Theory of Stability of Continuous Elastic Structures

An Introduction to Stability Analysis of Elastic Structural Systems, Introduction, A Review of the Common Approaches to Stability Analysis in Structural Engineering, A Review of the Energy Criteria of Stability for Finite Degrees of Freedom Systems, Conclusions, A Review of Some Functional Analysis Concepts, Metric Spaces, Normed Spaces, and Branch Spaces, Finite and Infinite Dimensional Normed Spaces; Equivalence and Nonequivalence of Norms, Dense Subsets, Total Bounded, and Compact Spaces, Operators, Inner Product Spaces-Hilbert Spaces, Symmetric Positive,, and Positive-Definite Operators and Their Energy Spaces, Calculus of Operators and Functionals-Extreme Values of Functionals, Generalized Derivatives and Sobolev Spaces, General Stability Analysis of Continuous Elastic Systems, Formal Analysis of Stability, The Requirement of the Stability at the Unstressed State for a Physically Acceptable Theory of Stability-The Choice of the Energy Norm, Stability Analysis with Respect to the Energy Norm, Equilibrium Stability of Continuous Elastic Structures, Buckling and Stability Analysis of the Undimensional Beam Model, Torsional-Flexural Buckling of Inextensible Rods, Basic Problems in Stability Analysis of Plates and Shells, Tridimensional Elasticity, Buckling of Continuous Elastic Structures, The Structural Continuum-The General Formulation of the Neutral Equilibrium, The Additional Internal Work and the Neutral Equilibrium Equation, Comparisons with Other Formulations, Pure Strains in Curvilinear Coordinates, Buckling of Bars, Buckling by Torsion and Flexure of Thin-Walled Open Cross Sections, Lateral Buckling of Deep Beams, Buckling of Shells, Bifurcation or Snapping at the Critical State of Continuous Elastic Structures, Equilibrium Paths of General Nonlinear Elastic Systems, Bifurcation of Perfect Systems, General Aspects of the Postcritical Behavior of Quasiperfect Structural Systems, Some Applications of the Initial Postbuckling Analysis.