Stability Theory Of Elastic Rods
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| 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, Pflger'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.
| Author | : Teodor Atanackovic |
| Publisher | : World Scientific |
| Total Pages | : 441 |
| Release | : 1997-01-16 |
| Genre | : Technology & Engineering |
| ISBN | : 9814497703 |
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, Pflüger'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.
| Author | : N.A. Alfutov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 3540490981 |
The subject discussed in this book is the stability of thin-walled elastic systems under static loads. The presentation of these problems is based on modern approaches to elastic-stability theory. Special attention is paid to the formulation of elastic-stability criteria, to the statement of column, plate and shell stability problems, to the derivation of basic relationships, and to a discussion of the boundaries of the application of analytic relationships. The author has tried to avoid arcane, nonstandard problems and elaborate and unexpected solutions, which bring real pleasure to connoisseurs, but confuse students and cause bewilderment to some practical engineers. The author has an apprehension that problems which, though interesting, are limited in application can divert the reader's attention from the more prosaic but no less sophisticated general problems of stability theory.
| Author | : Warner Tjardus Koiter |
| Publisher | : |
| Total Pages | : 226 |
| Release | : 1967 |
| Genre | : Elasticity |
| ISBN | : |
| Author | : D. Iesan |
| Publisher | : CRC Press |
| Total Pages | : 386 |
| Release | : 2008-11-14 |
| Genre | : Mathematics |
| ISBN | : 1420086502 |
Reflecting new developments in the study of Saint-Venant's problem, Classical and Generalized Models of Elastic Rods focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material. The author presents a method to construct Saint-Venant's solutions, minim
| Author | : Arnold M. A. van der Heijden |
| Publisher | : Cambridge University Press |
| Total Pages | : 233 |
| Release | : 2008-08-11 |
| Genre | : Science |
| ISBN | : 1139471333 |
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.
| Author | : I︠A︡kov Gilelevich Panovko |
| Publisher | : |
| Total Pages | : 436 |
| Release | : 1973 |
| Genre | : Elastic solids |
| ISBN | : |
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.
| Author | : M. Khalid Jawed |
| Publisher | : Springer |
| Total Pages | : 127 |
| Release | : 2018-05-04 |
| Genre | : Technology & Engineering |
| ISBN | : 3319769650 |
This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.
| Author | : Warner Tjardus Koiter |
| Publisher | : |
| Total Pages | : 326 |
| Release | : 1970 |
| Genre | : Cylinders |
| ISBN | : |
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.
| Author | : Luis A. Godoy |
| Publisher | : CRC Press |
| Total Pages | : 454 |
| Release | : 1999-11-01 |
| Genre | : Science |
| ISBN | : 9781560328575 |
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.
