Theory of Elastic Stability is an extensive guide to the stability of thin-walled structures: beams, plates and shells. It covers a wide range of problems related to tension, compression and torsion of various thin-walled constructions with different boundary conditions. Critical loads which separate stable and unstable behavior of the structures are determined. Buckling of structures under various loading conditions is studied. The book assumes working knowledge of the basics of ordinary and partial differential equations and thus could be recommended to advanced undergraduate and graduate students. It will also make a wonderful reference material for professionals working with thin-walled constructions.
Chapters 1 through 6 are dedicated to buckling and stability of beams and frames. The differential equations for the displacements of beams are obtained for a wide range of loadings and their combinations, such as lateral and compressive axial loading, and also torsion. End-point conditions studied include built-in ends, simply supported ends, and ends with elastic restraints and supports. The critical loads on the beams are determined for many loading and end-point configurations. Inelastic buckling of beams is considered in the chapter 3. Some of the available experimental results are presented in the chapter 4. Part of this chapter is also dedicated to the explanation of disparity between observed experimental results and theoretical predictions.
Chapter 7 is dedicated to the bending of thin rings, curved bars and arches. The differential equation of bending is obtained for a circular arch or a ring. This equation is solved for the cases of a uniformly compressed ring or an arch. Critical values of the uniform pressure are determined, and the buckling of the ring or an arch is studied. Buckling of very flat curved bars is considered in this chapter as well.
Chapters 8 and 9 of the book are dedicated to bending of thin plates. The derivations of partial differential equations of bending of thin plates are presented in detail. The cases of bending caused by bending moments applied to the edges, by distributed lateral loads, and also by combined bending and tension or compression of the plates are considered. The edge conditions include built-in edges, simply supported edges, elastically supported edges, and elastically built-in edges. The case of bending of plates with small initial curvature and bending of plates of non-rectangular shape are considered as well. The critical loads are computed, and buckling of plates under many combinations of loading and edge conditions is studied. A large amount of numerical data and discussion of experiments is provided as well.
Finally, the last two chapters of the book are dedicated to the study of bending and buckling of thin shells. Special attention here is devoted to the cases of circular cylindrical shells and spherical shells. Partial differential equations of equilibrium are obtained for these cases. Buckling of cylindrical shells under uniform axial or lateral pressure is studied and comparison with experimental results is given.
The book rigorously covers a large amount of practically important problems of stability of thin-walled constructions. I am happy to recommend this book to engineers and applied mathematicians interested in the subject.
Anna Zemlyanova is an Assistant Professor at the Department of Mathematics, Kansas State University, Manhattan, KS, USA.