Theory of Stability of Continuous Elastic Structure

An Introduction to Stability Analysis of Elastic Structural SystemsIntroductionA Review of the Common Approaches to Stability Analysis in Structural EngineeringA Review of the Energy Criteria of Stability for Finite Degrees of Freedom SystemsConclusionsReferencesA Review of Some Functional Analysis ConceptsIntroductionMetric Spaces, Normed Spaces, and Branch SpacesFinite and Infinite Dimensional Normed Spaces; Equivalence and Nonequivalence of NormsDense Subsets, Total Bounded, and Compact SpacesOperatorsInner Product Spaces-Hilbert SpacesSymmetric Positive, and Positive-Definite Operators and Their Energy SpacesCalculus of Operators and Functionals-Extreme Values of FunctionalsGeneralized Derivatives and Sobolev SpacesReferencesGeneral Stability Analysis of Continuous Elastic SystemsIntroductionFormal Analysis of StabilityThe Requirement of the Stability at the Unstressed State for a Physically Acceptable Theory of Stability-The Choice of the Energy NormStability Analysis with Respect to the Energy NormReferencesEquilibrium Stability of Continuous Elastic StructuresIntroductionBuckling and Stability Analysis of the Undimensional Beam ModelTorsional-Flexural Buckling of Inextensible RodsBasic Problems in Stability Analysis of Plates and ShellsTridimensional ElasticityReferencesBuckling of Continuous Elastic StructuresIntroductionThe Structural Continuum-The General Formulation of the Neutral EquilibriumThe Additional Internal Work and the Neutral Equilibrium EquationComparisons with Other FormulationsPure Strains in Curvilinear CoordinatesBuckling of BarsBuckling by Torsion and Flexure of Thin-Walled Open Cross SectionsLateral Buckling of Deep BeamsBuckling of ShellsReferencesBifurcation or Snapping at the Critical State of Continuous Elastic StructuresIntroductionEquilibrium Paths of General Nonl