This book provides an overview of direct methods such as limit and shakedown analysis, which are intended to do away with the need for cumbersome step-by-step calculations and determine the loading limits of mechanical structures under monotone, cyclic or variable loading with unknown loading history. The respective contributions demonstrate how tremendous advances in numerical methods, especially in optimization, have contributed to the success of direct methods and their practical applicability to engineering problems in structural mechanics, pavement and general soil mechanics, as well as the design of composite materials. The content reflects the outcomes of the workshop "Direct Methods: Methodological Progress and Engineering Applications," which was offered as a mini-symposium of PCM-CMM 2019, held in Cracow, Poland in September 2019.

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.

Articles in this book examine various materials and how to determine directly the limit state of a structure, in the sense of limit analysis and shakedown analysis. Apart from classical applications in mechanical and civil engineering contexts, the book reports on the emerging field of material design beyond the elastic limit, which has further industrial design and technological applications. Readers will discover that "Direct Methods" and the techniques presented here can in fact be used to numerically estimate the strength of structured materials such as composites or nano-materials, which represent fruitful fields of future applications. Leading researchers outline the latest computational tools and optimization techniques and explore the possibility of obtaining information on the limit state of a structure whose post-elastic loading path and constitutive behavior are not well defined or well known. Readers will discover how Direct Methods allow rapid and direct access to requested information in mathematically constructive manners without cumbersome step-by-step computation. Both researchers already interested or involved in the field and practical engineers who want to have a panorama of modern methods for structural safety assessment will find this book valuable. It provides the reader with the latest developments and a significant amount of references on the topic.

Knowing the safety factor for limit states such as plastic collapse, low cycle fatigue or ratcheting is always a major design consideration for civil and mechanical engineering structures that are subjected to loads. Direct methods of limit or shakedown analysis that proceed to directly find the limit states offer a better alternative than exact time-stepping calculations as, on one hand, an exact loading history is scarcely known, and on the other they are much less time-consuming. This book presents the state of the art on various topics concerning these methods, such as theoretical advances in limit and shakedown analysis, the development of relevant algorithms and computational procedures, sophisticated modeling of inelastic material behavior like hardening, non-associated flow rules, material damage and fatigue, contact and friction, homogenization and composites.

To predict loading limits for structures and structural elements is one of the oldest and most important tasks of engineers. Among the theoretical and numericalmethodsavailableforthispurpose, so-called"DirectMethods,"- bracing Limit- and Shakedown Analysis, play an eminent role due to the fact that they allow rapid access to the requested information in mathematically constructive manners. The collection of papers in this book is the outcome of a workshop held at Aachen University of Technology in November 2007. The individual c- tributions stem in particular from the areas of new numerical developments renderingthemethodsmoreattractive forindustrialdesign, extensionsofthe general methodology to new horizons of application, probabilistic approaches and concrete technological applications. The papers are arranged according to the order of the presentations in the workshop and give an excellent insight into state-of-the-art developments in this broad and growing ?eld of research. The editors warmly thank all the scientists, who have contributed by their outstanding papers to the quality of this edition. Special thanks go to Jaan Simon for his great help in putting together the manuscript to its ?nal shape.

The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

This book provides an overview of direct methods such as limit and shakedown analysis, which are intended to do away with the need for cumbersome step-by-step calculations and determine the loading limits of mechanical structures under monotone, cyclic or variable loading with unknown loading history. The respective contributions demonstrate how tremendous advances in numerical methods, especially in optimization, have contributed to the success of direct methods and their practical applicability to engineering problems in structural mechanics, pavement and general soil mechanics, as well as the design of composite materials. The content reflects the outcomes of the workshop "Direct Methods: Methodological Progress and Engineering Applications," which was offered as a mini-symposium of PCM-CMM 2019, held in Cracow, Poland in September 2019.

Knowing the safety factor for limit states such as plastic collapse, low cycle fatigue or ratcheting is always a major design consideration for civil and mechanical engineering structures that are subjected to loads. Direct methods of limit or shakedown analysis that proceed to directly find the limit states offer a better alternative than exact time-stepping calculations as, on one hand, an exact loading history is scarcely known, and on the other they are much less time-consuming. This book presents the state of the art on various topics concerning these methods, such as theoretical advances in limit and shakedown analysis, the development of relevant algorithms and computational procedures, sophisticated modeling of inelastic material behavior like hardening, non-associated flow rules, material damage and fatigue, contact and friction, homogenization and composites.

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 aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

To predict loading limits for structures and structural elements is one of the oldest and most important tasks of engineers. Among the theoretical and numericalmethodsavailableforthispurpose, so-called"DirectMethods,"- bracing Limit- and Shakedown Analysis, play an eminent role due to the fact that they allow rapid access to the requested information in mathematically constructive manners. The collection of papers in this book is the outcome of a workshop held at Aachen University of Technology in November 2007. The individual c- tributions stem in particular from the areas of new numerical developments renderingthemethodsmoreattractive forindustrialdesign, extensionsofthe general methodology to new horizons of application, probabilistic approaches and concrete technological applications. The papers are arranged according to the order of the presentations in the workshop and give an excellent insight into state-of-the-art developments in this broad and growing ?eld of research. The editors warmly thank all the scientists, who have contributed by their outstanding papers to the quality of this edition. Special thanks go to Jaan Simon for his great help in putting together the manuscript to its ?nal shape.

This book deals with the safety assessment of structures and structural components, possibly operating beyond the elastic limits under variable repeated thermo-mechanical loads. Examples of such situations can be found both in mechanical and civil engineering (e.g. transportation technologies, pressure vessels, pipelines, offshore platforms, dams, pavements and buildings in seismic zones). So-called "direct" methods are focused, based on the shakedown theorems and their specialisation to limit theorems. These methods are receiving increased attention for the prediction of structural failure because they provide the information that is essential in practice (e.g. safety factor and collapse mechanisms) by more economical procedures than step-by-step inelastic analysis; also, they only need a minimum of information on the evolution of loads as functions of time. The addressed audience are primarily engineers and scientists active in Structural Engineering and Safety and Reliability Analysis.