9R18. Non-Classical Problems in the Theory of Elastic Stability. - E Elishakoff (Dept of Mech Eng. Florida Atlantic Univ, Boca Raton FL 33431-0991), Y Li (Alpine Engineered Prod), and JH Starnes Jr (Struct Mech Branch, NASA Langley Res Center, Hampton VA 23665). Cambridge UP, New York, 2001. 336 pp. ISBN 0-521-78210-4. $85.00.

Reviewed by JA Cheney (Dept of Civil and Env Eng. UC, Davis CA 95616).

This monograph presents two competing yet complementary theories which incorporate ever-present uncertainty in the stability of elastic structures in the real world. These uncertainties are first and foremost due to unavoidable initial imperfections, deviations of the structure from its intended, nominal, ideal shape. Other uncertainties are in material properties and/or realizations of the boundary conditions. These considerations are addressed by a unified probabilistic theory of stability and the alternative, based on the notion of anti-optimization, that is useful when the necessary information for probabilistic analysis is absent. The book is non-classical in the sense that it goes beyond deterministic methods to probabalistic and set-theory approaches to the buckling of structures.

The first two chapters are devoted to some new deterministic problems in local buckling of multispan plates and columns and the influence of thickness variation of perfect or imperfect, isotropic or composite, circular cylindrical shells. Chapters 3 and 4 deal with stochastic buckling of structures with random imperfections. Chapter 3 uses the Monte Carlo technique while Chapter 4 discusses approximate analytical and numerical techniques, including the asymptotic analysis, the first-order second moment method, the mode localization due to random displacements, and the finite element method for structures with random material properties.

What is called convex modeling of uncertainty in buckling problems is presented in Chapter 5 wherein data scarcity and uncertain material properties are involved in an ensemble of plates and shells. Chapter 6 discusses the Godunov-Conte shooting method, and Chapter 7 deals with the applications of computerized symbolic algebra.

The treatment is scholarly, having about 900 items in the bibliography and additional contributors in the writing of almost every chapter. In addition to the extensive bibliography, an author index of those referenced in the text and a subject index are included. This reviewer believes that Non-Classical Problems in the Theory of Elastic Stability should be a useful reference for researchers, engineers, and graduate students in aeronautical, mechanical, civil, nuclear, and marine engineering, and in applied mechanics.