(Ebook) Introduction to Continuum Mechanics Solutions manual 3rd Edition by W Michael Lai, David Rubin, Erhard Krempl ISBN 9780080422602 0080422608

Chapter 1. Introduction

1.1 Continuum Theory

1.2 Contents of Continuum Mechanics

Index

Chapter 2. Tensors

Part A The Indicial Notation

Part B Tensors

Part C Tensor Calculus

Part D Curvilinear Coordinates

Chpter 3. Kinematics of a Continuum

3.1 Description of Motions of a Continuum

3.2 Material Description and Spatial Description

3.3 Material Derivative

3.4 Acceleration of a Particle in a Continuum

3.5 Displacement Field

3.6 Kinematic Equations For Rigid Body Motion

3.7 Infinitesimal Deformations

3.8 Geometrical Meaning of the Components of the Infinitesimal Strain Tensor

3.9 Principal Strain

3.10 Dilatation

3.11 The Infinitesimal Rotation Tensor

3.12 Time Rate of Change of a Material Element

3.13 The Rate of Deformation Tensor

3.14 The Spin Tensor and the Angular Velocity Vector

3.15 Equation of Conservation of Mass

3.16 Compatibility Conditions for Infinitesimal Strain Components

3.17 Compatibility Conditions for the Rate of Deformation Components

3.18 Deformation Gradient

3.19 Local Rigid Body Displacements

3.20 Finite Deformation

3.21 Polar Decomposition Theorem

3.22 Calculation of the Stretch Tensor from the Deformation Gradient

3.23 Right Cauchy-Green Deformation Tensor

3.24 Lagrangian Strain Tensor

3.25 Left Cauchy-Green Deformation Tensor

3.26 Eulerian Strain Tensor

3.27 Compatibility Conditions for Components of Finite Deformation Tensor

3.28 Change of Area due to Deformation

3.29 Change of Volume due to Deformation

3.30 Components of Deformation Tensors in other Coordinates

3.31 Current Configuration as the Reference Configuration

Problems

Chapter 4. Stress

4.1 Stress Vector

4.2 Stress Tensor

4.3 Components of Stress Tensor

4.4 Symmetry of Stress Tensor - Principle of Moment of Momentum

4.5 Principal Stresses

4.6 Maximum Shearing Stress

4.7 Equations of Motion - Principle of Linear Momentum

4.8 Equations of Motion in Cylindrical and Spherical Coordinates

4.9 Boundary Condition for the Stress Tensor

4.10 Piola Kirchhoff Stress Tensors

4.11 Equations of Motion Written With Respect to the Reference Configuration

4.12 Stress Power

4.13 Rate of Heat Flow Into an Element by Conduction

4.14 Energy Equation

4.15 Entropy Inequality

Problems

Chapter 5. The Elastic Solid

Part A Linear Isotropie Elastic Solid

Part B Linear Anisotropie Elastic Solid

Part C Constitutive Equation For Isotropie Elastic Solid Under Large Deformation

Problems

Chapter 6. Newtonian Viscous Fluid

6.1 Fluids

6.2 Compressible and Incompressible Fluids

6.3 Equations Of Hydrostatics

6.4 Newtonian Fluid

6.5 Interpretation of A and μ

6.6 Incompressible Newtonian Fluid

6.7 Navier-Stokes Equation For Incompressible Fluids

6.8 Navier-Stokes Equations for Incompressible Fluids in Cylindrical and Spherical coordinates

6.9 Boundary Conditions

6.10 Streamline, Pathline, Streakline, Steady, Unsteady, Laminar and Turbulent Flow

6.11 Plane Couette Flow

6.12 Plane-Poiseuille Flow

6.13 Hagen-Poiseuille Flow

6.14 Plane Couette Flow of Two Layers of Incompressible Fluids

6.15 Couette Flow

6.16 Flow Near an Oscillating Plate

6.17 Dissipation Functions for Newtonian Fluids

6.18 Energy Equation For a Newtonian Fluid

6.19 Vorticity Vector

6.20 Irrotational Flow

6.21 Irrotational Flow of an Inviscid Incompressible Fluid of Homogeneous Density

6.22 Irrotational Flows as Solutions of Navier-Stokes Equation

6.23 Vorticity Transport Equation for Incompressible Viscous Fluid with a Constant Density

6.24 Concept of a Boundary Layer

6.25 Compressible Newtonian Fluid

6.26 Energy Equation in Terms of Enthalpy

6.27 Acoustic Wave

6.28 Irrotational, Barotropic Flows of Inviscid Compressible Fluid

6.29 One-Dimensional Flow of a Compressible Fluid

Problems

Chapter 7. Integral Formulation of General Principles

7.1 Green's Theorem

7.2 Divergence Theorem

7.3 Integrals over a Control Volume and Integrals over a Material Volume

7.4 Reynolds Transport Theorem

7.5 Principle of Conservation of Mass

7.6 Principle of Linear Momentum

7.7 Moving Frames

7.8 Control Volume Fixed with respect to a Moving Frame

7.9 Principle of Moment of Momentum

7.10 Principle of Conservation of Energy

Problems

Chapter 8. Non-Newtonian Fluids

Part A Linear Viscoelastic Fluid

Part B Nonlinear Viscoelastic Fluid

Part C Viscometric Flows of an Incompressible Simple Fluid

Problems

Appendix: Matrices

Answer to Problems

References

Index