Non-classical problems in the theory of elastic stability.

*(English)*Zbl 0995.74002
Cambridge: Cambridge University Press. xvi, 336 p. £55.00; $ 90.00/hbk (2001).

This book treats stability problems of elastic elements, rods, plates and shells that have imperfections in shape and material properties and in boundary conditions. The authors introduce a reliability concept, i.e. the probability that the structure will not fail prior to a preselected load level. Many important examples are treated, most of them originally solved by the first author and his collaborators. The book is divided into 7 chapters and contains well-organized and carefully selected bibliography. In chapter 1 the mode localization is treated, chapter 2 presents stability analysis of shells with variable thickness (deterministic approach), in chapter 3 stochastic buckling is introduced and reliability concept is presented, chapter 4 deals with non Monte Carlo techniques for stochastic buckling, in chapter 5 the stability analysis is presented in the case of uncertainties in elastic moduli, and probabilistic and convex analysis method are compared, chapter 6 deals with Godunov-Conte shooting method applied to buckling analysis, and finally, chapter 7 deals with computerized symbolic algebra used in buckling analysis.

General conclusion is that the present book is an important contribution to stability analysis since it treats non-classical problems whose importance in applications is growing. The book will be of interest to those working in stability of elastic structures, as well as to graduate students in mechanical civil and aeronautical engineering.

General conclusion is that the present book is an important contribution to stability analysis since it treats non-classical problems whose importance in applications is growing. The book will be of interest to those working in stability of elastic structures, as well as to graduate students in mechanical civil and aeronautical engineering.

Reviewer: Teodor Atanackovic (Novi Sad)

##### MSC:

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74G60 | Bifurcation and buckling |

74Sxx | Numerical and other methods in solid mechanics |

74Kxx | Thin bodies, structures |