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El. knyga: Classical And Computational Solid Mechanics (Second Edition)

(Utc Aerospace Systems, Usa), (Univ Of California, San Diego, Usa & Hong Kong Univ Of Science & Technology, Hong Kong), (Univ Of California, San Diego, Usa)
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The second edition provides an update of the recent developments in classical and computational solid mechanics. The structure of the book is also updated to include five new areas: Fundamental Principles of Thermodynamics and Coupled Thermoelastic Constitutive Equations at Large Deformations, Functional Thermodynamics and Thermoviscoelasticity, Thermodynamics with Internal State Variables and Thermo-Elasto-Viscoplasticity, Electro-Thermo-Viscoelasticity/Viscoplasticity, and Meshless Method. These new topics are added as self-contained sections or chapters. Many books in the market do not cover these topics.This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives the first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions.
Preface To The Second Edition vii
1 Introduction 1(21)
1.1 Hooke's Law
2(6)
1.2 Plasticity and Viscoelasticity
8(1)
1.3 Vibrations
8(3)
1.4 Prototype of Wave Dynamics
11(3)
1.5 Biomechanics
14(3)
1.6 Historical Remarks
17(5)
2 Tensor Analysis 22(31)
2.1 Notation and Summation Convention
22(2)
2.2 Coordinate Transformation
24(2)
2.3 Euclidean Metric Tensor
26(3)
2.4 Scalars, Contravariant Vectors, Covariant Vectors
29(1)
2.5 Tensor Fields of Higher Rank
30(1)
2.6 Some Important Special Tensors
31(1)
2.7 The Significance of Tensor Characteristics
32(1)
2.8 Rectangular Cartesian Tensors
33(1)
2.9 Contraction
34(1)
2.10 Quotient Rule
35(1)
2.11 Partial Derivatives in Cartesian Coordinates
36(1)
2.12 Covariant Differentiation of Vector Fields
37(2)
2.13 Tensor Equations
39(2)
2.14 Geometric Interpretation of Tensor Components
41(6)
2.15 Geometric Interpretation of Covariant Derivatives
47(1)
2.16 Physical Components of a Vector
48(5)
3 Stress Tensor 53(29)
3.1 Stresses
53(3)
3.2 Laws of Motion
56(1)
3.3 Cauchy's Formula
57(3)
3.4 Equations of Equilibrium
60(4)
3.5 Transformation of Coordinates
64(2)
3.6 Plane State of Stress
66(2)
3.7 Principal Stresses
68(3)
3.8 Shearing Stresses
71(1)
3.9 Mohr's Circles
72(1)
3.10 Stress Deviations
72(1)
3.11 Octahedral Shearing Stress
73(2)
3.12 Stress Tensor in General Coordinates
75(4)
3.13 Physical Components of a Stress Tensor in General Coordinates
79(1)
3.14 Equations of Equilibrium in Curvilinear Coordinates
80(2)
4 Analysis Of Strain 82(26)
4.1 Deformation
82(3)
4.2 Strain Tensors in Rectangular Cartesian Coordinates
85(2)
4.3 Geometric Interpretation of Infinitesimal Strain Components
87(1)
4.4 Rotation
88(2)
4.5 Finite Strain Components
90(2)
4.6 Compatibility of Strain Components
92(4)
4.7 Multiply Connected Regions
96(3)
4.8 Multivalued Displacements
99(2)
4.9 Properties of the Strain Tensor
101(2)
4.10 Physical Components
103(2)
4.11 Example - Spherical Coordinates
105(1)
4.12 Example - Cylindrical Polar Coordinates
106(2)
5 Conservation Laws 108(10)
5.1 Gauss' Theorem
108(1)
5.2 Material and Spatial Description of Changing Configurations
109(3)
5.3 Material Derivative of Volume Integral
112(1)
5.4 The Equation of Continuity
113(1)
5.5 The Equations of Motion
114(1)
5.6 Moment of Momentum
115(1)
5.7 Other Field Equations
116(2)
6 Elastic And Plastic Behavior Of Materials 118(55)
6.1 Generalized Hooke's Law
118(1)
6.2 Stress-Strain Relationship for Isotropic Elastic Materials
119(3)
6.3 Ideal Plastic Solids
122(6)
6.4 Some Experimental Information
128(4)
6.5 A Basic Assumption of the Mathematical Theory of Plasticity: Existence of Yield Function
132(1)
6.6 Loading and Unloading Criteria
133(1)
6.7 Isotropic Stress Theories of Yield Function
134(2)
6.8 Further Examples of Yield Functions
136(5)
6.9 Work Hardening Drucker's Hypothesis and Definition
141(1)
6.10 Ideal Plasticity
142(3)
6.11 Flow Rule for Work Hardening Materials
145(5)
6.12 Subsequent Loading Surfaces - Isotropic and Kinematic Hardening Rules
150(10)
6.13 Mroz's, Dafalias and Popov's, and Valanis' Plasticity Theories
160(5)
6.14 Strain Space Formulations
165(4)
6.15 Deformation Theory of Plasticity
169(1)
6.16 Finite Deformation
170(1)
6.17 Plastic Deformation of Crystals
170(3)
7 Linearized Theory Of Elasticity 173(31)
7.1 Basic Equations of Elasticity
173(2)
7.2 Equilibrium Under Zero Body Force
175(1)
7.3 Boundary Value Problems
176(3)
7.4 Equilibrium and Uniqueness of Solutions
179(3)
7.5 Saint-Venant's Theory of Torsion
182(8)
7.6 Soap Film Analogy
190(1)
7.7 Bending of Beams
191(5)
7.8 Plane Elastic Waves
196(1)
7.9 Rayleigh Surface Waves
197(4)
7.10 Love Waves
201(3)
8 Solution Of Problems In Linearized Theory Of Elasticity By Potentials 204(32)
8.1 Scalar and Vector Potentials for Displacement Vector Fields
204(2)
8.2 Equations of Motion in Terms of Displacement Potentials
206(2)
8.3 Strain Potential
208(2)
8.4 Galerkin Vector
210(2)
8.5 Equivalent Galerkin Vectors
212(1)
8.6 Example - Vertical Load on the Horizontal Surface of a Semi-Infinite Solid
213(2)
8.7 Love's Strain Function
215(1)
8.8 Kelvin's Problem - A Single Force Acting in the Interior of an Infinite Solid
216(3)
8.9 Perturbation of Elasticity Solutions by a Change of Poisson's Ratio
219(3)
8.10 Boussinesq's Problem
222(1)
8.11 On Biharmonic Functions
223(3)
8.12 Neuber-Papkovich Representation
226(2)
8.13 Reflection and Refraction of Plane P and S Waves
228(2)
8.14 Lamb's Problem - Line Load Suddenly Applied on Elastic Half-Space
230(6)
9 Two-Dimensional Problems In Linearized Theory Of Elasticity 236(28)
9.1 Plane State of Stress or Strain
236(2)
9.2 Airy Stress Functions for 2-D Problems
238(5)
9.3 Airy Stress Function in Polar Coordinates
243(5)
9.4 General Case
248(4)
9.5 Representation of Two-Dimensional Biharmonic Functions by Analytic Functions of a Complex Variable
252(1)
9.6 Kolosoff-Muskhelishvili Method
253(11)
10 Variational Calculus, Energy Theorems, Saint-Venant's Principle 264(55)
10.1 Minimization of Functionals
264(5)
10.2 Functional Involving Higher Derivatives of the Dependent Variable
269(1)
10.3 Several Unknown Functions
270(2)
10.4 Several Independent Variables
272(2)
10.5 Subsidiary Conditions - Lagrange multipliers
274(3)
10.6 Natural Boundary Conditions
277(1)
10.7 Theorem of Minimum Potential Energy Under Small Variations of Displacements
278(4)
10.8 Example of Application: Static Loading on a Beam - Natural and Rigid End Conditions
282(4)
10.9 The Complementary Energy Theorem Under Small Variations of Stresses
286(6)
10.10 Variational Functionals Frequently Used in Computational Mechanics
292(6)
10.11 Saint-Venant's Principle
298(3)
10.12 Saint-Venant's Principle - Boussinesq-Von Mises-Sternberg Formulation
301(3)
10.13 Practical Applications of Saint-Venant's Principle
304(3)
10.14 Extremum Principles for Plasticity
307(3)
10.15 Limit Analysis
310(9)
11 Hamilton's Principle, Wave Propagation, Applications Of Generalized Coordinates 319(25)
11.1 Hamilton's Principle
319(3)
11.2 Example of Application - Equation of Vibration of a Beam
322(9)
11.3 Group Velocity
331(3)
11.4 Hopkinson's Experiment
334(2)
11.5 Generalized Coordinates
336(1)
11.6 Approximate Representation of Functions
337(2)
11.7 Approximate Solution of Differential Equations
339(1)
11.8 Direct Methods of Variational Calculus
339(5)
12 Thermodynamics And Thermoelasticity 344(39)
12.1 Laws of Thermodynamics
344(4)
12.2 Energy Equation
348(2)
12.3 Stability Conditions of Thermodynamic Systems
350(1)
12.4 Irreversible Thermodynamics
351(3)
12.5 Phenomenological Relations - Onager Principle
354(3)
12.6 Basic Equations of Thermomechanics
357(1)
12.7 Energy Density Function and Dissipation Potential for Hyper-Thermoelasticity
358(2)
12.8 Coupled Thermoelastic Constitutive Relations
360(2)
12.9 Strain and Complementary Energy Functions
362(2)
12.10 Thermal Effects: Kelvin's Formula
364(1)
12.11 Uncoupled, Quasi-Static Thermoelastic Theory
365(4)
12.12 Plane Strain (Plane Stress)
369(3)
12.13 Variational Principle for Uncoupled Thermoelasticity
372(4)
12.14 Variational Principle for Coupled Thermoelasticity
376(2)
12.15 Lagrangian Equations for Heat Conduction and Thermoelasticity
378(5)
13 Large Deformation 383(61)
13.1 Coordinate Systems and Tensor Notation
383(5)
13.2 Deformation Gradient
388(2)
13.3 Strains
390(2)
13.4 Right and Left Stretch and Rotation Tensors
392(1)
13.5 Strain Rates
393(1)
13.6 Material Derivatives of Line, Area and Volume Elements
394(2)
13.7 Stresses
396(6)
13.8 Example: Combined Tension and Torsion Loads
402(4)
13.9 Objectivity
406(4)
13.10 Equation of Motion
410(2)
13.11 Constitutive Equations of Thermoelastic Bodies
412(12)
13.12 Variational Principles for Nonlinear Elasticity: Compressible Materials
424(4)
13.13 Variational Principles for Nonlinear Elasticity: Nearly Incompressible or Incompressible Materials
428(4)
13.14 Small Deflection of Thin Plates
432(6)
13.15 Large Deflections of Plates
438(6)
14 Viscoelasticity And Thermoviscoelasticity 444(39)
14.1 Linear Solids with Memory
444(2)
14.2 Anisotropic Linear Viscoelastic Materials
446(4)
14.3 Stress-Strain Relations in Differential Equation Form
450(4)
14.4 Steady State Harmonic Oscillation
454(2)
14.5 Boundary-Value Problems and Integral Transforms
456(2)
14.6 Waves in an Infinite Medium
458(2)
14.7 Quasi-Static Problems
460(2)
14.8 Problems of Constant Poisson's Ratio
462(2)
14.9 Reciprocity Relations
464(4)
14.10 Functional Thermodynamics and Coupled Constitutive Relations
468(7)
14.10.1 Fundamental principles
469(1)
14.10.2 Coupled constitutive relations based on Helmholtz free energy functional
469(3)
14.10.3 Coupled constitutive relations based on Gibbs free energy functional
472(3)
14.11 Coupled Thermoviscoelastic Boundary-Initial Value Problems
475(1)
14.12 Linearized Theory and Integral Transforms
476(2)
14.13 Representation of Thermodynamic Property Functions for Materials with Memory on Intrinsic Time Scale
478(5)
14.13.1 Thermo-rheological and piezo-rheological simple materials
478(2)
14.13.2 Effective time theory for aging materials
480(1)
14.13.3 Time-aging-temperature-strain superposition
481(1)
14.13.4 Time-aging-temperature-stress superposition
481(2)
15 Thermodynamics With Internal State Variables And Thermo-Elasto-Viscoplasticity 483(14)
15.1 Thermodynamics with Internal State Variables
483(3)
15.2 Energy-Momentum Tensor and Invariant Integral
486(2)
15.3 Potentials or Pseudo-Potentials of Dissipation
488(1)
15.4 Alternative Formulation of Theories of Plasticity
489(3)
15.4.1 Thermo-elasto-plasticity
489(2)
15.4.2 Thermo-elasto-viscoplasticity
491(1)
15.5 Connecting Viscoplasticity to Viscoelasticity with Intrinsic Time Scale
492(5)
16 Electro-Thermo- Viscoelasticity/ iscoplasticity 497(20)
16.1 Introduction
497(1)
16.2 Physical Notations
497(5)
16.2.1 Electromagnetic field quantities
497(1)
16.2.2 Electromagnetic body force and couple
498(2)
16.2.3 Electromagnetic stress tensor and momentum vector
500(1)
16.2.4 Electromagnetic power
501(1)
16.3 Basic Field Equations for Electrosensitive Materials
502(1)
16.4 Augmented Helmholtz and Gibbs Free Energy Functionals
503(2)
16.4.1 Expansion of augmented Helmholtz free energy functional
503(1)
16.4.2 Expansion of augmented Gibbs free energy functional
504(1)
16.5 Finite Electro-Thermo-Viscoelasticity
505(4)
16.5.1 Finite electro-thermo-viscoelasticity based on augmented Helmholtz free energy functional
505(3)
16.5.2 Finite electro-thermo-viscoelasticity based on augmented Gibbs free energy functional
508(1)
16.6 Boundary-Initial Value Problems for Electrosensitive Materials
509(1)
16.7 Linearized Theory and Integral Transforms
510(2)
16.8 Representation of Thermodynamic Property Functions for Electrosensitive Materials with Memory on Intrinsic Time Scale
512(2)
16.8.1 Time-aging-temperature-strain-electric displacement supetposition
513(1)
16.8.2 Time-aging-temperature-stress-electric field superposition
513(1)
16.9 Reduction to Electro-Thermo-Elasticity
514(3)
17 Incremental Approach To Solving Some Nonlinear Problems 517(30)
17.1 Updated Lagrangian Description
517(2)
17.2 Linearized Rate of Deformation
519(2)
17.3 Linearized Rates of Stress Measures
521(3)
17.4 Incremental Equations of Motion
524(2)
17.5 Constitutive Laws
526(4)
17.6 Incremental Variational Principles in Terms of T
530(5)
17.7 Incremental Variational Principles in Terms of r
535(1)
17.8 Incompressible and Nearly Incompressible Materials
536(4)
17.9 Updated Solution
540(3)
17.10 Incremental Loads
543(2)
17.11 Infinitesimal Strain Theory
545(2)
18 Finite Element Methods 547(94)
18.1 Basic Approach
548(2)
18.2 One-Dimensional Problems Governed by Second Order Differential Equations
550(7)
18.3 Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations
557(4)
18.4 Assembling and Constraining Global Matrices
561(3)
18.5 Equation Solving
564(4)
18.6 Two-Dimensional Problems by One-Dimensional Elements
568(1)
18.7 General Finite Element Formulation
569(5)
18.8 Convergence
574(1)
18.9 Two-Dimensional Shape Functions
575(6)
18.10 Element Matrices for Second-Order Elliptical Equations
581(3)
18.11 Coordinate Transformation
584(1)
18.12 Triangular Elements with Curved Sides
585(2)
18.13 Quadrilateral Elements
587(6)
18.14 Plane Elasticity
593(8)
18.15 Three-Dimensional Shape Functions
601(4)
18.16 Three-Dimensional Elasticity
605(4)
18.17 Dynamic Problems of Elastic Solids
609(8)
18.18 Numerical Integration
617(4)
18.19 Patch Test
621(3)
18.20 Locking-Free Elements
624(11)
18.21 Spurious Modes in Reduced Integration
635(4)
18.22 Perspective
639(2)
19 Mixed And Hybrid Formulations 641(25)
19.1 Mixed Formulations
641(3)
19.2 Hybrid Formulations
644(5)
19.3 Hybrid Singular Elements (Super-Elements)
649(7)
19.4 Elements for Heterogeneous Materials
656(1)
19.5 Elements for Infinite Domain
656(6)
19.6 Incompressible or Nearly Incompressible Elasticity
662(4)
20 Finite Element Methods For Plates And Shells 666(36)
20.1 Linearized Bending Theory of Thin Plates
666(6)
20.2 Reissner-Mindlin Plates
672(6)
20.3 Mixed Functional of Reissner Plate Theory
678(4)
20.4 Hybrid Formulation for Plates
682(2)
20.5 General Shell Elements
684(10)
20.6 Locking and Stabilization in Shell Applications
694(3)
20.7 Elements for Heterogeneous Materials
697(5)
21 Finite Element Modeling Of Nonlinear Elasticity, Viscoelasticity, Plasticity, Viscoplasticity, And Creep 702(32)
21.1 Updated Lagrangian Solution for Large Deformation
703(2)
21.2 Incremental Solution
705(1)
21.3 Dynamic Solution
706(1)
21.4 Newton-Raphson Iteration Method
707(2)
21.5 Viscoelasticity
709(2)
21.6 Plasticity
711(9)
21.7 Viscoplasticity
720(1)
21.8 Creep
721(2)
21.9 Return Mapping Formulation with Von Mises Yield Surface
723(7)
21.10 Implicit Scheme For General Yield Surfaces
730(4)
22 Meshless Local Petrov-Galerkin And Eshelby-Atluri Methods 734(40)
22.1 Weak Forms
734(2)
22.2 Interpolation with a Local Support
736(10)
22.2.1 Moving least-square interpolation
736(7)
22.2.2 Shepard functions
743(1)
22.2.3 Interpolation errors
744(2)
22.2.4 Summary
746(1)
22.3 Domain Discretization
746(8)
22.3.1 Weight functions as test functions
747(4)
22.3.2 Dirac delta function as test function
751(1)
22.3.3 Heaviside step function as test function in OmegateI
752(1)
22.3.4 Shape function as test function
753(1)
22.3.5 Summary
754(1)
22.4 Approximation in Rigid Boundary Condition
754(3)
22.5 Numerical Integration of the Weak Forms
757(3)
22.6 Eshelby-Atluri Methods (EAMs)
760(13)
22.6.1 Balance laws of Eshelby stress tensor T
760(3)
22.6.2 Stress tensors tau, P, S, T
763(2)
22.6.3 Noether/Eshelby energy-momentum conservation laws in terms of tau, P, S, T
765(1)
22.6.4 Tangential material stiffness coefficients of Noether/Eshelby energy-momentum conservation laws
765(1)
22.6.5 MLPG weak-forms of energy-momentum conservation laws
766(7)
22.7 Summary
773(1)
Bibliography 774(35)
Author Index 809(10)
Subject Index 819
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