Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories

Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories

by Zdenek P. Bazant, Luigi Cedolin

ISBN-10: 0195055292

ISBN-13: 9780195055290

Pub. Date: 02/01/1991

Publisher: Oxford University Press, USA

A vital element of structural and continuum mechanics, stability theory has limitless applications in civil, mechanical, and aerospace engineering. This text explores the principles and applications of stability analysis, offering first-year graduate students solid footing in the subject; it also functions as a convenient reference for engineers and scientists…  See more details below


A vital element of structural and continuum mechanics, stability theory has limitless applications in civil, mechanical, and aerospace engineering. This text explores the principles and applications of stability analysis, offering first-year graduate students solid footing in the subject; it also functions as a convenient reference for engineers and scientists researching basic approaches and concepts. In addition to conventional aspects of elastic stability, the text emphasizes nonelastic stability. Topics include modern stability problems of fracture and damage, the thermodynamic principles of stability in irreversible systems, viscoelastic and viscoplastic buckling, and other key areas. The authors focus on supplying coverage of basic principles, rather than detailed solutions of specialized problems, and their treatment of each subject progresses from simple examples to general concepts and rigorous formulations. Numerous examples and 700 exercise problems encourage a firm grasp of this important subject.

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Product Details

Oxford University Press, USA
Publication date:
Oxford Engineering Science Series
Product dimensions:
6.94(w) x 9.56(h) x 2.20(d)

Table of Contents

IElastic Theories
1Buckling of Elastic Columns by Equilibrium Analysis3
1.1Theory of Bending4
1.2Euler Load, Adjacent Equilibrium, and Bifurcation5
1.3Differential Equations of Beam-Columns9
1.4Critical Loads of Perfect Columns with Various End Restraints12
1.5Imperfect Columns and the Southwell Plot19
1.6Code Specifications for Beam-Columns27
1.7Effect of Shear and Sandwich Beams30
1.8Pressurized Pipes and Prestressed Columns35
1.9Large Deflections38
1.10Spatial Buckling of Beams under Torque and Axial Force46
2Buckling of Elastic Frames by Equilibrium Analysis53
2.1Stiffness and Flexibility Matrices of Beam-Columns54
2.2Critical Loads of Frames and Continuous Beams61
2.3Buckling as a Matrix Eigenvalue Problem and Use of Finite Elements74
2.4Large Regular Frames78
2.5Postcritical Reserve in Redundant Trusses86
2.6Postcritical Behavior of Frames89
2.7Built-Up Columns and Regular Frames as Columns with Shear102
2.8High Arches108
2.9Long-Wave Buckling of Regular Frames118
2.10Continuum Approximation for Large Regular Frames129
3Dynamic Analysis of Stability144
3.1Vibration of Columns or Frames and Divergence144
3.2Nonconservative Loads and Flutter151
3.3Pulsating Loads and Parametric Resonance162
3.4Other Types of Dynamic Loads170
3.5Definition of Stability174
3.6Theorems of Lagrange-Dirichlet and of Liapunov178
3.7Stability Criteria for Dynamic Systems184
3.8Stability of Continuous Elastic Systems187
3.9Nonlinear Oscillations and Chaos189
4Energy Methods199
4.1Positive-Definite Matrices, Eigenvalues, and Eigenvectors199
4.2Potential Energy for Discrete Elastic Systems207
4.3Bifurcation Buckling at Small Deflections216
4.4Snapthrough and Flat Arches227
4.5Large-Deflection Postcritical Behavior and Types of Bifurcation238
4.6Koiter's Theory, Imperfection Sensitivity, and Interaction of Modes261
4.7Catastrophe Theory and Breakdown of Symmetry270
4.8Snapdown at Displacement-Controlled Loading278
4.9Incremental Work Criterion at Equilibrium Displacements294
5Energy Analysis of Continuous Structures and Approximate Methods305
5.1Indirect Variational Method and Euler Equation306
5.2Beam on Elastic Foundation314
5.3Rayleigh Quotient323
5.4Timoshenko Quotient and Relations between Various Bounds331
5.5Bound Approximation for Columns, Frames, and High Arches339
5.6Rayleigh-Ritz Variational Method348
5.7Galerkin Variational Method356
5.8Method of Successive Approximations and Lower Bounds358
5.9Nonlinear Problems; Large Deflections of Columns361
6Thin-Walled Beams370
6.1Potential Energy and Differential Equations371
6.2Axial-Torsional Buckling of Columms381
6.3Lateral Buckling of Beams and Arches384
6.4Beams of Arbitrary Open Cross Section392
6.5Large Deflections401
6.6Box Girders408
7Plates and Shells419
7.1Classical Plate Theory420
7.2Differential Equation and Strain Energy422
7.3Buckling of Rectangular Plates431
7.4Large Deflections and Postcritical Reserve of Plates440
7.5Axisymmetric Buckling of Cylindrical Shells449
7.6Shallow or Quasi-Shallow Shells453
7.7Nonlinear Analysis of Shell Buckling and Imperfections466
7.8Sandwich Plates and Shells474
IIInelastic, Damage, and Fracture Theories
8Elastoplastic Buckling485
8.1Perfect Columns or Structures and Shanley's Bifurcation486
8.2Imperfect Columns and Structures506
8.3Effect of Residual Stresses513
8.4Metal Columns and Structures: Design and Code Specifications517
8.5Concrete Columns and Structures: Design and Code Specifications532
8.6Perfectly Plastic Large-Deflection Buckling, Impact, and Blast556
8.7Geometric Tensile Instability, Localization, and Necking569
9Creep Buckling584
9.1Viscoelastic Stress-Strain Relations585
9.2Viscoelastic Buckling590
9.3Viscoplastic Buckling597
9.4Buckling of Aging Viscoelastic Structures603
9.5Effect of Creep Deflection on Concrete Column Strength615
9.6Nonlinear Creep and Long-Time Strength of Concrete Structures619
9.7Creep Buckling at Finite Deflections623
10Stability of Inelastic Structures, Bifurcation and Thermodynamic Basis633
10.1Thermodynamic Criteria of Stable State633
10.2Thermodynamic Criteria of Stable Path650
10.3Application to Elastoplastic Columns and Broader Implications658
10.4Critical States of Stability and Bifurcation670
10.5Stability at Infinitesimal Loading Cycles680
10.6Drucker's and Il'yushin's Postulates for Stable Materials685
10.7Stability of Frictional Materials and Structures693
11Three-Dimensional Continuum Instabilities and Effects of Finite Strain Tensor706
11.1Finite Strain707
11.2Stresses, Work, and Equilibrium at Finite Strain715
11.3Incremental Equilibrium and Objective Stress Rates720
11.4Tangential Moduli at Large Initial Stress726
11.5Stable States and Paths for Multidimensional Continuous Bodies732
11.6Column or Plate with Shear: Finite-Strain Effect734
11.7Surface Buckling and Internal Buckling of Anisotropic Solids741
11.8Consistent Geometric Stiffness Matrix of Finite Elements748
11.9Buckling of Curved Fibers in Composites750
12Fracture as a Stability Problem760
12.1Linear Elastic Fracture Mechanics760
12.2Nonlinear Fracture Mechanics and Size Effect772
12.3Crack Stability Criterion and R-Curve782
12.4Snapback Instability of a Crack and Ligament Tearing788
12.5Stable States and Stable Paths of Interacting Cracks798
12.6Crack Spacing816
13Damage and Localization Instabilities829
13.1Wave in Strain-Softening Materials830
13.2Series-Coupling Model for Localization Due to Softening845
13.3Localization of Softening Damage into Planar Bands857
13.4Localization of Softening Damage into Ellipsoidal Regions869
13.5Localization of Softening Damage into Spherical or Circular Regions880
13.6Localization in Beams and Softening Hinges887
13.7Friction: Static and Dynamic902
13.8Bifurcations Due to Interaction of Softening Damage Zones907
13.9Size Effect, Mesh Sensitivity, and Energy Criterion for Crack Bands914
13.10Nonlocal Continuum and Its Stability921
13.11Constitutive Equations for Strain Softening937
Glossary of Symbols953
Author Index963
Subject Index973
Appendix to the Dover Edition985

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