Non-Classical Problems in the Theory of Elastic Stability

Non-Classical Problems in the Theory of Elastic Stability
Author: Isaac Elishakoff
Publisher: Cambridge University Press
Total Pages: 354
Release: 2001-01-29
Genre: Mathematics
ISBN: 0521782104

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.

Theory of Elastic Stability

Theory of Elastic Stability
Author: Luis A. Godoy
Publisher: CRC Press
Total Pages: 452
Release: 2024-11-01
Genre: Technology & Engineering
ISBN: 1040285341

This book gives a unified presentation of the field of stability. Buckling and post-buckling states are studied on the basis of total potential energy of structural systems. Emphasis is placed throughout the text on post-buckling analysis and behaviour. The sensitivity of buckling and post-buckling states to changes in design parameters is also discussed as well as changes due to imperfections and damage.

Stability Theory of Elastic Rods

Stability Theory of Elastic Rods
Author: Teodor M. Atanackovic
Publisher: World Scientific
Total Pages: 441
Release: 1997
Genre: Technology & Engineering
ISBN: 9810230540

This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.

Stability of Discrete Non-conservative Systems

Stability of Discrete Non-conservative Systems
Author: Jean Lerbet
Publisher: Elsevier
Total Pages: 291
Release: 2020-11-27
Genre: Technology & Engineering
ISBN: 0081027656

Stability of Discrete Non-conservative Systems first exposes the general concepts and results concerning stability issues. It then presents an approach of stability that is different from Lyapunov which leads to the second order work criterion. Thanks to the new concept of Kinematic Structural Stability, a complete equivalence between two approaches of stability is obtained for a divergent type of stability. Extensions to flutter instability, to continuous systems, and to the dual questions concerning the measure of non-conservativeness provides a full, fresh look at these fundamental questions. A special chapter is devoted to applications for granular systems. - Presents a structured review on stability questions - Provides analytical methods and key concepts that may be used in non-conservative frameworks like hypoelasticity

Non-Conservative Systems

Non-Conservative Systems
Author: Kurt Ingerle
Publisher: CRC Press
Total Pages: 108
Release: 2018-03-05
Genre: Technology & Engineering
ISBN: 1351394444

Non-Conservative Systems: New Static and Dynamic Stability Criteria summarizes the essential properties of non-conservative elastic systems (static stability and post-critical behavior), and the importance of novel stability criteria for such systems. Beginning with the history of non-conservative systems theory, the text goes on to propose new theories regarding static stability in massless non-conservative systems, and dynamic stability in systems with mass. Experiments are included, as are computational models developed by the author, along with an extensive bibliography. This new work is a valuable new resource for those working in the area of structural stability.

Resolution Of The Twentieth Century Conundrum In Elastic Stability

Resolution Of The Twentieth Century Conundrum In Elastic Stability
Author: Isaac E Elishakoff
Publisher: World Scientific
Total Pages: 350
Release: 2014-05-29
Genre: Technology & Engineering
ISBN: 9814583553

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.