3R28. Stability of Elastic Structures. Foundations of Engineering Mechanics. - NA Alfutov (M-1 Dept, Moscow State Univ of Tech, 2-nd Baumanskaya Str 5, Moscow, 107005, Russia). Springer-Verlag, Berlin. 2000. 337 pp. ISBN 3-540-65700-2. $99.00.
Reviewed by J Wauer (Inst fur Tech Mec, Univ Karlsruhe, Kaiserstr 12, Karlsruhe, D-76128, Germany).
The stability loss of slender structural systems under loading is still an actual field of research in mechanics. Every engineer nowadays has to know the occurring phenomena and the analytical methods to explain them. In general, such stability investigations have to be based on a dynamic approach. However, in many practical applications, a static approach can be applied, and this is the objective of the present book. It is clearly pointed out by the author that only the static stability of elastic systems is considered, and that the complete mathematical framework is explained for classical structural members such as columns, plates, and (cylindrical) shells. The drawback of this restriction is being compensated for by the demand to give a very clear and straightforward introduction into the basics of this part of an important field.
The book is arranged in seven chapters (and an appendix) together with a list of references and a subject index both covering the complete content of the book.
Chapter 1 deals with the basic theory of elastic stability. It stresses the equilibrium paths for deformed systems, stable or unstable equilibrium states and bifurcation points as well as limit points and critical loads, including energy criteria for bifurcational stability loss and a corresponding method using homogeneous linearized equations. It also discusses the supercritical behavior and the stability of elastic structures under combined loading. A summarizing statement on stability problems for slender structures concludes the chapter.
Chapter 2 discusses the energy method more in detail starting with the principle of virtual displacements and variational approaches in the linear theory of elasticity. Two basic forms of the presented energy criterion for bifurcational stability loss are introduced and generalized as the Bryan and the Timoshenko form. The significance of the Rayleigh-Ritz method in the stability analysis is addressed, and the Galerkin method and its relationship to the Rayleigh-Ritz method is explained.
Chapter 3 covers the stability of straight columns, essentially under axial forces. Elastic foundations and elastic supports are included in the analysis, and the stability of self-gravitating column is examined. In addition, the problem of lateral-torsional beam buckling is dealt with, and the influence of transverse shear strains is also addressed.
Chapters 4 and 5 concern the stability of plates. Chapter 4 discusses the differential equation approach while Chapter 5 is focused on the energy method. Both rectangular and circular plates under mid-plane distributed force-loading are considered. Transverse shear effects, thermoelastic buckling, and plates under local loads are supplementing topics.
Chapter 6 is devoted to the stability of (cylindrical) shells starting with corresponding considerations on circular rings. Axial compression and external radial pressure are the preferred load cases, but shells under torsion and transverse bending also find attention. Finally, stiffened shells (by elastic frames) are addressed.
Chapter 7 gives an outlook to nonlinear problems starting with a discussion of the supercritical behavior of a compressed bar after stability loss and extending the examination to plates and shells including initial imperfections.
The appendix gives a compact introduction into eigenvalue problems, stationary values, and extrema of functions and functionals.
The restriction mentioned at the beginning detracts from the value of the book for all persons interested in receiving a general view of the whole field of structural stability. On the other hand, to find a clear introduction about the static stability and to understand the peculiar phenomena in this area, it might be better to concentrate on the basics for simple structural members. In this sense, Stability of Elastic Structures can be recommended for all undergraduate and also graduate courses in engineering science, in particular civil and aeronautic engineering. Also, for practical engineers in these fields, it is a good reference. The book is well written with good quality figures and illustrations. It is worth being purchased by every engineering library.