are full of complex phenomena, which sometimes can be observed but rarely follow our hypotheses. The best we can do is to build a parametric model and then try to adjust the unknown parameters based on the available observations. This topic, called parameter identification, is discussed in this book for materials and structures. The present volume of lecture notes follows a very successful advanced school, which we had the honor to coordinate in Udine, October 6-10, 2003. The authors of this volume present a wide spectrum of theories, methods and applications related to inverse and parameter identification problems. We thank the invited lecturers and the authors of this book for their contributions, the participants of the course for their active participation and the interesting discussions as well as the people of CISMfor their hospitality and their well-known professional help. Zenon Mroz Georgios E. Stavroulakis CONTENTS Preface An overview of enhanced modal identification by L. Bolognini 1 The reciprocity gap functional for identifying defects and cracks by H. D. Bui, A. Constantinescu and H. Maigre 17 Some innovative industrial prospects centered on inverse analyses by G. Maier, M. Bocciarelli andR. Fedele 55 Identification of damage in beam and plate structures using parameter dependent modal changes and thermographic methods by Z. Mroz andK. Dems 95 Crack and flaw identification in statics and dynamics, using filter algorithms and soft computing by G. E, Stavroulakis, M. Engelhardt andH.