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A general theory of elastic stability is presented. In contrast to previous works in the field, the present analysis is augmented by an investigation of the behavior of the buckled structure in the immediate neighborhood of the bifurcation point. This investigation explains why some structures, e.g., a flat plate supported along its edges and subjected to thrust in its plane, are capable of carrying loads considerably above the buckling load, while other structures, e.g., an axially loaded cylindrical shell, collapse at loads far below the theoretical critical load.
Problems such as jumps in elastic systems, problems of aeroelasticity, problems of frictional self-oscillations, and self-synchronization are discussed. The stability of equilibrium shapes of elastic systems is examined. Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces.
A general theory of elastic stability is presented. In contrast to previous works in the field, the present analysis is augmented by an investigation of the behavior of the buckled structure in the immediate neighborhood of the bifurcation point. This investigation explains why some structures, e.g., a flat plate supported along its edges and subjected to thrust in its plane, are capable of carrying loads considerably above the buckling load, while other structures, e.g., an axially loaded cylindrical shell, collapse at loads far below the theoretical critical load.
It is not my intention to present a treatise of elasticity in the follow ing pages. The size of the volume would not permit it, and, on the other hand, there are already excellent treatises. Instead, my aim is to develop some subjects not considered in the best known treatises of elasticity but nevertheless basic, either from the physical or the analytical point of view, if one is to establish a complete theory of elasticity. The material presented here is taken from original papers, generally very recent, and concerning, often, open questions still being studied by mathematicians. Most of the problems are from the theory of finite deformations [non-linear theory], but a part of this book concerns the theory of small deformations [linear theory], partly for its interest in many practical questions and partly because the analytical study of the theory of finite strain may be based on the infinitesimal one.
This book deals with the elastic stability of solids and structures. It begins with fundamental aspects of stability, relating the basic notions of dynamic stability to more traditional quasi-static approaches. The book is concerned not only with buckling, or linear instability, but most importantly with nonlinear post-buckling behavior and imperfection-sensitivity. After laying out the general theory, Koiter applies the theory to a number of applications, with a chapter devoted to each. These include a variety of beam, plate, and shell structural problems and some basic continuum elasticity problems. Koiter's classic results on the nonlinear buckling and imperfection-sensitivity of cylindrical and spherical shells are included. The treatments of both the fundamental aspects and the applications are completely self contained. This book was recorded as a detailed set of notes by Arnold van der Heijden from W. T. Koiter's last set of lectures on stability theory, at TU Delft.
The Stability of Elastic Systems presents some of the most important aspects of the stability and the non-linear behavior at finite deformations of several types of structural elastic systems, which are important for a more precise understanding of the static performance of such systems. This book is divided into eight chapters that aim to complete parts of classical, eigenvalue, theories of buckling and to demonstrate the important role played by finite deformations in the theoretical analyses of stability. Other chapters discuss the properties of prismatic members and the post-buckling behavior of plane frameworks. A chapter describes the elastic buckling and stability of statically determinate space frameworks. The remaining chapters cover the elastic buckling of statically indeterminate pin-jointed systems and space frameworks. These chapters also examine the non-conservative aspects of structural systems. This book will be of great value to practicing engineers and students.