Stability Of Structures: Elastic, Inelastic, Fracture And Damage Theories

by Zdenek P Bazant, Luigi Cedolin

Overview

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.

Product Details

ISBN-13:	9789814317030
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	08/17/2010
Edition description:	New Edition
Pages:	1040
Product dimensions:	6.40(w) x 9.70(h) x 1.40(d)

About the Author

Northwestern University

Politecnico di Milano

Table of Contents

	Preface	vii
	Introduction	xxi
I	Elastic Theories
1	Buckling of Elastic Columns by Equilibrium Analysis	3
1.1	Theory of Bending	4
1.2	Euler Load, Adjacent Equilibrium, and Bifurcation	5
1.3	Differential Equations of Beam-Columns	9
1.4	Critical Loads of Perfect Columns with Various End Restraints	12
1.5	Imperfect Columns and the Southwell Plot	19
1.6	Code Specifications for Beam-Columns	27
1.7	Effect of Shear and Sandwich Beams	30
1.8	Pressurized Pipes and Prestressed Columns	35
1.9	Large Deflections	38
1.10	Spatial Buckling of Beams under Torque and Axial Force	46
2	Buckling of Elastic Frames by Equilibrium Analysis	53
2.1	Stiffness and Flexibility Matrices of Beam-Columns	54
2.2	Critical Loads of Frames and Continuous Beams	61
2.3	Buckling as a Matrix Eigenvalue Problem and Use of Finite Elements	74
2.4	Large Regular Frames	78
2.5	Postcritical Reserve in Redundant Trusses	86
2.6	Postcritical Behavior of Frames	89
2.7	Built-Up Columns and Regular Frames as Columns with Shear	102
2.8	High Arches	108
2.9	Long-Wave Buckling of Regular Frames	118
2.10	Continuum Approximation for Large Regular Frames	129
3	Dynamic Analysis of Stability	144
3.1	Vibration of Columns or Frames and Divergence	144
3.2	Nonconservative Loads and Flutter	151
3.3	Pulsating Loads and Parametric Resonance	162
3.4	Other Types of Dynamic Loads	170
3.5	Definition of Stability	174
3.6	Theorems of Lagrange-Dirichlet and of Liapunov	178
3.7	Stability Criteria for Dynamic Systems	184
3.8	Stability of Continuous Elastic Systems	187
3.9	Nonlinear Oscillations and Chaos	189
4	Energy Methods	199
4.1	Positive-Definite Matrices, Eigenvalues, and Eigenvectors	199
4.2	Potential Energy for Discrete Elastic Systems	207
4.3	Bifurcation Buckling at Small Deflections	216
4.4	Snapthrough and Flat Arches	227
4.5	Large-Deflection Postcritical Behavior and Types of Bifurcation	238
4.6	Koiter's Theory, Imperfection Sensitivity, and Interaction of Modes	261
4.7	Catastrophe Theory and Breakdown of Symmetry	270
4.8	Snapdown at Displacement-Controlled Loading	278
4.9	Incremental Work Criterion at Equilibrium Displacements	294
5	Energy Analysis of Continuous Structures and Approximate Methods	305
5.1	Indirect Variational Method and Euler Equation	306
5.2	Beam on Elastic Foundation	314
5.3	Rayleigh Quotient	323
5.4	Timoshenko Quotient and Relations between Various Bounds	331
5.5	Bound Approximation for Columns, Frames, and High Arches	339
5.6	Rayleigh-Ritz Variational Method	348
5.7	Galerkin Variational Method	356
5.8	Method of Successive Approximations and Lower Bounds	358
5.9	Nonlinear Problems; Large Deflections of Columns	361
6	Thin-Walled Beams	370
6.1	Potential Energy and Differential Equations	371
6.2	Axial-Torsional Buckling of Columms	381
6.3	Lateral Buckling of Beams and Arches	384
6.4	Beams of Arbitrary Open Cross Section	392
6.5	Large Deflections	401
6.6	Box Girders	408
7	Plates and Shells	419
7.1	Classical Plate Theory	420
7.2	Differential Equation and Strain Energy	422
7.3	Buckling of Rectangular Plates	431
7.4	Large Deflections and Postcritical Reserve of Plates	440
7.5	Axisymmetric Buckling of Cylindrical Shells	449
7.6	Shallow or Quasi-Shallow Shells	453
7.7	Nonlinear Analysis of Shell Buckling and Imperfections	466
7.8	Sandwich Plates and Shells	474
II	Inelastic, Damage, and Fracture Theories
8	Elastoplastic Buckling	485
8.1	Perfect Columns or Structures and Shanley's Bifurcation	486
8.2	Imperfect Columns and Structures	506
8.3	Effect of Residual Stresses	513
8.4	Metal Columns and Structures: Design and Code Specifications	517
8.5	Concrete Columns and Structures: Design and Code Specifications	532
8.6	Perfectly Plastic Large-Deflection Buckling, Impact, and Blast	556
8.7	Geometric Tensile Instability, Localization, and Necking	569
9	Creep Buckling	584
9.1	Viscoelastic Stress-Strain Relations	585
9.2	Viscoelastic Buckling	590
9.3	Viscoplastic Buckling	597
9.4	Buckling of Aging Viscoelastic Structures	603
9.5	Effect of Creep Deflection on Concrete Column Strength	615
9.6	Nonlinear Creep and Long-Time Strength of Concrete Structures	619
9.7	Creep Buckling at Finite Deflections	623
10	Stability of Inelastic Structures, Bifurcation and Thermodynamic Basis	633
10.1	Thermodynamic Criteria of Stable State	633
10.2	Thermodynamic Criteria of Stable Path	650
10.3	Application to Elastoplastic Columns and Broader Implications	658
10.4	Critical States of Stability and Bifurcation	670
10.5	Stability at Infinitesimal Loading Cycles	680
10.6	Drucker's and Il'yushin's Postulates for Stable Materials	685
10.7	Stability of Frictional Materials and Structures	693
11	Three-Dimensional Continuum Instabilities and Effects of Finite Strain Tensor	706
11.1	Finite Strain	707
11.2	Stresses, Work, and Equilibrium at Finite Strain	715
11.3	Incremental Equilibrium and Objective Stress Rates	720
11.4	Tangential Moduli at Large Initial Stress	726
11.5	Stable States and Paths for Multidimensional Continuous Bodies	732
11.6	Column or Plate with Shear: Finite-Strain Effect	734
11.7	Surface Buckling and Internal Buckling of Anisotropic Solids	741
11.8	Consistent Geometric Stiffness Matrix of Finite Elements	748
11.9	Buckling of Curved Fibers in Composites	750
12	Fracture as a Stability Problem	760
12.1	Linear Elastic Fracture Mechanics	760
12.2	Nonlinear Fracture Mechanics and Size Effect	772
12.3	Crack Stability Criterion and R-Curve	782
12.4	Snapback Instability of a Crack and Ligament Tearing	788
12.5	Stable States and Stable Paths of Interacting Cracks	798
12.6	Crack Spacing	816
13	Damage and Localization Instabilities	829
13.1	Wave in Strain-Softening Materials	830
13.2	Series-Coupling Model for Localization Due to Softening	845
13.3	Localization of Softening Damage into Planar Bands	857
13.4	Localization of Softening Damage into Ellipsoidal Regions	869
13.5	Localization of Softening Damage into Spherical or Circular Regions	880
13.6	Localization in Beams and Softening Hinges	887
13.7	Friction: Static and Dynamic	902
13.8	Bifurcations Due to Interaction of Softening Damage Zones	907
13.9	Size Effect, Mesh Sensitivity, and Energy Criterion for Crack Bands	914
13.10	Nonlocal Continuum and Its Stability	921
13.11	Constitutive Equations for Strain Softening	937
	Glossary of Symbols	953
	Author Index	963
	Subject Index	973
	Appendix to the Dover Edition	985