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Theory of Stability of Continuous Elastic Structures



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ISBN 9780849389900
Published June 29, 1995 by CRC Press
272 Pages

 
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Book Description

Theory of Stability of Continuous Elastic Structures presents an applied mathematical treatment of the stability of civil engineering structures. The book's modern and rigorous approach makes it especially useful as a text in advanced engineering courses and an invaluable reference for engineers.

Table of Contents

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

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