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The two simultaneous nonlinear first-order differential equations characterizing the problems that were derived by the senior author in a paper in 1956 and were at that time solved for a few cases by numerical integration are solved here analytically with the aid of a few simplifying assumptions. The very simple formula derived in this manner is used to compute the critical times of a series of shells tested in the laboratory. It is found that the formula predicts somewhat larger values for the critical time than the experimental results. (Author).
This book contains eight chapters treating the stability of all major areas of the flexural theory. It covers the stability of structures under mechanical and thermal loads and all areas of structural, loading and material types. The structural element may be assumed to be made of a homogeneous/isotropic material, or of a functionally graded material. Structures may experience the bifurcation phenomenon, or they may follow the postbuckling path. This volume explains all these aspects in detail. The book is self-contained and the necessary mathematical concepts and numerical methods are presented in such a way that the reader may easily follow the topics based on these basic tools. It is intended for people working or interested in areas of structural stability under mechanical and/or thermal loads. Some basic knowledge in classical mechanics and theory of elasticity is required.
Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.
* Edited by Josef Singer, the world's foremost authority on structural buckling. * Time-saving and cost-effective design data for all structural, mechanical, and aerospace engineering researchers.
This book provides comprehensive coverage of stress and strain analysis of circular cylinders and pressure vessels, one of the classic topics of machine design theory and methodology. Whereas other books offer only a partial treatment of the subject and frequently consider stress analysis solely in the elastic field, Circular Cylinders and Pressure Vessels broadens the design horizons, analyzing theoretically what happens at pressures that stress the material beyond its yield point and at thermal loads that give rise to creep. The consideration of both traditional and advanced topics ensures that the book will be of value for a broad spectrum of readers, including students in postgraduate, and doctoral programs and established researchers and design engineers. The relations provided will serve as a sound basis for the design of products that are safe, technologically sophisticated, and compliant with standards and codes and for the development of innovative applications.
Thin-walled metal shell structures are highly efficient in their use of material, but they are particularly sensitive to failure by buckiling. Many different forms of buckling can occur for different geometries and different loading conditions. Because this field of knowledge is both complex and industrially important, it is of great interest and concern in a wide range of industries. This book presents a compilation and synthesis of a wealth of research, experience and knowledge of the subject. Information that was previously widely scattered throughout the literature is assembled in a concise and convenient form that is easy to understand, and state-of-the-art research findings are thoroughly examined. This book is useful for those involved in the structural design of silos, tanks, pipelines, biodigestors, chimneys, towers, offshore platforms, aircraft and spacecraft. Buckling of Thin Metal Shells is essential reading for designers, researchers and code writers involved with thin-walled metal shell structures.