Stability of Structures Elastic Inelastic Fracture and Damage Theories 1st Edition by Zdenek P Bazant,Luigi Cedolin ISBN 9814317039 9789814317030

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ISBN 10: 9814317039

ISBN 13: 9789814317030 

Author: Zdenek P Bazant, Luigi Cedolin

A crucial element of structural and continuum mechanics, stability theory has limitless applications in civil, mechanical, aerospace, naval and nuclear engineering. This text of unparalleled scope presents a comprehensive exposition of the principles and applications of stability analysis. It has been proven as a text for introductory courses and various advanced courses for graduate students. It is also prized as an exhaustive reference for engineers and researchers.The authors’ focus on understanding of the basic principles rather than excessive detailed solutions, and their treatment of each subject proceed from simple examples to general concepts and rigorous formulations. All the results are derived using as simple mathematics as possible. Numerous examples are given and 700 exercise problems help in attaining a firm grasp of this central aspect of solid mechanics.The book is an unabridged republication of the 1991 edition by Oxford University Press and the 2003 edition by Dover, updated with 18 pages of end notes.

Table of contents:

Preface
Introduction

I Elastic Theories
1 Buckling of Elastic Columns by Equilibrium Analysis
1.1 Theory of Bending
1.2 Euler Load, Adjacent Equilibrium, and Bifurcation
1.3 Differential Equations of Beam-Columns
1.4 Critical Loads of Perfect Columns with Various End Restraints
1.5 Imperfect Columns and the Southwell Plot
1.6 Code Specifications for Beam-Columns
1.7 Effect of Shear and Sandwich Beams
1.8 Pressurized Pipes and Prestressed Columns
1.9 Large Deflections
1.10 Spatial Buckling of Beams under Torque and Axial Force

2 Buckling of Elastic Frames by Equilibrium Analysis
2.1 Stiffness and Flexibility Matrices of Beam-Columns
2.2 Critical Loads of Frames and Continuous Beams
2.3 Buckling as a Matrix Eigenvalue Problem and Use of Finite Elements
2.4 Large Regular Frames
2.5 Postcritical Reserve in Redundant Trusses
2.6 Postcritical Behavior of Frames
2.7 Built-Up Columns and Regular Frames as Columns with Shear
2.8 High Arches
2.9 Long-Wave Buckling of Regular Frames
2.10 Continuum Approximation for Large Regular Frames

3 Dynamic Analysis of Stability
3.1 Vibration of Columns or Frames and Divergence
3.2 Nonconservative Loads and Flutter
3.3 Pulsating Loads and Parametric Resonance
3.4 Other Types of Dynamic Loads
3.5 Definition of Stability
3.6 Theorems of Lagrange-Dirichlet and of Liapunov
3.7 Stability Criteria for Dynamic Systems
3.8 Stability of Continuous Elastic Systems
3.9 Nonlinear Oscillations and Chaos

4 Energy Methods
4.1 Positive-Definite Matrices, Eigenvalues, and Eigenvectors
4.2 Potential Energy for Discrete Elastic Systems
4.3 Bifurcation Buckling at Small Deflections
4.4 Snapthrough and Flat Arches
4.5 Large-Deflection Postcritical Behavior and Types of Bifurcation
4.6 Koiter’s Theory, Imperfection Sensitivity, and Interaction of Modes
4.7 Catastrophe Theory and Breakdown of Symmetry
4.8 Snapdown at Displacement-Controlled Loading
4.9 Incremental Work Criterion at Equilibrium Displacements

5 Energy Analysis of Continuous Structures and Approximate Methods
5.1 Indirect Variational Method and Euler Equation
5.2 Beam on Elastic Foundation
5.3 Rayleigh Quotient
5.4 Timoshenko Quotient and Relations between Various Bounds
5.5 Bound Approximation for Columns, Frames, and High Arches
5.6 Rayleigh-Ritz Variational Method
5.7 Galerkin Variational Method
5.8 Method of Successive Approximations and Lower Bounds
5.9 Nonlinear Problems; Large Deflections of Columns

6 Thin-Walled Beams
6.1 Potential Energy and Differential Equations
6.2 Axial-Torsional Buckling of Columns
6.3 Lateral Buckling of Beams and Arches
6.4 Beams of Arbitrary Open Cross Section
6.5 Large Deflections
6.6 Box Girders

7 Plates and Shells
7.1 Classical Plate Theory
7.2 Differential Equation and Strain Energy
7.3 Buckling of Rectangular Plates
7.4 Large Deflections and Postcritical Reserve of Plates
7.5 Axisymmetric Buckling of Cylindrical Shells
7.6 Shallow or Quasi-Shallow Shells
7.7 Nonlinear Analysis of Shell Buckling and Imperfections
7.8 Sandwich Plates and Shells

II Inelastic, Damage, and Fracture Theories
8 Elastoplastic Buckling
8.1 Perfect Columns or Structures and Shanley’s Bifurcation
8.2 Imperfect Columns and Structures
8.3 Effect of Residual Stresses
8.4 Metal Columns and Structures: Design and Code Specifications
8.5 Concrete Columns and Structures: Design and Code Specifications
8.6 Perfectly Plastic Large-Deflection Buckling, Impact, and Blast
8.7 Geometric Tensile Instability, Localization, and Necking

9 Creep Buckling
9.1 Viscoelastic Stress-Strain Relations
9.2 Viscoelastic Buckling
9.3 Viscoplastic Buckling
9.4 Buckling of Aging Viscoelastic Structures
9.5 Effect of Creep Deflection on Concrete Column Strength
9.6 Nonlinear Creep and Long-Time Strength of Concrete Structures
9.7 Creep Buckling at Finite Deflections

10 Stability of Inelastic Structures, Bifurcation and Thermodynamic Basis
10.1 Thermodynamic Criteria of Stable State
10.2 Thermodynamic Criteria of Stable Path
10.3 Application to Elastoplastic Columns and Broader Implications
10.4 Critical States of Stability and Bifurcation
10.5 Stability at Infinitesimal Loading Cycles
10.6 Drucker’s and Il’yushin’s Postulates for Stable Materials
10.7 Stability of Frictional Materials and Structures

11 Three-Dimensional Continuum Instabilities and Effects of Finite Strain Tensor
11.1 Finite Strain
11.2 Stresses, Work, and Equilibrium at Finite Strain
11.3 Incremental Equilibrium and Objective Stress Rates
11.4 Tangential Moduli at Large Initial Stress
11.5 Stable States and Paths for Multidimensional Continuous Bodies
11.6 Column or Plate with Shear: Finite-Strain Effect
11.7 Surface Buckling and Internal Buckling of Anisotropic Solids
11.8 Consistent Geometric Stiffness Matrix of Finite Elements
11.9 Buckling of Curved Fibers in Composites

12 Fracture as a Stability Problem
12.1 Linear Elastic Fracture Mechanics
12.2 Nonlinear Fracture Mechanics and Size Effect
12.3 Crack Stability Criterion and R-Curve
12.4 Snapback Instability of a Crack and Ligament Tearing
12.5 Stable States and Stable Paths of Interacting Cracks
12.6 Crack Spacing

13 Damage and Localization Instabilities
13.1 Wave in Strain-Softening Materials
13.2 Series-Coupling Model for Localization Due to Softening
13.3 Localization of Softening Damage into Planar Bands
13.4 Localization of Softening Damage into Ellipsoidal Regions
13.5 Localization of Softening Damage into Spherical or Circular Regions
13.6 Localization in Beams and Softening Hinges
13.7 Friction: Static and Dynamic
13.8 Bifurcations Due to Interaction of Softening Damage Zones
13.9 Size Effect, Mesh Sensitivity, and Energy Criterion for Crack Bands
13.10 Nonlocal Continuum and Its Stability
13.11 Constitutive Equations for Strain Softening

Glossary of Symbols
Author Index
Subject Index
Appendix to the Dover Edition

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Tags: Zdenek P Bazant, Luigi Cedolin, Stability, Structures, Elastic, Inelastic, Fracture, Damage, Theories