مقدمه اي بر مكانيك محيط هاي پيوسته

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مقدمه اي بر مكانيك محيط هاي پيوسته

۵۱ بازديد

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كتاب مقدمه اي بر مكانيك محيط هاي پيوسته (Introduction to Continuum Mechanics)، مشتمل بر 252 صفحه، در 14 فصل، با فرمت PDF، به زبان انگليسي، همراه با مثال ها و تمرينات متعدد به ترتيب زير گردآوري شده است:

Chapter 1: Introduction

  • Concept of a Continuum
  • Sequence of Topics

Chapter 2: Cartesian Tensors

  • Index Notation and Summation Convention
  • Kronecker Delta and Permutation Symbol
  • Example: Skew Symmetry
  • Example: Products
  • Coordinate System
  • Coordinate Transformations
  • Vectors
  • Tensors
  • Examples of Tensors
  • Quotient Rule
  • Inner Products: Notation
  • Quadratic Forms and Eigenvalue Problems
  • Example: Eigenvalue Problem
  • Diagonalization and Polar Decomposition
  • Example: Polar Decomposition

Chapter 3: General Tensors

  • Vectors and Tensors
  • Physical Components
  • Tensor Calculus
  • Curvature Tensors
  • Applications
  • Example: Incompressible Flow
  • Example:Equilibrium of Stresses

Chapter 4: Integral Theorems

  • Gauss Theorem
  • Stokes Theorem

Chapter 5: Deformation

  • Lagrangian and Eulerian Descriptions
  • Deformation Gradients
  • Deformation Gradient Vectors
  • Curvilinear Systems
  • Strain Tensors
  • Decomposition of Displacement Gradients
  • Stretch
  • Extension
  • Infinitesimal Strains and Rotations
  • Deformation Ellipsoids
  • Polar Decomposition of the Deformation Gradient
  • Stretch and Rotation
  • Example: Polar Decomposition
  • Example: Square Root of a Matrix
  • Logarithmic Strain
  • Change of Volume
  • Change of Area
  • Compatibility Equations
  • Spatial Rotation and Two-Point Tensors
  • Curvilinear Coordinates

Chapter 6: Motion

  • Material Derivative
  • Some Terminology
  • Example: Path Line, Stream Line, and Streak Line
  • Length, Volume, and Area Elements
  • Length
  • Volume
  • Area
  • Material Derivatives of Integrals
  • Line Integrals
  • Area Integrals
  • Volume Integrals
  • Deformation Rate, Spin, and Vorticity
  • Strain Rate
  • Rotation Rate of Principal Axis

Chapter 7: Fundamental Laws of Mechanics

  • Mass
  • Conservation and Balance Laws
  • Conservation of Mass
  • Balance of Linear Momentum
  • Balance of Angular Momentum
  • Balance of Energy
  • Entropy Production
  • Axiom of Material Frame Indifference
  • Objective Measures of Rotation
  • Integrity Basis

Chapter 8: Stress Tensor

  • External Forces and Moments
  • Internal Forces and Moments
  • Cauchy Stress and Couple Stress Tensors
  • Transformation of the Stress Tensor
  • Principal Stresses
  • Shear Stress
  • Hydrostatic Pressure and Deviatoric Stresses
  • Objective Stress Rates
  • Local Conservation and Balance Laws
  • Conservation of Mass
  • Balance of Linear Momentum
  • Balance of Moment of Momentum (Angular Momentum)
  • Material Description of the Equations of Motion
  • First Piola–******chhoff Stress Tensor
  • Second Piola–******chhoff Stress Tensor

Chapter 9: Energy and Entropy Constraints

  • Classical Thermodynamics
  • Balance of Energy
  • Clausius–Duhem Inequality
  • Fourier’s Law of Heat Conduction
  • Newton’s Law of Visغير مجاز مي باشدity
  • Onsager’s Principle
  • Strain Energy Density
  • Ideal Gas
  • Internal Energy
  • Legendre or Contact Transformation
  • Surface Energy
  • Method of Jacobians in Thermodynamics

Chapter 10: Constitutive Relations

  • Invariance Principles
  • Principles of Exclusion
  • Principle of Coordinate Invariance
  • Principle of Spatial Invariance
  • Principle of Material Invariance
  • Principle of Dimensional Invariance
  • Principle of Consistency
  • Simple Materials
  • Elastic Materials
  • Elastic Materials of Cauchy
  • Elastic Materials of Green
  • Stokes Fluids
  • Invariant Surface Integrals
  • Singularities

Chapter 11: Hyperelastic Materials

  • Finite Elasticity
  • Homogeneous Deformation
  • Simple Extension
  • Hydrostatic Pressure
  • Simple Shear
  • Torsion of a Circular Cylinder
  • Approximate Strain Energy Functions
  • Hookean Materials
  • Small-Strain Approximation
  • Plane Stress and Plane Strain
  • Integrated Elasticity
  • Example: Incremental Loading
  • A Variational Principle for Static Elasticity
  • Isotropic Thermoelasticity
  • Specific Heats and Latent Heats
  • Strain Cooling
  • Adiabatic and Isothermal Elastic Modulus
  • Example: Rubber Elasticity
  • Linear Anisotropic Materials
  • Invariant Integrals

Chapter 12: Fluid Dynamics

  • Basic Equations
  • Approximate Constitutive Relations
  • Newtonian Fluids
  • Inviscid Fluids
  • Shearing Flow
  • Pipe Flow
  • Rotating Flow
  • Navier–Stokes Equations
  • Incompressible Flow
  • Compressible Flow
  • Inviscid Flow
  • Speed of Sound
  • Method of Characteristics
  • Bernoulli Equation
  • Invariant Integrals

Chapter 13: Viscoelasticity

  • Kelvin–Voigt Solid
  • Maxwell Fluid
  • Standard Linear Solid
  • Superposition Principle
  • Constitutive Laws in the Operator Form
  • Three-Dimensional Linear Constitutive Relations
  • Anisotropy
  • Biot’s Theory
  • Minimum Entropy Production Rate
  • Creep in Metals
  • Nonlinear Theories of Viscoelasticity
  • K-BKZ Model for Viscoelastic Fluids

Chapter 14: Plasticity

  • Idealized Theories
  • Rigid Perfectly Plastic Material
  • Elastic Perfectly Plastic Material
  • Elastic Linearly Hardening Material
  • Three-Dimensional Theories
  • Postyield Behavior
  • Levy–Mises Flow Rule
  • Prandtl–Reuss Flow Rule
  • General Yield Condition and Plastic Work
  • Plane Stress and Plane Strain
  • Rigid Plasticity and Slip-Line Field
  • Example: Symmetric External Cracks
  • Drucker’s Definition of Stability
  • Il´ıushin’s Postulate
  • Work-Hardening Rules
  • Perfectly Plastic Material
  • Isotropic Hardening
  • Kinematic Hardening
  • Hencky’s Deformation Theory
  • Endochronic Theory of Valanis
  • Plasticity and Damage
  • Minimum Dissipation Rate Principle

جهت دانلود كتاب مقدمه اي بر مكانيك محيط هاي پيوسته (Introduction to Continuum Mechanics)، برلينك زير كليك نماييد.

 

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