Non Classical Problems In The Theory Of Elastic Stability

When a structure is put under an increasing compressive load, it becomes unstable and buckling occurs. Buckling is a particularly significant concern in designing shell structures such as aircraft, automobiles, ships, or bridges. This book discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that exist in real systems. The techniques are based on two complementary theories which are developed in the text. First, the probabilistic theory of stability is presented, with particular emphasis on reliability. Both theoretical and computational issues are discussed. Secondly, the authors present the alternative to probability based on the notion of 'anti-optimization', a theory that is valid when the necessary information for probabilistic analysis is absent, that is, when only scant data are available. Design engineers, researchers, and graduate students in aerospace, mechanical, marine, and civil engineering who are concerned with issues of structural integrity will find this book a useful reference source.

This book presents an analysis of eight non-classical problems of fracture and failure mechanics mainly obtained by research in the department of dynamics and stability of continuum of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (NAS of Ukraine). It focusses on the application of the 3D (three-dimensional) theories of stability, dynamics, and statics of solid mechanics to the investigation of non-classical problems of fracture and failure mechanics.

Written by world-renowned authorities on mechanics, this classic ranges from theoretical explanations of 2- and 3-D stress and strain to practical applications such as torsion, bending, and thermal stress. 1961 edition.

This book treats dynamic stability of structures under nonconservative forces. it is not a mathematics-based, but rather a dynamics-phenomena-oriented monograph, written with a full experimental background. Starting with fundamentals on stability of columns under nonconservative forces, it then deals with the divergence of Euler’s column under a dead (conservative) loading from a view point of dynamic stability. Three experiments with cantilevered columns under a rocket-based follower force are described to present the verifiability of nonconservative problems of structural stability. Dynamic stability of columns under pulsating forces is discussed through analog experiments, and by analytical and experimental procedures together with related theories. Throughout the volume the authors retain a good balance between theory and experiments on dynamic stability of columns under nonconservative loading, offering a new window to dynamic stability of structures, promoting student- and scientist-friendly experiments.

There have been stability theories developed for beams, plates and shells — the most significant elements in mechanical, aerospace, ocean and marine engineering. For beams and plates, the theoretical and experimental values of buckling loads are in close vicinity. However for thin shells, the experimental predictions do not conform with the theory, due to presence of small geometric imperfections that are deviations from the ideal shape.This fact has been referred to in the literature as ‘embarrassing’, ‘paradoxical’ and ‘perplexing’. Indeed, the popular adage, “In theory there is no difference between theory and practice. In practice there is”, very much applies to thin shells whose experimental buckling loads may constitute a small fraction of the theoretical prediction based on classical linear theory; because in practice, engineers use knockdown factors that are not theoretically substantiated.This book presents a uniform approach that tames this prima-donna-like and capricious behavior of structures that has been dubbed the ‘imperfection sensitivity’ — thus resolving the conundrum that has occupied the best minds of elastic stability throughout the twentieth century.

Stability of structures is one of the most important and interesting fields in mechanics. This book is dedicated to fundamental concepts, problems and methods of structural stability along with qualitative understanding of instability phenomena. The methods presented are constructive and easy to implement in computer programs. Recent exciting experiments on dynamic stability of non-conservative systems are described and shown by many photographs.