한티미디어 / (주)한티에듀

Continuum Mechanics

: Elasticity, Plasticity, Viscoelasticity

역/저자	Ellis H. Dill

ISBN	9780849397790

판형	235*166

페이지	352

정가	65,000 원

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This volume is intended as a reference for professional engineers as well as a teaching text for first-year graduate students in engineering. It features concise, yet thorough coverage of the following aspects of continuum mechanics: elasticity, fluid mechanics, plasticity, and viscoelasticity. It also provides an introduction to the continuum model for fatigue and fracture mechanics as well as a complete derivation of the basic equations and solution procedures for the finite element method. Direct solutions of the basic equations are not discussed beyond the simple deformations. Dill teaches mechanical and aerospace engineering at Rutgers U. Annotation ⓒ2007 Book News, Inc., Portland, OR (booknews.com)

Chapter 1 Fundamentals of Continuum Mechanics 1(48)
1.1 Material Models 1(2)
1.2 Classical Space-Time 3(1)
1.3 Material Bodies 4(2)
1.4 Strain 6(4)
1.5 Rate of Strain 10(3)
1.6 Curvilinear Coordinate Systems 13(3)
1.7 Conservation of Mass 16(2)
1.8 Balance of Momentum 18(7)
1.8.1 Virtual Work 22(1)
1.8.2 Physical Components 23(2)
1.9 Balance of Energy 25(1)
1.10 Constitutive Equations 26(2)
1.11 Thermodynamic Dissipation 28(1)
1.12 Objectivity: Invariance for Rigid Motions 29(3)
1.13 Coleman-Mizel Model 32(3)
1.13.1 Nonlinear Kelvin-Voigt Materials 34(1)
1.14 Fluid Mechanics 35(10)
1.14.1 Objectivity 36(1)
1.14.2 Dissipation Principle 37(3)
1.14.3 Thermodynamics of Fluids 40(3)
1.14.4 Couette Flow 43(2)
1.15 Problems for Chapter 1 45(3)
1.16 Bibliography 48(1)
Chapter 2 Nonlinear Elasticity 49(64)
2.1 Thermoelasticity 49(4)
2.2 Material Symmetries 53(2)
2.3 Isotropic Materials 55(8)
2.3.1 Principal Stresses and Principal Extensions 58(3)
2.3.2 Tensile Test 61(2)
2.4 Incompressible Materials 63(2)
2.5 Conjugate Measures of Stress and Strain 65(3)
2.6 Some Symmetry Groups 68(5)
2.7 Rate Formulations for Elastic Materials 73(4)
2.8 Energy Principles 77(2)
2.8.1 Potential Energy 77(2)
2.8.2 Complementary Energy 79(1)
2.9 Geometry of Small Deformations 79(2)
2.10 Linear Elasticity 81(5)
2.10.1 Anisotropic Materials 85(1)
2.11 Special Constitutive Models for Isotropic Materials 86(19)
2.11.1 Linear Stress?train Model 91(2)
2.11.2 Kirchhoff Model 93(1)
2.11.3 Blatz-Ko Model 94(2)
2.11.4 Generalized Mooney-Rivlin Model 96(3)
2.11.5 Ogden Foam 99(1)
2.11.6 Logarithmic Strain 100(1)
2.11.7 Gent Model 101(2)
2.11.8 Yeoh Model 103(2)
2.12 Mechanical Restrictions on the Constitutive Relations 105(5)
2.12.1 Tensile Test 106(1)
2.12.2 Volumetric Strain 107(1)
2.12.3 The Pressure-Compression (P-C) Inequality 107(1)
2.12.4 The Tension-Extension Inequality 107(1)
2.12.5 Extension-Tension (E-T) Inequalities 108(1)
2.12.6 Ordered Forces (O-F) Inequalities 108(1)
2.12.7 General Condition of Monotonicity (GCM) 108(2)
2.13 Problems for Chapter 2 110(2)
2.14 Bibliography 112(1)
Chapter 3 Linear Elasticity 113(46)
3.1 Basic Equations 113(4)
3.2 Plane Strain 117(1)
3.3 Plane Stress 118(1)
3.4 Properties of Solutions 119(3)
3.5 Potential Energy 122(4)
3.5.1 Proof of Minimum Potential Energy 124(2)
3.6 Special Matrix Notation 126(1)
3.7 The Finite Element Method of Solution 127(12)
3.7.1 Basic Equations in Matrix Notation 133(2)
3.7.2 Basic Equations Using Virtual Work 135(1)
3.7.3 Displacements Are Underestimated 136(1)
3.7.4 Dynamical Equations 137(2)
3.7.5 Example Problem 139(1)
3.8 General Equations for an Assembly of Elements 139(10)
3.8.1 Generalized Variational Principle 141(1)
3.8.2 Potential Energy 142(1)
3.8.3 Hybrid Displacement Functional 143(1)
3.8.4 Hybrid Stress and Complementary Energy 143(2)
3.8.5 Mixed Methods of Analysis 145(3)
3.8.6 Nearly Incompressible Materials 148(1)
3.9 Finite Element Analysis for Large Deformations 149(7)
3.9.1 Example Problem 155(1)
3.10 Problems for Chapter 3 156(2)
3.11 Bibliography 158(1)
Chapter 4 Plasticity 159(54)
4.1 Classical Theory of Plasticity 159(4)
4.2 Work Principle 163(2)
4.3 von Mises-Type Yield Criterion 165(3)
4.4 Hill Yield Criterion for Orthotropic Materials 168(4)
4.4.1 Orthotropic Materials 169(1)
4.4.2 Transverse Isotropy 170(1)
4.4.3 Bauschinger Effect 171(1)
4.5 Isotropic Hardening 172(5)
4.5.1 Strain Hardening 172(4)
4.5.2 Work Hardening 176(1)
4.6 Kinematic Hardening 177(5)
4.6.1 Theory of Prager 177(4)
4.6.2 Theory of Ziegler 181(1)
4.7 Combined Hardening laws 182(5)
4.7.1 Isotropic Strain Hardening with Prager's Rule for Kinematic Hardening 182(2)
4.7.2 Isotropic Work Hardening and Prager's Rule 184(1)
4.7.3 Isotropic Strain Hardening with Ziegler's Rule for Kinematic Hardening 185(1)
4.7.4 Chaboche's Model 186(1)
4.8 General Equations of Plasticity 187(3)
4.9 Strain Formulation of Plasticity 190(7)
4.9.1 Work Postulate 191(6)
4.10 Finite Element Analysis 197(2)
4.10.1 Example Problem 198(1)
4.11 Large Deformations 199(8)
4.11.1 Approximation for the Materially Linear Case 203(1)
4.11.2 Work Postulate 204(2)
4.11.3 Rate Formulations 206(1)
4.12 Thermodynamics of Elastic-Plastic Materials 207(3)
4.13 Problems for Chapter 4 210(1)
4.14 Bibliography 211(2)
Chapter 5 Viscoelasticity 213(26)
5.1 Linear Viscoelasticity 213(17)
5.1.1 General Model 221(5)
5.1.2 Slow or Rapid Deformations 226(1)
5.1.3 Symmetry of the Relaxation Modulus 226(4)
5.2 Effect of Temperature 230(4)
5.3 Nonlinear Viscoelasticity 234(1)
5.4 Thermodynamics of Materials with Fading Memory 235(3)
5.5 Problems for Chapter 5 238(1)
5.6 Bibliography 238(1)
Chapter 6 Fracture and Fatigue 239(14)
6.1 Fracture Criterion 239(2)
6.2 Plane Crack through a Sheet 241(3)
6.3 Fracture Modes 244(1)
6.4 Calculation of the Stress Intensity Factor 245(2)
6.5 Crack Growth 247(4)
6.6 Problems for Chapter 6 251(1)
6.7 Bibliography 251(2)
Chapter 7 Mathematical Tools for Continuum Mechanics 253(80)
7.1 Sets of Real Numbers 253(7)
7.1.1 Indicial Notation 253(1)
7.1.2 Summation Convention 253(1)
7.1.3 The Kronecker Delta 254(2)
7.1.4 The Permutation Symbol 256(1)
7.1.5 Symmetry and Skew-Symmetry 257(2)
7.1.6 Integral Transformations 259(1)
7.2 Matrices 260(12)
7.2.1 Matrix Notation 260(3)
7.2.2 Matrix Addition and Multiplication 263(1)
7.2.3 Special Matrices 264(2)
7.2.4 Kronecker Products 266(3)
7.2.5 Determinants 269(2)
7.2.6 Inverse Matrix 271(1)
7.2.7 Linear Algebraic Equations 271(1)
7.3 Vector Analysis 272(15)
7.3.1 Vector Algebra 272(4)
7.3.2 Derivatives of Vectors 276(1)
7.3.3 Base Vectors 276(4)
7.3.4 Curvilinear Coordinates and Covariant Base Vectors 280(4)
7.3.5 Gradient, Divergence, and Curl of Vectors 284(1)
7.3.6 Cylindrical Coordinates 285(2)
7.4 Tensors 287(24)
7.4.1 Tensor Algebra 287(2)
7.4.2 Tensor Product of Vectors and Components of Tensors 289(4)
7.4.3 Derivatives of Tensors 293(1)
7.4.4 Trace of a Tensor 294(1)
7.4.5 Transpose of a Tensor and Dot from the Left 295(2)
7.4.6 Principal Invariants of Tensors 297(2)
7.4.7 Regular, Singular, and Inverse Tensors 299(2)
7.4.8 Eigenvalues, Eigenvectors, and Eigenprojections of Symmetric Tensors 301(3)
7.4.9 Canonical Representation of Tensors 304(3)
7.4.10 Polar Decomposition of Tensors 307(1)
7.4.11 Cayley-Hamilton Theorem and Alternate Invariants 308(1)
7.4.12 Higher-Order Tensors 309(2)
7.5 Isotropic Functions 311(5)
7.5.1 Scalar-Valued Functions of One Tensor 311(1)
7.5.2 Scalar-Valued Functions of Two Tensors 312(2)
7.5.3 Linear Isotropic Tensor-Valued Functions of a Tensor 314(1)
7.5.4 General Isotropic Tensor-Valued Functions of a Tensor 315(1)
7.6 Abstract Derivatives 316(8)
7.6.1 Real-Valued Functions of Vectors 316(2)
7.6.2 Vector-Valued Functions of Vectors 318(1)
7.6.3 Scalar-Valued Functions of Tensors 319(3)
7.6.4 Tensor-Valued Functions of Tensors 322(1)
7.6.5 Multiple Arguments and the Chain Rule 323(1)
7.7 Some Basic Mathematical Definitions and Theorems 324(5)
7.7.1 Fields 324(1)
7.7.2 Vector Spaces 324(1)
7.7.3 Metric Spaces 325(1)
7.7.4 Normed Spaces, Banach Spaces 326(1)
7.7.5 Scalar Product and Hilbert Space 327(1)
7.7.6 Fading Memory Space 327(1)
7.7.7 Derivative of a Function 328(1)
7.8 Problems for Chapter 7 329(2)
7.9 Bibliography 331(2)
Index 333