1R22. Theory of Elastic Stability: Analysis and Sensitivity. - LA Godoy (Dept of Eng, Univ of Puerto Rico, Mayaguez, Puerto Rico). Taylor & Francis, Philadelphia. 2000. 434 pp. ISBN 1-56032-857-6. $95.00.
Reviewed by Long-Yuan Li (Dept of Civil Eng, Aston Univ, Aston Triangle, Birmingham, B4 7ET, UK).
This book is primarily written for professionals and graduate students in civil, mechanical, and aeronautical engineering. The book gives a unified presentation of the field of stability, provides a basic understanding of the fundamentals of the elastic stability of structures, and applies these fundamentals to solve, analytically, a spectrum of engineering problems.
The emphasis of the book is placed on the formulation of engineering problems rather than on the proof of the fundamental principles. The formulation presented is based on the total potential energy of the discrete system from which analyses of equilibrium, stability, postcritical states, design sensitivity, and imperfection sensitivity are conducted. The second feature of the book is the use of perturbation techniques as part of the formulation and also of the analyses. This reduces the effort necessary to understand the solution of nonlinear systems.
Following a brief introduction of the subject in Chapter 1, Chapter 2 reviews basic concepts of the theory of nonlinear elasticity and main equations of elasticity under nonlinear kinematic assumptions. The formulation is written in terms of the total potential energy of structural components using generalized coordinates. Chapter 3 provides an introduction of the techniques of perturbation which serves as a tool in the analyses presented in later chapters.
Chapter 4 presents the concept of stability of equilibrium states. In addition to that, the question of stability of a path is also addressed. Critical states are presented in Chapter 5. Again, the conditions for the presence of a critical state are formulated in terms of the energy function. Chapter 5 also contains examples of simple structural components for which the critical states are computed.
The limit point and bifurcation point, the two types of the critical point, are discussed in Chapters 6 and 7, respectively. Conditions for both limit point and bifurcation point are presented. Examples are also provided in these two chapters.
Chapter 8 presents the equilibrium of systems with imperfections. Equilibrium and stability of systems with imperfections are discussed. Nonlinear analyses of limit point and bifurcation systems are provided. Chapter 9 deals with the influence of nonlinear material behavior on buckling states. Systems with both stable and unstable postbuckling behavior are discussed. Examples are provided.
Imperfection sensitivity of critical points is discussed in Chapter 10, which includes the sensitivity of limit points to imperfections and imperfection sensitivity in symmetric and asymmetric bifurcation systems.
Chapter 11 deals with sensitivity of bifurcation points to changes in design parameters, which includes sensitivity to geometrical imperfections and sensitivity to changes in design parameters that are relevant in optimization, stochastic analysis, etc. The sensitivity of postcritical behavior with respect to changes in design parameters is discussed in Chapter 12.
Chapter 13 provides the W-formulation for bifurcation states in which the postcritical path is written in terms of sliding coordinates, and equations to obtain the asymptotic coefficients are derived. The analysis using sliding coordinates is entirely similar to that presented in Chapter 7, but the resulting equations are simpler.
Mode interaction and corresponding sensitivity to imperfections of problems with mode interactions are discussed in Chapters 14 and 15, respectively. Examples are provided which include a thin-walled I composite column under axial load, in which the modes are set to coincide by design.
In summary, Theory of Elastic Stability: Analysis and Sensitivity presents the material in an instructive manner, suitable for self-study. It emphasizes analytical treatment of the subject, which is essential for handling modern numerical methods as well as assessing and creating software packages. The author provides generous explanations, systematic derivations, and detailed discussions, supplemented by a variety of problems and solved examples. The book has good quality figures and a good subject index. It is a good textbook for graduate engineering students and equally useful as a reference for researchers and thus should be in all engineering libraries.