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 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.

The question whether a structure or a machine component can carry the applied loads, and with which margin of safety, or whether it will become unserviceable due to collapse or excessive inelastic deformations, has always been a major concern for civil and mechanical engineers. The development of methods to answer this technologically crucial question without analysing the evolution of the system under varying loads, has a long tradition that can be traced back even to the times of emerging mechanical sciences in the early 17th century. However, the scientific foundations of the theories underlying these methods, nowadays frequently called "direct", were established sporadically in the Thirties of the 20th century and systematically and rigorously in the Fifties. Further motivations for the development of direct analysis techniques in applied mechanics of solids and structures arise from the circumstance that in many engineering situations the external actions fluctuate according to time histories not a priori known except for some essential features, e.g. variation intervals. In such situations the critical events (or "limit states") to consider, besides plastic collapse, are incremental collapse (or "ratchetting") and alternating plastic yielding, namely lack of "shakedown". Non evolutionary, direct methods for ultimate limit state analysis of structures subjected to variably-repeated external actions are the objectives of most papers collected in this book, which also contains a few contributions on related topics.

This book provides an overview of direct methods, such as limit and shakedown analysis, which are intended for avoiding cumbersome step-by-step calculations to determine the limit states of mechanical structures under monotone, cyclic or variable actions with unknown loading history. The book comprises several contributions that demonstrate how tremendous advances in numerical methods, especially in optimization, have contributed to the success of direct methods and their applicability to practical engineering problems in structural mechanics and mechanics of materials. The contents reflect the outcomes of the workshop “Direct Methods for Limit State of Materials and Structures,” held in Cosenza, Italy in June 2022.

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.

The aim of this major reference work is to provide a first point of entry to the literature for the researchers in any field relating to structural integrity in the form of a definitive research/reference tool which links the various sub-disciplines that comprise the whole of structural integrity. Special emphasis will be given to the interaction between mechanics and materials and structural integrity applications. Because of the interdisciplinary and applied nature of the work, it will be of interest to mechanical engineers and materials scientists from both academic and industrial backgrounds including bioengineering, interface engineering and nanotechnology. The scope of this work encompasses, but is not restricted to: fracture mechanics, fatigue, creep, materials, dynamics, environmental degradation, numerical methods, failure mechanisms and damage mechanics, interfacial fracture and nano-technology, structural analysis, surface behaviour and heart valves. The structures under consideration include: pressure vessels and piping, off-shore structures, gas installations and pipelines, chemical plants, aircraft, railways, bridges, plates and shells, electronic circuits, interfaces, nanotechnology, artificial organs, biomaterial prostheses, cast structures, mining... and more. Case studies will form an integral part of the work.

This collection of 23 articles is the output of lectures in special sessions on “The History of Theoretical, Material and Computational Mechanics” within the yearly conferences of the GAMM in the years 2010 in Karlsruhe, Germany, 2011 in Graz, Austria, and in 2012 in Darmstadt, Germany; GAMM is the “Association for Applied Mathematics and Mechanics”, founded in 1922 by Ludwig Prandtl and Richard von Mises. The contributions in this volume discuss different aspects of mechanics. They are related to solid and fluid mechanics in general and to specific problems in these areas including the development of numerical solution techniques. In the first part the origins and developments of conservation principles in mechanics and related variational methods are treated together with challenging applications from the 17th to the 20th century. Part II treats general and more specific aspects of material theories of deforming solid continua and porous soils. and Part III presents important theoretical and engineering developments in fluid mechanics, beginning with remarkable inventions in old Egypt, the still dominating role of the Navier-Stokes PDEs for fluid flows and their complex solutions for a wide field of parameters as well as the invention of pumps and turbines in the 19th and 20th century. The last part gives a survey on the development of direct variational methods – the Finite Element Method – in the 20th century with many extensions and generalizations.

Composite structures and products have developed tremendously since the publication of the first edition of this work in 1986. This new edition of the now classic 1986 text has been written to educate the engineering reader in the various aspects of mechanics for using composite materials in the design and analysis of composite structures and products. Areas dealt with include manufacture, micromechanical properties, structural design, joints and bonding and a much needed introduction to composite design philosophy. Each chapter is concluded by numerous problems suitable for home assignments or examination. A solution guide is available on request from the authors.