This book is based on lecture notes made after Professor Koiter's last official course at Delft University of Technology in 1978–79. During his career, Warner Koiter was acknowledged as a world leader in the field of elastic stability. Although the notes that form this text were prepared in close collaboration with Professor Koiter, they are written in the author's own style. The contents cover the entire field of elastic stability, although more recent developments in the field of stiffened plates and shells are not included. A primary intent of the book is to reflect some of the atmosphere of Professor Koiter's unique lectures.
The first two chapters are devoted to fundamental aspects of stability, relating the basic notions of dynamic stability to more traditional quasi-static approaches. In addition to linear buckling problems, solution procedures for the more complex issues of non-linear post-buckling behaviour and imperfection sensitivity are formulated. This section of the text is elegantly written and takes the reader through the fundamental concepts of stability, by discussion of discrete systems, before establishing the theorems and relations for continuous elastic systems necessary for the solution of practical problems. Of particular importance is the establishment of stability limits through energy minimisation procedures, consideration of equilibrium states in the neighbourhood of a limit point and a rigorous analysis of the influence of imperfections.
The remainder of the book (some three-quarters) is concerned with application of the theoretical concepts to the solution of engineering problems. The section commences with the treatment of bars subjected to various loads and boundary conditions, including the problem of a laterally supported beam, before considering simple two-bar frames. The important engineering problem of bending and torsion of thin-walled sections subjected to compression is then discussed, followed by the torsion of shafts including the case when a Cardan (Hooke's) joint is present, which introduces the possibility of large rotations.
After using the problem of lateral buckling of a beam loaded in bending as a means of introduction, a comprehensive treatment of the lateral buckling of plates loaded in their plane is provided. This includes a discussion of post-buckling behaviour, which is of extreme importance from a practical engineering viewpoint. Essentially, solutions are developed for rectangular plates subjected to combinations of compressive loading and shear traction loading, with a variety of boundary conditions.
The final part of the application section is devoted to the solution of buckling problems arising in shells. Firstly, a shallow-shell theory approach is developed and applied to a spherical shell under uniform external pressure, where it is demonstrated that the solution is extremely sensitive to imperfections. The same problem is then examined using the general theory of shells. After summarising the essential expressions of general shell theory, variation of the energy function provides expressions for the buckling modes, as well as defining stability conditions for the critical bifurcation load. The application section concludes by providing solutions for the buckling of circular cylindrical shells under various loading conditions, where again the behaviour is examined both with respect to critical loads and post-buckling response.
In addition to providing a concise summary of the concepts of elastic stability and the formal solution of a range of buckling problems of importance in engineering, the book provides considerable insight into the views and approach of Warner Koiter to the subject of elastic stability. Although some thirty years old, his notes have stood the test of time and still represent current methodology in the analytical treatment of stability effects. In spite of the fact that numerical techniques have largely overtaken analytical methods for the solution of engineering instability problems, these closed-form solutions nevertheless provide valuable insight into the non-linear performance of slender structures under compressive loads and their sensitivity to imperfections. The book is highly recommended to serious students of the topic of elastic stability, both for its technical content and for the opportunity to follow the thinking and logic of a remarkable academic and researcher.
