Self-contained text focuses on Koiter postbuckling analyses, with mathematical notions of stability of motion. Basing minimum energy principles for static stability upon dynamic concepts of stability of motion, it develops asymptotic buckling and postbuckling analyses from potential energy considerations, with applications to columns, plates, and arches. 1974 edition.

Table of Contents for Stability Theory and Its Applications to Structural Mechanics

Preface
1. General notions; agenda
2. Some geometric theory
2.1 Definitions of stability
2.2 Equilibrium phase plane analysis
2.3 General phase plane analysis
2.4 Summary
References
3. Autonomous system stability
3.1 Criteria for linear autonomous systems
3.2 The Lyapunov function--Definition and stability theorems
3.3 Some Lyapunov function applications
3.4 The theorem of minimum potential energy
3.5 Summary
References
4. Stability concepts for continuous systems
4.1 Lyapunov functionals for column stability
4.2 Definitions and theorems for Lyapunov functionals
4.3 The minimum potential energy criterion
4.4 Summary
References
5. Some results from nonlinear elasticity theory
5.1 Large bending deflections of columns
5.2 The von Kármán theory of plates
5.3 Some arch equations
5.4 Summary
References
6. Buckling and postbuckling of elastic columns
6.1 Energy criteria for column buckling
6.2 Imperfection and kinetic criteria for buckling
6.3 The elastica
6.4 Asymptotic analysis--Initial postbuckling behavior
6.5 Discussion of the Koiter asymptotic analysis
6.6 Asymptotic analysis--the Budiansky-Hutchinson approach
6.7 Summary
References
7. Buckling and postbuckling of elastic plates
7.1 Energy criteria for rectangular plates
7.2 Buckling of circular plates
7.3 Postbuckling behavior of circular plates
7.4 Postbuckling of rectangular plates
7.5 Summary
References
8. Buckling and postbuckling of circular arches
8.1 The shallow arch--A closed-form solution
8.2 Asymptotic analysis for arches
8.3 Shallow arch results
8.4 Steep arch results
8.5 Summary
References
9. Some applications of Lyapunov functionals
9.1 The wave equation
9.2 A hydrodynamics problem
9.3 Linear anisotropic elasticity
9.4 An aeroelastic problem
9.5 Instability of an Euler column
9.6 A bounding example
9.7 Summary
References
Index to authors; Subject index

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