Theory of Elastic Stability: Analysis and Sensitivity

Abstract

Basic Concepts about Stability -- Some Historical Remarks about Developments in Stability -- Equilibrium States in Nonlinear Elasticity -- Total Potential Energy -- Stationary Total Potential Energy and Equilibrium -- Energy Formulation in Terms of Generalized Coordinates -- Perturbation Techniques -- Taylor Series Expansion -- Regular Perturbations via Implicit Differentiation -- Perturbations via Explicit Substitution -- Degenerate Perturbation Problems -- Singular Perturbation Problems -- Equilibrium Path of a Shallow Arch -- Stability of an Equilibrium State -- Some Basic Concepts about Stability Criteria -- Stability Criteria of Lyapunov -- The Total Potential Energy Criterion -- Stability in Terms of a Diagonal Quadratic Form -- Stability of an Equilibrium Path -- Dynamic Criterion of Stability -- Static Criterion of Stability -- Critical States -- Detecting Critical States along an Equilibrium Path -- The Specialized System -- Critical States along Nonlinear Equilibrium Paths -- Stability of a Critical State -- The Axially Loaded Column -- Column on an Elastic Foundation -- The Axially Loaded Strut -- A Two-Bar Frame -- Circular Arch under Central Point Load -- Rectangular Plate under In-Plane Loads -- Circular Ring -- Torsional Buckling of Compressed Elements -- Finite Elements for Buckling Loads -- Concluding Remarks -- The Limit Point -- Perturbation Equations -- The Conditions at a Limit Point -- The Specialized System -- The Shallow Arch -- Bifurcation States -- Conditions for Bifurcation Points.