1300 187 187
This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives 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. The classical part is a revision of the well-known text Foundations of Solid Mechanics, with a much-expanded discussion on the theories of plasticity and large elastic deformation with finite strains. The computational part is all new and is aimed at solving many major linear and nonlinear boundary-value problems.
| Introduction | p. 1 |
| Hooke's Law | p. 2 |
| Linear Solids with Memory | p. 9 |
| Sinusoidal Oscillations in Viscoelastic Material: Models of Viscoelasticity | p. 12 |
| Plasticity | p. 14 |
| Vibrations | p. 15 |
| Prototype of Wave Dynamics | p. 18 |
| Biomechanics | p. 22 |
| Historical Remarks | p. 25 |
| Tensor Analysis | p. 30 |
| Notation and Summation Convention | p. 30 |
| Coordinate Transformation | p. 33 |
| Euclidean Metric Tensor | p. 34 |
| Scalars, Contravariant Vectors, Covariant Vectors | p. 38 |
| Tensor Fields of Higher Rank | p. 39 |
| Some Important Special Tensors | p. 40 |
| The Significance of Tensor Characteristics | p. 42 |
| Rectangular Cartesian Tensors | p. 43 |
| Contraction | p. 44 |
| Quotient Rule | p. 45 |
| Partial Derivatives in Cartesian Coordinates | p. 46 |
| Covariant Differentiation of Vector Fields | p. 48 |
| Tensor Equations | p. 49 |
| Geometric Interpretation of Tensor Components | p. 52 |
| Geometric Interpretation of Covariant Derivatives | p. 58 |
| Physical Components of a Vector | p. 60 |
| Stress Tensor | p. 66 |
| Stresses | p. 66 |
| Laws of Motion | p. 69 |
| Cauchy's Formula | p. 71 |
| Equations of Equilibrium | p. 73 |
| Transformation of Coordinates | p. 78 |
| Plane State of Stress | p. 79 |
| Principal Stresses | p. 82 |
| Shearing Stresses | p. 85 |
| Mohr's Circles | p. 86 |
| Stress Deviations | p. 87 |
| Octahedral Shearing Stress | p. 88 |
| Stress Tensor in General Coordinates | p. 90 |
| Physical Components of a Stress Tensor in General Coordinates | p. 94 |
| Equations of Equilibrium in Curvilinear Coordinates | p. 95 |
| Analysis of Strain | p. 97 |
| Deformation | p. 97 |
| Strain Tensors in Rectangular Cartesian Coordinates | p. 100 |
| Geometric Interpretation of Infinitesimal Strain Components | p. 103 |
| Rotation | p. 104 |
| Finite Strain Components | p. 106 |
| Compatibility of Strain Components | p. 108 |
| Multiply Connected Regions | p. 113 |
| Multivalued Displacements | p. 117 |
| Properties of the Strain Tensor | p. 118 |
| Physical Components | p. 121 |
| Example--Spherical Coordinates | p. 123 |
| Example--Cylindrical Polar Coordinates | p. 125 |
| Conservation Laws | p. 127 |
| Gauss' Theorem | p. 127 |
| Material and Spatial Descriptions of Changing Configurations | p. 128 |
| Material Derivative of Volume Integral | p. 131 |
| The Equation of Continuity | p. 133 |
| Equations of Motion | p. 134 |
| Moment of Momentum | p. 135 |
| Other Field Equations | p. 136 |
| Elastic and Plastic Behavior of Materials | p. 138 |
| Generalized Hooke's Law | p. 138 |
| Stress-Strain Relationship for Isotropic Elastic Materials | p. 140 |
| Ideal Plastic Solids | p. 143 |
| Some Experimental Information | p. 146 |
| A Basic Assumption of the Mathematical Theory of Plasticity | p. 150 |
| Loading and Unloading Criteria | p. 156 |
| Isotropic Stress Theories of Yield Function | p. 157 |
| Further Examples of Yield Functions | p. 159 |
| Work Hardening--Drucker's Hypothesis and Definition | p. 166 |
| Ideal Plasticity | p. 167 |
| Flow Rule for Work-Hardening Materials | p. 171 |
| Subsequent Loading Surfaces--Isotropic and Kinematic Hardening Rules | p. 177 |
| Mroz's, Dafalias and Popov's, and Valanis' Plasticity Theories | p. 189 |
| Strain Space Formulations | p. 195 |
| Finite Deformation | p. 199 |
| Plastic Deformation of Crystals | p. 200 |
| Linearized Theory of Elasticity | p. 203 |
| Basic Equations of Elasticity for Homogeneous Isotropic Bodies | p. 203 |
| Equilibrium of an Elastic Body Under Zero Body Force | p. 206 |
| Boundary Value Problems | p. 207 |
| Equilibrium and Uniqueness of Solutions | p. 210 |
| Saint Venant's Theory of Torsion | p. 213 |
| Soap Film Analogy | p. 222 |
| Bending of Beams | p. 224 |
| Plane Elastic Waves | p. 229 |
| Rayleigh Surface Wave | p. 231 |
| Love Wave | p. 235 |
| Solutions of Problems in Linearized Theory of Elasticity by Potentials | p. 238 |
| Scalar and Vector Potentials for Displacement Vector Fields | p. 238 |
| Equations of Motion in Terms of Displacement Potentials | p. 241 |
| Strain Potential | p. 243 |
| Galerkin Vector | p. 246 |
| Equivalent Galerkin Vectors | p. 249 |
| Example--Vertical Load on the Horizontal Surface of a Semi-Infinite Solid | p. 250 |
| Love's Strain Function | p. 252 |
| Kelvin's Problem--A Single Force Acting in the Interior of an Infinite Solid | p. 254 |
| Perturbation of Elasticity Solutions by a Change of Poisson's Ratio | p. 259 |
| Boussinesq's Problem | p. 262 |
| On Biharmonic Functions | p. 263 |
| Neuber-Papkovich Representation | p. 268 |
| Other Methods of Solution of Elastostatic Problems | p. 270 |
| Reflection and Refraction of Plane P and S Waves | p. 270 |
| Lamb's Problem--Line Load Suddenly Applied on Elastic Half-Space | p. 273 |
| Two-Dimensional Problems in Linearized Theory of Elasticity | p. 280 |
| Plane State of Stress or Strain | p. 280 |
| Airy Stress Functions for Two-Dimensional Problems | p. 282 |
| Airy Stress Function in Polar Coordinates | p. 288 |
| General Case | p. 295 |
| Representation of Two-Dimensional Biharmonic Functions by Analytic Functions of a Complex Variable | p. 299 |
| Kolosoff-Muskhelishvili Method | p. 301 |
| Variational Calculus, Energy Theorems, Saint-Venant's Principle | p. 313 |
| Minimization of Functionals | p. 313 |
| Functional Involving Higher Derivatives of the Dependent Variable | p. 319 |
| Several Unknown Functions | p. 320 |
| Several Independent Variables | p. 323 |
| Subsidiary Conditions--Lagrangian Multipliers | p. 325 |
| Natural Boundary Conditions | p. 328 |
| Theorem of Minimum Potential Energy Under Small Variations of Displacements | p. 330 |
| Example of Application: Static Loading on a Beam--Natural and Rigid End Conditions | p. 335 |
| The Complementary Energy Theorem Under Small Variations of Stresses | p. 339 |
| Variational Functionals Frequently Used in Computational Mechanics | p. 346 |
| Saint-Venant's Principle | p. 355 |
| Saint-Venant's Principle-Boussinesq-Von Mises-Sternberg Formulation | p. 359 |
| Practical Applications of Saint-Venant's Principle | p. 362 |
| Extremum Principles for Plasticity | p. 365 |
| Limit Analysis | p. 369 |
| Hamilton's Principle, Wave Propagation, Applications of Generalized Coordinates | p. 379 |
| Hamilton's Principle | p. 379 |
| Example of Application--Equation of Vibration of a Beam | p. 383 |
| Group Velocity | p. 393 |
| Hopkinson's Experiment | p. 396 |
| Generalized Coordinates | p. 398 |
| Approximate Representation of Functions | p. 399 |
| Approximate Solution of Differential Equations | p. 402 |
| Direct Methods of Variational Calculus | p. 402 |
| Elasticity and Thermodynamics | p. 407 |
| The Laws of Thermodynamics | p. 407 |
| The Energy Equation | p. 412 |
| The Strain Energy Function | p. 414 |
| The Conditions of Thermodynamic Equilibrium | p. 416 |
| The Positive Definiteness of the Strain Energy Function | p. 418 |
| Thermodynamic Restrictions on the Stress-Strain Law of an Isotropic Elastic Material | p. 419 |
| Generalized Hooke's Law, Including the Effect of Thermal Expansion | p. 421 |
| Thermodynamic Functions for Isotropic Hookean Materials | p. 423 |
| Equations Connecting Thermal and Mechanical Properties of a Solid | p. 425 |
| Irreversible Thermodynamics and Viscoelasticity | p. 428 |
| Basic Assumptions | p. 428 |
| One-Dimensional Heat Conduction | p. 431 |
| Phenomenological Relations-Onsager Principle | p. 432 |
| Basic Equations of Thermomechanics | p. 436 |
| Equations of Evolution for a Linear Hereditary Material | p. 440 |
| Relaxation Modes | p. 444 |
| Normal Coordinates | p. 447 |
| Hidden Variables and the Force-Displacement Relationship | p. 450 |
| Anisotropic Linear Viscoelastic Materials | p. 454 |
| Thermoelasticity | p. 456 |
| Basic Equations | p. 456 |
| Thermal Effects Due to a Change of Strain; Kelvin's Formula | p. 459 |
| Ratio of Adiabatic to Isothermal Elastic Moduli | p. 459 |
| Uncoupled, Quasi-Static Thermoelastic Theory | p. 461 |
| Temperature Distribution | p. 462 |
| Thermal Stresses | p. 464 |
| Particular Integral: Goodier's Method | p. 466 |
| Plane Strain | p. 467 |
| An Example--Stresses in a Turbine Disk | p. 470 |
| Variational Principle for Uncoupled Thermoelasticity | p. 473 |
| Variational Principle for Heat Conduction | p. 474 |
| Coupled Thermoelasticity | p. 478 |
| Lagrangian Equations for Heat Conduction and Thermoelasticity | p. 481 |
| Viscoelasticity | p. 487 |
| Viscoelastic Material | p. 487 |
| Stress-Strain Relations in Differential Equation Form | p. 491 |
| Boundary-Value Problems and Integral Transformations | p. 497 |
| Waves in an Infinite Medium | p. 500 |
| Quasi-Static Problems | p. 503 |
| Reciprocity Relations | p. 507 |
| Large Deformation | p. 514 |
| Coordinate Systems and Tensor Notation | p. 514 |
| Deformation Gradient | p. 521 |
| Strains | p. 525 |
| Right and Left Stretch Strain and Rotation Tensors | p. 526 |
| Strain Rates | p. 528 |
| Material Derivatives of Line, Area, and Volume Elements | p. 529 |
| Stresses | p. 532 |
| Example: Combined Tension and Torsion Loads | p. 539 |
| Objectivity | p. 543 |
| Equations of Motion | p. 548 |
| Constitutive Equations of Thermoelastic Bodies | p. 550 |
| More Examples | p. 557 |
| Variational Principles for Finite Elasticity: Compressible Materials | p. 562 |
| Variational Principles for Finite Elasticity: Nearly Incompressible or Incompressible Materials | p. 568 |
| Small Deflection of Thin Plates | p. 573 |
| Large Deflection of Plates | p. 581 |
| Incremental Approach to Solving Some Nonlinear Problems | p. 587 |
| Updated Lagrangian Description | p. 587 |
| Linearized Rates of Deformation | p. 590 |
| Linearized Rates of Stress Measures | p. 593 |
| Incremental Equations of Motion | p. 597 |
| Constitutive Laws | p. 598 |
| Incremental Variational Principles in Terms of T | p. 604 |
| Incremental Variational Principles in Terms of r | p. 610 |
| Incompressible and Nearly Incompressible Materials | p. 612 |
| Updated Solution | p. 617 |
| Incremental Loads | p. 620 |
| Infinitesimal Strain Theory | p. 622 |
| Finite Element Methods | p. 624 |
| Basic Approach | p. 626 |
| One Dimensional Problems Governed by a Second Order Differential Equation | p. 629 |
| Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations | p. 638 |
| Assembling and Constraining Global Matrices | p. 643 |
| Equation Solving | p. 651 |
| Two Dimensional Problems by One-Dimensional Elements | p. 655 |
| General Finite Element Formulation | p. 657 |
| Convergence | p. 664 |
| Two-Dimensional Shape Functions | p. 665 |
| Element Matrices for a Second-Order Elliptical Equation | p. 672 |
| Coordinate Transformation | p. 676 |
| Triangular Elements with Curved Sides | p. 679 |
| Quadrilateral Elements | p. 682 |
| Plane Elasticity | p. 690 |
| Three-Dimensional Shape Functions | p. 702 |
| Three Dimensional Elasticity | p. 708 |
| Dynamic Problems of Elastic Solids | p. 714 |
| Numerical Integration | p. 726 |
| Patch Tests | p. 731 |
| Locking-Free Elements | p. 735 |
| Spurious Modes in Reduced Integration | p. 750 |
| Perspective | p. 754 |
| Mixed and Hybrid Formulations | p. 756 |
| Mixed Formulations | p. 756 |
| Hybrid Formulations | p. 760 |
| Hybrid Singular Elements (Super-Elements) | p. 767 |
| Elements for Heterogeneous Materials | p. 782 |
| Elements for Infinite Domain | p. 782 |
| Incompressible or Nearly Incompressible Elasticity | p. 788 |
| Finite Element Methods for Plates and Shells | p. 795 |
| Linearized Bending Theory of Thin Plates | p. 795 |
| Reissner-Mindlin Plates | p. 805 |
| Mixed Functionals for Reissner Plate Theory | p. 813 |
| Hybrid Formulations for Plates | p. 819 |
| Shell as an Assembly of Plate Elements | p. 822 |
| General Shell Elements | p. 832 |
| Locking and Stabilization in Shell Applications | p. 843 |
| Finite Element Modeling of Nonlinear Elasticity, Viscoelasticity, Plasticity, Viscoplasticity and Creep | p. 848 |
| Updated Lagrangian Solution for Large Deformation | p. 849 |
| Incremental Solution | p. 852 |
| Dynamic Solution | p. 854 |
| Newton-Raphson Iteration Method | p. 855 |
| Viscoelasticity | p. 857 |
| Plasticity | p. 859 |
| Viscoplasticity | p. 869 |
| Creep | p. 870 |
| Bibliography | p. 873 |
| Author Index | p. 909 |
| Subject Index | p. 919 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9789810241247
ISBN-10: 9810241240
Series: Advanced Series in Engineering Science
Audience:
Professional
Format:
Paperback
Language:
English
Number Of Pages: 952
Published: 29th June 2001
Dimensions (cm): 23.0 x 15.4
x 5.0
Weight (kg): 1.347
9am - 4pm AEST, Monday - Friday
