- 连续介质力学中的数学模型(第2版英文版)
- - 作者：(美)特马姆
  - 出版社：世界图书出版公司
  - ISBN：9787510084454
  - 出版日期：2015/01/01
  - 页数：342
- 售价：27.2

内容大纲
作者介绍
目录
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 Cauehy stress tensor and the Piola-Kirchhoff
    tensor Applications
     3.1  Hypotheses on the cohesion forces
     3.2  The Cauchy 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 theology: 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 irrotational 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  Thermohydraulics
     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 biomechanies
     17.1  The equations of nonlinear elasticity
     17.2  Boundary conditions - boundary value problems
     17.3  Hyperelastic materials
     17.4  Hvoerelastic 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 Sehrodinger 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

内容大纲

作者介绍

目录

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