Our topic is irreversible or plastic deformation of structural elements composed of relatively thin ductile materials. These deformations are commonly used in sheet metal forming operations to produce lightweight parts of any particular shape. In another context, this type of plastic deformation is described as impact damage in the case of structural components involved in collision. Here we are concerned with mechanics of both static and dynamic deformation processes. The purpose is to use typical material properties and structural characteristics to calculate the deformation for certain types of load; in particular to find the final deflection and shape of the deformed structure and to illustrate how the development of this final shape depends on the constitutive model used to represent the material behavior. The major issue to be addressed is which structural and constitutive properties are important for calculating response to either static or brief but intense dynamic loads. Furthermore, how do the results of various constitutive models compare with observed behavior.

The chapters of this book were written by structural engineers. The approach, therefore, is not aiming toward a scientific modelling of the response but to the definition of engineering procedures for detecting and avoiding undesired phenomena. In this sense chaotic and stochastic behaviour can be tackled in a similar manner. This aspect is illustrated in Chapter 1. Chapters 2 and 3 are entirely devoted to Stochastic Dynamics and cover single-degree-of-freedom systems and impact problems, respectively. Chapter 4 provides details on the numerical tools necessary for evaluating the main indexes useful for the classification of the motion and for estimating the response probability density function. Chapter 5 gives an overview of random vibration methods for linear and nonlinear multi-degree-of-freedom systems. The randomness of the material characteristics and the relevant stochastic models ar considered in Chapter 6. Chapter 7, eventually, deals with large engineering sytems under stochastic excitation and allows for the stochastic nature of the mechanical and geometrical properties.

This text explores how academics face up to radical changes in the learning environment. With the implementation of new technologies to support teaching and learning there is a need for more strategic approaches to teaching and learning. At the same time there are requirements to respond to a much more diverse student body and therfore a greater need for staff developments to help the teachers and the learners to cope with the new environments for learning.

Slender structures, such as towers, masis, high-rise buildings and bridges, are especially prone to wind excited vibrations. The lectures show how the susceptibility of a structure to wind excited vibrations can be assessed in early stages of design, and what measures are effective for control or avoidance of vibrations. The book will be a help for all dealing with dynamic response of structures.

This state of the art report provides an in-depth, comprehensive technical survey of the three main coating protection systems for steel reinforcement: hot-dip galvanizing epoxy-coating PVC-coating

This book was developed while teaching a graduate course at several universities in the United States. Europe and Israel. during the last two decades. The purpose of the book is to introduce the fundamentals and applications of optimum structural design. Much work has been done in this area recently and many studies have been published. The book is an attempt to collect together selected topics of this literature and to present them in a unified approach. It meets the need for an introductory text covering the basic concepts of modem structural optimization. A previous book by the author on this subject ("Optimum Structural Design." published by McGraw-Hill New York in 1981 and by Maruzen Tokyo in 1983). has been used extensively as a text in many universities throughout the world. The present book reflects the rapid progress and recent developments in this area. A major difficulty in studying structural optimization is that integration of concepts used in several areas. such as structural analysis. numerical optimization and engineering design. is necessary in order to solve a specific problem. To facilitate the study of these topics. the book discusses in detail alternative problem formulations. the fundamentals of different optimization methods and various considerations related to structural design. The advantages and the limitations of the presented approaches are illustrated by numerous examples.

As an emerging discrete structural model, the Hencky bar-chain/net model (HBM) has shown its advantages over other numerical methods in some problems. Owing to the discrete properties of HBM, it is also a suitable model for nano-scale structures which are currently a very hot research topic in mechanics.This book introduces the concepts and previous research of the Hencky bar-chain/net model, before demonstrating how beams, columns, arches, rectangular plates and circular plates could be successfully modelled by HBM. HBM comprises rigid bars connected by frictionless hinges with elastic rotational springs (and a system of torsional springs in the cells for plates). In the treatment of the above-mentioned structures, HBM is found to be mathematically equivalent to the first order central finite difference method (FDM). So HBM may be regarded as the physical structural model behind the FDM.This book is a compilation of the authors' research on the development of the Hencky bar-chain/net model, and is organized according to the development and application of HBM for beams, columns, frames, arches and rings, and plates. Exercises are provided at the end of each chapter to aid comprehension and guide learning. It is a useful reference for students, researchers, academics and practitioners in the field of structural analysis.

This volume strives to give complete information about the main aspect of the stability behaviour of steel structures and their members. In following this objective, the volume presents a complete scientific background (profiting from the fact that the authors of the individual parts of the publication have personally been very active in the corresponding field of research for an extended period of time now), but also establishes recommendations, procedures and formulae for practical design. The significance of the volume may be seen in its challenging current concepts of stability analysis, encouraging progress in the field and thereby establishing an advanced basis for more reliable and economical design.

State-of-the-art nonlinear computational analysis of shells, nonlinearities due to large deformations and nonlinear material behavior, alternative shell element formulations, algorithms and implementational aspects, composite and sandwich shells, local and global instabilities, optimization of shell structures and concepts of shape finding methods of free from shells. Furthermore, algorithms for the treatment of the nonlinear stability behavior of shell structures (including bifurcation and snap-through buckling) are presented in the book.

Shape and layout optimization represent some of the most useful but also most difficult classes of problems in structural design, which have been investigated in detail only during the last few years. "Shape optimization" is concerned with the optimal shape of boundaries of continua or of interfaces between two materials in composites. "Layout" "optimization" deals with the simultaneous optimization of the topology, geometry and cross-sectional sizes of structural systems. In spite of its complextiy, layout optimization is a very rewarding task, because it results in much greater savings than the optimization of cross-sectional sizes only. Because of their important role in shape and layout optimization, the book also covers in detail new "optimality " "criteria methods," which are capable of handling many thousand design variables and active design contraints. Shape and layout optimization is becoming an indispensable tool in the design of aeroplanes, space structures, cars, ships, building and civil engineering structures, power stations, chemical plants, artificial organs, sporting equipment, and all other solid systems where stresses and deformations play an important role.

A synthetic presentation of the theory of yield design is illustrated by examples such as the stability analysis of reinforced soil structures and the resistance of long fiber reinforced composite materials. The classical limit analysis theory when standard elastic perfectly plastic behaviour can be assumed yields a more precise assessment of the global bearing capacities of structures and makes optimal limit design possible. Structural optimal design is also studied with respect to eigenvalues as well as Structural Topology and Design Optimization.

This volume deals with the most modern and topical problems of bridge design. The topics presented allow to tackle both theoretical-analytical as well as technical-constructive aspects of the design problem, pointing out how in the case of bridges, specifically for long span bridges, the two aspects are absolutely inseparable. In modern bridges, reasons of technical and economic feasibility oblige an extreme parceling of the construction process, with the consequent need to revise, with respect to the past, both design concepts as well as the theoretical apparatus of analysis that governs it. All this can clearly be derived from reading the present volume, in which the different contributions stress theoretical and technical questions of particular interest and topicality, without claiming to approach them systematically, but offering clear procedural rules and trend indications. With reference to the theoretical approach, some of particular importance are reviewed, such as the possibility of using limit analysis, the simplification of the design process for bridges, durability, and computer aided design. For what concerns the bridge typologies and the corresponding constructive problems, the emphasis is mostly on the ones still in an evolutionary phase, that is long span suspended/stayed bridges and cantilever built bridges with prefabricated segments.

Virtual distortions are incompatible deIormations imposed on structures (e. g. , by nonhomogeneous heating or by local imperIections) causing a compatible state OI deIormation (initial deformations) and a selI-equilibrated state OI stress (initial stresses). The theory OI virtual distortions provides an eIIicient tool which can be used to treat many problems that diIIer Irom the physical point OI view. Thermal stresses, material deIects, residual stresses in plasticity are examples OI problems that can be analysed emploing the virtual distortions approach, where the temperature Iield, dislocations and plastic distortions (permanent plastic deIormations) are described by virtual distortions. The presented approach allows the development OI eIIicient computational methods Ior numerical analysis OI such problems. States OI compatible deIormations and selI-equi1 ibrated stresses caused by virtual distortions in homogeneous and compound (biphase) bodies are analysed in the Iirst part OI the book. The results OI these considerations are explored in the next two chapters. The Iormulation OI the approach discussed in Chapter 1 and based on continuum mechanics was presented previously in the papers [5,17] while its application to the analysis OI skeletal structures was discussed in [47].

This proceedings volume contains 38 papers presented at the 4th Working Conference on "Rel iability* and Optimization of Structural Systems", held at the Technical University of Munich, Germany, September 11- 13, 1991. The Working Conference was organised by the IFIP (Interna tional Federation for Information Processing) Working Group 7.5 of Technical Committee 7 and was the fourth in a series, following similar conferences held at the University of Aalborg, Den mark, May 1987, at the Imperial College, London, UK, September 1988 and at the University of California, Berkeley, California, USA, March 1990. The Working Conference was attended by 54 participants from 16 countries. The objectives of Working Group 7.5 are: * to promote modern structural systems optimization and reliability theory, * to advance international cooperation in the field of structural system optimization and reliability theory, * to stimulate research, development and application of structural system optimization and reli ability theory, * to further the dissemination and exchange of information on reliability and optimization of structural systems * to encourage education in structural system optimization and reliability theory. At present the members of the Working Group are: A. H.-S. Ang, U.S.A. M. Grimmelt, FRG G. A ugwti, Italy N. C. Lind, Canada M. J. Baker, UK H. O. Mad&en, Denmark P. Bjerager, Norway R. E. Melcher~, Australia C. A. Cornell, U.S.A. F. Mo~e~, U.S.A.

This book presents a method which is capable of evaluating the deformation characteristics of thin shell structures A free vibration analysis is chosen as a convenient means of studying the displacement behaviour of the shell, enabling it to deform naturally without imposing any particular loading conditions. The strain-displacement equations for thin shells of arbitrary geometry are developed. These relationships are expressed in general curvilinear coordinates and are formulated entirely in the framework of tensor calculus. The resulting theory is not restricted to shell structures characterized by any particular geometric form, loading or boundary conditions. The complete displacement and strain equations developed by Flugge are approximated by the curvilinear finite difference method and are applied to computing the natural frequencies and mode shapes of general thin shells. This approach enables both the displacement components and geometric properties of the shell to be approximated numerically and accurately. The selection of an appropriate displacement field to approximate the deformation of the shell within each finite difference mesh is discussed in detail. In addition, comparisons are made between the use of second and third-order finite difference interpolation meshes.

1. 1 Introduction As offshore oil production moves into deeper water, compliant structural systems are becoming increasingly important. Examples of this type of structure are tension leg platfonns (TLP's), guyed tower platfonns, compliant tower platfonns, and floating production systems. The common feature of these systems, which distinguishes them from conventional jacket platfonns, is that dynamic amplification is minimized by designing the surge and sway natural frequencies to be lower than the predominant frequencies of the wave spectrum. Conventional jacket platfonns, on the other hand, are designed to have high stiffness so that the natural frequencies are higher than the wave frequencies. At deeper water depths, however, it becomes uneconomical to build a platfonn with high enough stiffness. Thus, the switch is made to the other side of the wave spectrum. The low natural frequency of a compliant platfonn is achieved by designing systems which inherently have low stiffness. Consequently, the maximum horizontal excursions of these systems can be quite large. The low natural frequency characteristic of compliant systems creates new analytical challenges for engineers. This is because geometric stiffness and hydrodynamic force nonlinearities can cause significant resonance responses in the surge and sway modes, even though the natural frequencies of these modes are outside the wave spectrum frequencies. High frequency resonance responses in other modes, such as the pitch mode of a TLP, are also possible.

The field of structural optimization is still a relatively new field undergoing rapid changes in methods and focus. Until recently there was a severe imbalance between the enormous amount of literature on the subject, and the paucity of applications to practical design problems. This imbalance is being gradually redressed. There is still no shortage of new publications, but there are also exciting applications of the methods of structural optimizations in the automotive, aerospace, civil engineering, machine design and other engineering fields. As a result of the growing pace of applications, research into structural optimization methods is increasingly driven by real-life problems. t-.Jost engineers who design structures employ complex general-purpose software packages for structural analysis. Often they do not have any access to the source program, and even more frequently they have only scant knowledge of the details of the structural analysis algorithms used in this software packages. Therefore the major challenge faced by researchers in structural optimization is to develop methods that are suitable for use with such software packages. Another major challenge is the high computational cost associated with the analysis of many complex real-life problems. In many cases the engineer who has the task of designing a structure cannot afford to analyze it more than a handful of times.

Structural safety of industrial systems and components raises a steadily growing public, scientific and engineering interest, and causes permanent development of methods and techniques used for its assessment. In addition to the well established engineering methods, applied in the field, several new methods and tools have emerged recently. Among them, the most novel ones are probably those related to expert system applica tions, appearing as an important possible improvement of the current engineering practice. The issue has been addressed by the international course EXPERT SYSTEMS IN STRUCTURAL SAFETY ASSESSMENT organized by MPA Stuttgart and JRC Ispra (Stuttgart, October 2-4, 1989), and the proceedings of the course are contained in this volume of the Lecture Notes ill Engineering. The contributions (invited lectures) tackle the issues usually confronting developers and users of expert systems applied in structural engineering, i.e. in structural safety and integrity assessment. Both the book and the course are a combination of a tutorial and of presentation of the current achievements in the field. Starting from the basic elements of expert systems (knowledge based systems), the book should "guide" the reader up to the applications in various particular sub-domains.

The Construction Sector Is Increasingly Focused On Repair As concrete structures are maintained longer for both environmental and financial reasons, the diagnosis, design, and selection of products, and repair work all depend on the individual condition of the buildings and require specialist knowledge from everyone involved. Concrete Repair to EN 1504: Diagnosis, Design, Principles and Practice provides relevant background and practical guidance on concrete repair. This book is based on the new European Standard EN 1504, which is used as the actual basis for concrete repair works, in Europe and beyond. Offers a Systematic and Thorough Approach It includes both practice and theory, and provides an ideal basis for understanding and designing repair works. It addresses building materials, deterioration mechanisms, diagnosis, load-bearing capacity and safety, repair principles and methods, repair materials, execution of repair works, quality control, inspections, monitoring, and maintenance and building management systems right through to building regulations and standards. It also covers deterioration mechanisms of concrete and steel reinforcement, diagnosis methods, principles of repair and protection, properties and fields of application of repair materials, as well as methods of execution, including quality control to EN 1504. Describes the theoretical background of corrosion and diagnosis methods (which are not covered by the EN 1504 series) Provides the systematics of principles and methods in detail Includes dedicated comprehensions which enables the reader to quickly access the knowledge The text provides a complete overview and is a practical resource for owners, designers, product suppliers, testing institutes, and consulting engineers, as well as for students in civil engineering.

This book presents a series of integrated computer programs in Fortran-90 for the dynamic analysis of structures, using the finite element method. Two dimensional continuum structures such as walls are covered along with skeletal structures such as rigid jointed frames and plane grids. Response to general dynamic loading of single degree freedom systems is calculated, and the author also examines multi degree of freedom systems (including earthquake analysis). Each chapter covers a different aspect of analytic theory and the corresponding program segments. It will be an essential tool for practising structural and civil engineers, whilst also being of interest to academics and postgraduate students.

This book brings together, in a concise format, the key elements of the loads produced from explosive sources, and how they interact with structures. Explosive sources include gas, high explosives, dust and nuclear materials. It presents quantitative information and design methods in a useable form without recourse to extensive mathematical analysis. The authors, Peter Smith and John Hetherington, are staff members at the Royal Military College of Science in Shrivenham and have been instrumental in establishing an active team studying the response of structures to blast and ballistic loading.

This proceedings volume contains 33 papers presented at the 3rd Working Conference on "Rel- iability and Optimization of Structural Systems", held at the University of California, Berkeley, California, USA, March 26 -28, 1990. The Working Conference was organised by the IFIP (Inter- national Federation for Information Processing) Working Group 7.5 of Technical Committee 7 and was the third in a series, following similar conferences held at the University of Aalborg, Denmark, May 1987 and at the Imperial College, London, UK, September 1988. The Working Conference was attended by 48 participants from 12 countries. The objectives of Working Group 7.5 are: * to promote modern structural systems optimization and reliability theory, * to advance international cooperation in the field of structural system optimization and reliability theory, * to stimulate research, development and application of structural system optimization and reli- ability theory, * to further the dissemination and exchange of information on reliability and optimization of structural systems * to encourage education in structural system optimization and reliability theory. At present the members of the Working Group are: A. H.-S. Ang, U.S.A. G. A ugusti, Italy M. J. Baker, United Kingdom P. Bjerager, Norway R. B. Corotis, U.S.A. C. A. Cornell, U.S.A. M. Grigoriu, U.S.A. A. Der Kiureghian, U.S.A. O. Ditlevsen, Denmark D. M. Frangopol, U.S.A. S. Garribba, Italy H. Furuta, Japan M. R. Gorman, U.S.A. M. Grimmelt, Germany, F. R.

In recent years, the Finite Element Methods FEM were more and more employed in development and design departments as very fast working tools in order to determine stresses, deformations, eigenfrequencies etc. for all kinds of constructions under complex loading conditions. Meanwhile. very effective software systems have been developed by various research teams although some mathematical problems (e. g. convergence) have not been solved satisfac torily yet. In order to make further advances and to find a common language between mathe maticians and mechanicians the "Society for Applied Mathematics and Mechanics" (GAMM) agreed on the foundation of a special Committee: "Discretization Methods in Solid Mechanics" focussing on the following problems: - Structuring of various methods (displacement functions, hybrid and mixed approaches, etc. >, - Survey of approach functions (Lagrange-/Hermite-polynominals, Spline-functions), - Description of singularities, - Convergence and stability, - Practical and theoretical optimality to all mentioned issues (single and interacting). One of the basic aims of the GAMM-Committee is the interdisciplinary cooperation between mechanicians, mathematicians, and users which shall be intensified. Thus, on September 22, 1985 the committee decided to hold a seminar on "Structural Optimization" in order to allow an exchange of experiences and thoughts between the experts of finite element methods and those of structural optimization. A GAMM-seminar entitled "Discretization Methods and Structural Optimization - Procedures and Applications" was hold on October 5-7, 1988 at the Unversity of Siegen."

Modernisation, Mechanisation and Industrialisation of Concrete Structures discusses the manufacture of high quality prefabricated concrete construction components, and how that can be achieved through the application of developments in concrete technology, information modelling and best practice in design and manufacturing techniques.

Civil engineering structures tend to be fabricated from materials that respond elastically at normal levels of loading. Most such materials, however, would exhibit a marked and ductile inelasticity if the structure were overloaded by accident or by some improbable but naturally occuring phenomeon. Indeed, the very presence of such ductility constitutes an important safety provision for large-scale constructions where human life is at risk. In the comprehensive evaluation of safety in structural design, it is therefore unrealistic not to consider the effects of ductility. This book sets out to show that the bringing together of the theory and methods of mathematical programming with the mathematical theory of plasticity furnishes a model which has a unifying theoretical nature and is entirely representative of observed structural behaviour. The contents of the book provide a review of the relevant aspects of mathematical programming and plasticity theory, together with a detailed presentation of the most interesting and potentially useful applications in both framed and continuum structures: ultimate strength and elastoplastic deformability; shakedown and practical upper bounds on deformation measures; evolutive dynamic response; large displacements and instability; stochastic and fuzzy programming for representing uncertainty in ultimate strength calculations. Besides providing a ready fund of computational algorithms, mathematical programming invests applications in mechanics with a refined mathematical formalism, rich in fundamental theorems, which often gives addi- tional insight into known results and occasionally lead to new ones. In addition to its obvious practical utility, the educational value of the material thoroughly befits a university discipline.