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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 | |
References | |
A Review of Some Functional Analysis Concepts | |
Introduction | |
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 | |
References | |
General Stability Analysis of Continuous Elastic Systems | |
Introduction | |
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 | |
References | |
Equilibrium Stability of Continuous Elastic Structures | |
Introduction | |
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 | |
References | |
Buckling of Continuous Elastic Structures | |
Introduction | |
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 | |
References | |
Bifurcation or Snapping at the Critical State of Continuous Elastic Structures | |
Introduction | |
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 | |
References |