مقدمه ای بر مکانیک محیط های پیوسته

Introduction to Continuum Mechanics -Part 1

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کتاب مقدمه ای بر مکانیک محیط های پیوسته (Introduction to Continuum Mechanics)، مشتمل بر 480 صفحه، در 9 فصل، با فرمت PDF، به زبان انگلیسی، همراه با مثال ها و تمرینات متعدد به ترتیب زیر گردآوری شده است:

Chapter 1: Introduction

  • Continuum Mechanics
  • A Look Forward
  • Summary
  • Problems

Chapter 2: VECTORS AND TENSORS

  • Background and Overview
  • Vector Algebra
  • Definition of a Vector
  • Vector addition
  • Multiplication of a vector by a scalar
  • Linear independence of vectors
  • Scalar and Vector Products
  • Scalar product
  • Vector product
  • Triple products of vectors
  • Plane Area as a Vector
  • Reciprocal Basis
  • Components of a vector
  • General basis
  • Ortho normal basis
  • The Gram–Schmidt ortho normalization
  • Summation Convention
  • Dummy index
  • Free index
  • Kronecker delta
  • Permutation symbol
  • Transformation Law for Different Bases
  • General transformation laws
  • Transformation laws for orthonormal systems
  • Theory of Matrices
  • Definition
  • Matrix Addition and Multiplication of a Matrix by a Scalar
  • Matrix Transpose
  • Symmetric and Skew Symmetric Matrices
  • Matrix Multiplication
  • Inverse and Determinant of a Matrix
  • Positive-Definite and Orthogonal Matrices
  • Vector Calculus
  • Differentiation of a Vector with Respect to a Scalar
  • .Curvilinear Coordinates
  • The Fundamental Metric
  • Derivative of a Scalar Function of aVector
  • The Del Operator
  • Divergence and Curl of a Vector
  • Cylindrical and Spherical Coordinate Systems
  • Gradient, Divergence, and Curl Theorems
  • Tensors
  • Dyads and Dyadics
  • Nonion Form of a Second-Order Tensor
  • Transformation of Components of a Tensor
  • Higher-Order Tensors
  • Tensor Calculus
  • Eigenvalues and Eigenvectors
  • Eigenvalue problem
  • Eigenvalues and eigen vectors of a real symmetric tensor
  • Spectral theorem
  • Calculation of eigenvalues and eigen vectors
  • Summary
  • Problems

Chapter 3: KINEMATICS OF CONTINUA

  • Introduction
  • Descriptions of Motion
  • Configurations of a Continuous Medium
  • Material Description
  • Spatial Description
  • Displacement Field
  • Analysis of Deformation
  • Deformation Gradient
  • Isochoric, Homogeneous, and In homogeneous Deformation
  • Isochoric deformation
  • Homogeneous deformation
  • Nonhomogeneous deformation
  • Change of Volume and Surface
  • Volume change
  • Area change
  • Strain Measures
  • Cauchy Green Deformation Tensors
  • Green Lagrange Strain Tensor
  • Physical Interpretation of Green–Lagrange Strain Components
  • Cauchy and Euler Strain Tensors
  • Transformation of Strain Components
  • Invariants and Principal Values of Strains
  • Infinitesimal Strain Tensor and Rotation Tensor
  • Infinitesimal Strain Tensor
  • Physical Interpretation of Infinitesimal Strain
  • Tensor Components
  • Infinitesimal Rotation Tensor
  • Infinitesimal Strains in Cylindrical and Spherical
  • Coordinate Systems
  • Cylindrical coordinate system
  • Spherical coordinate system
  • Velocity Gradient and Vorticity Tensors
  • Relationship Between D and ˙E
  • Compatibility Equations
  • Preliminary Comments
  • Infinitesimal Strains
  • Finite Strains
  • Rigid-Body Motions and Material Objectivity
  • Superposed Rigid-Body Motions
  • Introduction and rigid-body transformation
  • Effect on F
  • Effect on C and E
  • Effect on L and D
  • Material Objectivity
  • Observer transformation
  • Objectivity of various kinematic measures
  • Time rate of change in a rotating frame of reference
  • Polar Decomposition Theorem
  • Preliminary Comments
  • Rotation and Stretch Tensors
  • Objectivity of Stretch Tensors
  • Summary
  • Problems

Chapter 4: STRESS MEASURES

  • Introduction
  • Cauchy Stress Tensor and Cauchy’s Formula
  • Stress Vector
  • Cauchy’s Formula
  • Cauchy Stress Tensor
  • Transformation of Stress Components and Principal Stresses
  • Transformation of Stress Components
  • Invariants
  • Transformation equations
  • Principal Stresses and Principal Planes
  • Maximum Shear Stress
  • Other Stress Measures
  • Preliminary Comments
  • First Piola Kirchhoff Stress Tensor
  • Second Piola Kirchhoff Stress Tensor
  • Equilibrium Equations for Small Deformations
  • Objectivity of Stress Tensors
  • Cauchy Stress Tensor
  • First Piola Kirchhoff Stress Tensor
  • Second Piola Kirchhoff Stress Tensor
  • Summary
  • Problems

Chapter 5: CONSERVATION AND BALANCE LAWS

  • Introduction
  • Conservation of Mass
  • Preliminary Discussion
  • Material Time Derivative
  • Vector and Integral Identities
  • Vector identities
  • Integral identities
  • Continuity Equation in the Spatial Description
  • Continuity Equation in the Material Description
  • Reynolds Transport Theorem
  • Balance of Linear and Angular Momentum
  • Principle of Balance of Linear Momentum
  • Equations of motion in the spatial description
  • Equations of motion in the material description
  • Spatial Equations of Motion in Cylindrical and Spherical Coordinates
  • Cylindrical coordinates
  • Spherical coordinates
  • Principle of Balance of Angular Momentum
  • Mono polar case
  • Multi polar case
  • Thermodynamic Principles
  • Balance of Energy
  • Energy equation in the spatial description
  • Energy equation in the material description
  • Entropy Inequality
  • Homogeneous processes
  • In homogeneous processes
  • Conservation and Balance Equations in the Spatial Description
  • Conservation and Balance Equations in the Material Description
  • Closing Comments
  • Problems

Chapter 6: CONSTITUTIVE EQUATIONS

  • Introduction
  • General Comments
  • General Principles of Constitutive Theory
  • Material Frame Indifference
  • Restrictions Placed by the Entropy Inequality
  • Elastic Materials
  • Cauchy Elastic Materials
  • Green-Elastic or Hyper elastic Materials
  • Linearized Hyper elastic Materials: Infinitesimal Strains
  • Hookean Solids
  • Generalized Hooke’s Law
  • Material Symmetry Planes
  • Monoclinic Materials
  • Orthotropic Materials
  • Isotropic Materials
  • Nonlinear Elastic Constitutive Relations
  • Newtonian Fluids
  • Ideal Fluids
  • Viscous In compressible Fluids
  • Generalized Newtonian Fluids
  • Inelastic Fluids
  • Power law model
  • Carreau model
  • Bingham model
  • Visco elastic Constitutive Models
  • Differential models
  • Integral models
  • Heat Transfer
  • Fourier’s Heat Conduction Law
  • Newton’s Law of Cooling
  • Stefan–Boltzmann Law
  • Constitutive Relations for Coupled Problems
  • Electro magnetics
  • Maxwell’s equations
  • Constitutive relations
  • Thermo elasticity
  • Hygro thermal elasticity
  • Electro elasticity
  • Summary
  • Problems

Chapter 7: LINEARIZED ELASTICITY

  • Introduction
  • Governing Equations
  • Preliminary Comments
  • Summary of Equations
  • Strain displacement equations
  • Equations of motion
  • Constitutive equations
  • Boundary conditions
  • Compatibility conditions
  • The Navier Equations
  • The Beltrami Michell Equations
  • Solution Methods
  • Types of Problems
  • Types of Solution Methods
  • Examples of the Semi Inverse Method
  • Stretching and Bending of Beams
  • Superposition Principle
  • Uniqueness of Solutions
  • Clapeyron’s, Betti’s, and Maxwell’s Theorems
  • Clapeyron’s Theorem
  • Betti’s Reciprocity Theorem
  • Maxwell’s Reciprocity Theorem
  • Solution of Two-Dimensional Problems
  • Plane Strain Problems
  • Plane Stress Problems
  • Unification of Plane Stress and Plane Strain Problems
  • Airy Stress Function
  • Saint Venant’s Principle
  • Torsion of Cylindrical Members
  • Warping function
  • Prandtl’s stress function
  • Methods Based on Total Potential Energy
  • The Variational Operator
  • The Principle of the Minimum Total Potential Energy
  • Construction of the total potential energy functional
  • Euler’s equations and natural boundary conditions
  • Minimum property of the total potential energy functional
  • Castigliano’s TheoremI
  • The Ritz Method
  • The variational problem
  • Description of the method
  • Hamilton’s Principle
  • Hamilton’s Principle for a Rigid Body
  • Hamilton’s Principle for a Continuum
  • Summary
  • Problems

Chapter 8: FLUID MECHANICS AND HEAT TRANSFER

  • Governing Equations
  • Preliminary Comments
  • Summary of Equations
  • Fluid Mechanics Problems
  • Governing Equations of Viscous Fluids
  • In viscid Fluid Statics
  • Parallel Flow (Navier Stokes Equations)
  • Problems with Negligible Convective Terms
  • Energy Equation for One-Dimensional Flows
  • Heat Transfer Problems
  • Governing Equations
  • Heat Conduction in a Cooling Fin
  • Axisymmetric Heat Conduction in a Circular Cylinder
  • Two Dimensional Heat Transfer
  • Coupled Fluid Flow and Heat Transfer
  • Summary
  • Problems

Chapter 9: LINEARIZED VISCOELASTICITY

  • Introduction
  • Preliminary Comments
  • Initial Value Problem, the Unit Impulse, and the Unit Step Function
  • The Laplace Transform Method
  • Spring and Dashpot Models
  • Creep Compliance and Relaxation Modulus
  • Maxwell Element
  • Creep response
  • Relaxation response
  • Kelvin Voigt Element
  • Creep response
  • Relaxation response
  • Three Element Models
  • Four Element Models
  • Integral Constitutive Equations
  • Hereditary Integrals
  • Hereditary Integrals for Deviatoric Components
  • The Correspondence Principle
  • Elastic and Viscoelastic Analogies
  • Summary
  • Problems

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