连续介质力学中的数学模型 : 第2版

Preface

A few words about notations

PART I FUNDAMENTAL CONCEPTS IN CONTINUUM MECHANICS

1 Describing the motion of a system： geometry and kinematics

1.1 Deformations

1.2 Motion and its observation （kinematics）

1.3 Description of the motion of a system： Eulerian and Lagrangian derivatives

1.4 Velocity field of a rigid body： helicoidal vector fields

1.5 Differentiation of a volume integral depending on a parameter

2 The fundamental law of dynamics

2.1 The concept of mass

2.2 Forces

2.3 The fundamental law of dynamics and its first consequences

2.4 Application to systems of material points and to rigid bodies

2.5 Galilean frames： the fundamental law of dynamics expressed in a non—Galilean frame

3 The Canchy stress tensor and the Piola—Kirchhoff tensor.Applications

3.1 Hypotheses on the cohesion forces

3.2 The Canchy stress tensor

3.3 General equations of motion

3.4 Symmetry of the stress tensor

3.5 The Piola—Kirchhoff tensor

4 Real and virtual powers

4.1 Study of a system of material points

4.2 General material systems： rigidifying velocities

4.3 Virtual power of the cohesion forces： the general case

4.4 Real power： the kinetic energy theorem

5 Deformation tensor， deformation rate tensor，constitutive laws

5.1 Further properties of deformations

5.2 The deformation rate tensor

5.3 Introduction to rheology： the constitutive laws

5.4 Appendix.Change of variable in a surface integral

6 Energy equations and shock equations

6.1 Heat and energy

6.2 Shocks and the Rankine——Hugoniot relations

PART Ⅱ PHYSICS OF FLUIDS

7 General properties of Newtonian fluids

7.1 General equations of fluid mechanics

7.2 Statics of fluids

7.3 Remark on the energy of a fluid

8 Flows of inviscid fluids

8.1 General theorems

8.2 Plane h'rotational flows

8.3 Transsonic flows

8.4 Linear accoustics

9 Viscous fluids and thermohydraulics

9.1 Equations of viscous incompressible fluids

9.2 Simple flows of viscous incompressible fluids

9.3 Thermohydranlics

9.4 Equations in nondimensional form： similarities

9.5 Notions of stability and turbulence

9.6 Notion of boundary layer

10 Magnetohydrodynamics and inertial confinement of plasmas

10.1 The Maxwell equations and electromagnetism

10.2 Magnetohydrodynamics

10.3 The Tokamak machine

11 Combustion

11.1 Equations for mixtures of fluids

11.2 Equations of chemical kinetics

11.3 The equations of combustion

11.4 Stefan—Maxwell equations

11.5 A simplified problem： the two—species model

12 Equations of the atmosphere and of the ocean

12.1 Preliminaries

12.2 Primitive equations of the atmosphere

12.3 Primitive equations of the ocean

12.4 Chemistry of the atmosphere and the ocean Appendix.The differential operators in spherical coordinates

PART Ⅲ SOLID MECHANICS

13 The general equations of linear elasticity

13.1 Back to the stress—strain law of linear elasticity： the elasticity coefficients of a material

13.2 Boundary value problems in linear elasticity： the linearization principle

13.3 Other equations

13.4 The limit of elasticity criteria

14 Classical problems of elastostatics

14.1 Longitudinal traction——compression of a cylindrical bar

14.2 Uniform compression of an arbitrary body

14.3 Equilibrium of a spherical container subjected to external and internal pressures

14.4 Deformation of a vertical cylindrical body under the action of its weight

14.5 Simple bending of a cylindrical beam

14.6 Torsion of cylindrical shafts

14.7 The Saint—Venant principle

15 Energy theorems， duality， and variational formulations

15.1 Elastic energy of a material

15.2 Duality—generalization

15.3 The energy theorems

15.4 Variational formulations

15.5 Virtual power theorem and variational formulations

16 Introduction to nonlinear constitutive laws and to homogenization

16.1 Nonlinear constitutive laws （nonlinear elasticity）

16.2 Nonlinear elasticity with a threshold（Henky's elastoplastic model）

16.3 Nonconvex energy functions

16.4 Composite materials： the problem of homogenization

17 Nonlinear elasticity and an application to biomechanics

17.1 The equations of nonlinear elasticity

17.2 Boundary conditions—boundary value problems

17.3 Hyperelastic materials

17.4 Hyperelastic materials in biomechanics

PART Ⅳ INTRODUCTION TO WAVE PHENOMENA

18 Linear wave equations in mechanics

18.1 Returning to the equations of linear acoustics and of linear elasticity

18.2 Solution of the one—dimensional wave equation

18.3 Normal modes

18.4 Solution of the wave equation

18.5 Superposition of waves， beats， and packets of waves

19 The soliton equation： the Korteweg—de Vries equation

19.1 Water—wave equations

19.2 Simplified form of the water—wave equations

19.3 The Korteweg—de Vries equation

19.4 The soliton solutions of the KdV equation

20 The nonlinear Schrodinger equation

20.1 Maxwell equations for polarized media

20.2 Equations of the electric field： the linear case

20.3 General case

20.4 The nonlinear Schrodinger equation

20.5 Soliton solutions of the NLS equation

Appendix.The partial differential equations of mechanics

Hints for the exercises

References

Index

《连续介质力学中的数学模型（第2版）》是作者精心为广大读者朋友们编写而成的，可以让更多的读者朋友们从书中了解到更多的知识，从而提升读者朋友们自身的知识水平。让我们跟随作者的脚步来更好的阅读《连续介质力学中的数学模型（第2版）》中的内容。《连续介质力学中的数学模型（第2版）》可作为物理、力学专业高年级本科生及应用数学、物理学和工程类的研究生的教材和参考书。