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· 분류 : 외국도서 > 과학/수학/생태 > 과학 > 역학 > 역학 일반
· ISBN : 9781498708104
· 쪽수 : 786쪽
· 출판일 : 2014-12-29
목차
Introduction
Concepts and Mathematical Preliminaries
Introduction
Summation Convention
Dummy Index and Dummy Variables
Free Indices
Vector and Matrix Notation
Index Notation and Kronecker Delta
Permutation Tensor
Operations Using Vector, Matrix, and Einstein's Notation
Change of Reference Frame, Transformations, Tensors
Some Useful Relations
Summary
Kinematics of Motion, Deformation and Their Measures
Description of Motion
Lagrangian and Eulerian Descriptions
Material Particle Displacements
Continuous Deformation and Restrictions on the Motion
Material Derivative
Acceleration of a Material Particles
Coordinate Systems and Bases
Covariant Basis
Contravariant Basis
Alternate Way to Visualize Co- and Contra-Variant Bases
Jacobian of Deformation
Change of Description, Co- and Contra-Variant Measures
Notations For Covariant and Contravariant Measures
Deformation, Measures of Length and Change in Length
Covariant and Contravariant Measures of Strain
Changes in Strain Measures Due To Rigid Rotation of Frames
Invariants of Strain Tensors
Expanded Form of Strain Tensors
Physical Meaning of Strains
Polar Decomposition: Rotation and Stretch Tensors
Deformation of Areas and Volumes
Summary
Definitions and Measures of Stresses
Cauchy Stress Tensor
Contravariant and Covariant Stress Tensors
General Remarks
Summary of Stresses and Considerations in Their Derivations
General Considerations
Summary of Stress Measures
Conjugate Strain Measures
Relations between Stress Measures and Useful Relations
Summary
Rate of Deformation, Strain Rate, and Spin
Tensors
Rate of Deformation
Decomposition of [ L], the Spatial Velocity Gradient Tensor
Interpretation of the Components of [D]
Rate of Change or Material Derivative of Strain Tensors
Physical Meaning of Spin Tensor [ W ]
Vorticity Vector and Vorticity
Material Derivative of Determinant of J
Material Derivative of Volume
Rate of Change of Area: Material Derivative of Area
Stress And Strain Measures for Convected Time Derivatives
Convected Time Derivatives
Conjugate Convected Time Derivatives of Stress And Strain Tensors
Summary
Conservation and Balance Laws in Eulerian Description
Introduction
Mass Density
Conservation Of Mass: Continuity Equation
Transport Theorem
Conservation Of Mass: Continuity Equation
Balance of Linear Momenta
Kinetics of Continuous Media: Balance of Angular Momenta
First Law of Thermodynamics
Second Law of Thermodynamics
A Summary of Mathematical Models
Summary
Conservation and Balance Laws In Lagrangian Description
Introduction
Mathematical Model for Deforming Matter in Lagrangian Description
Conservation Of Mass: Continuity Equation
Balance of Linear Momenta
Balance of Angular Momenta
First Law of Thermodynamics
Second law of thermodynamics in terms of Φ
Second law of thermodynamics in terms of Ψ
Summary of Mathematical Models
First and Second Laws for Thermoelastic Solids
Summary
General Considerations in the Constitutive Theories
Introduction
Axioms of Constitutive Theory
Objective
Solid Matter
Fluids
Preliminary Considerations in the Constitutive Theories
General Approach of Deriving Constitutive Theories
Summary
Ordered Rate Constitutive Theories for Thermoelastic Solids
Introduction
Entropy inequality in Φ: Lagrangian description
Constitutive Theories for Thermoelastic Solids
Constitutive Theories Using Generators and Invariants
Strain energy density π: Lagrangian description
Stress in terms of Green strain based on π: Lagrangian
Stress in terms of Cauchy strain based on π: Lagrangian
Constitutive Theories for the Heat Vector: Lagrangian
Alternate Derivations: Strain In Terms Of Stress
Alternate Derivations: Heat Vector In Terms Of Stress
Summary
Thermoviscoelastic Solids without Memory
Introduction
Constitutive Theories Using Helmholtz Free Energy Density
Constitutive Theories Using Gibbs Potential
Comparisons of constitutive theories using Φ and Ψ
Thermoviscoelastic Solids with Memory
Introduction
Constitutive Theories Using Helmholtz Free Energy Density
Constitutive Theories Using Gibbs Potential
Comparisons of constitutive theories using Φ and Ψ
Ordered Rate Constitutive Theories for Thermofluids
Introduction
Second Law of Thermodynamics: Entropy Inequality
Dependent Variables and Their Arguments
Development of Constitutive Theory for Thermo Fluids
Rate Constitutive Theory of Order N
Rate Constitutive Theory of Order Two
Rate Constitutive Theory of Order One
Generalized Newtonian and Newtonian Fluids
Incompressible Ordered Thermo Fluids of Orders N, 2 And 1
Incompressible Generalized Newtonian, Newtonian Fluids
Conjugate Measures, Validity of Rate Constitutive Theories
Summary
Ordered Rate Constitutive Theories for Polymers
Introduction
Second Law of Thermodynamics: Entropy Inequality
Dependent Variables and Their Arguments
Development of Constitutive Theory for Polymers
Rate Constitutive Theory of Orders `M' and `N'
Rate Constitutive Theory of Orders M=1 and N=1
Rate Constitutive Theory of Orders M=1 and N=2
Constitutive Theories for Incompressible Polymers
Numerical Studies Using Giesekus Constitutive Model
Ordered Rate Constitutive Theories for Hypoelastic Solids
Introduction
Second Law of Thermodynamics: Entropy Inequality
Dependent Variables and Their Arguments
Development of Constitutive Theory for Hypo-Elastic Solids
Rate Constitutive Theory of Order `N'
Rate Constitutive Theory of Order Two
Rate Constitutive Theory of Order One
Compressible Generalized Hypo-Elastic Solids of Order One
Incompressible Ordered Hypo-Elastic Solids
Incompressible Generalized Hypo-Elastic Solids: Order One
Summary
Mathematical Models with Thermodynamic Relations
Introduction
Thermodynamic Pressure: Compressible Matter
Mechanical Pressure: Incompressible Matter
Specific Internal Energy
Variable Transport Properties or Material Coefficients
Final Form of the Mathematical Models
Summary
Principle of Virtual Work
Introduction
Hamilton's Principle in Continuum Mechanics
Euler-Lagrange Equation: Lagrangian Description
Euler-Lagrange Equation: Eulerian Description
Summary and Remarks
Appendices
